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<li id="toc-Basic_calculation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Basic_calculation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Basic calculation</span> </div> </a> <ul id="toc-Basic_calculation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Horizontal_dials" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Horizontal_dials"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Horizontal dials</span> </div> </a> <button aria-controls="toc-Horizontal_dials-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Horizontal dials subsection</span> </button> <ul id="toc-Horizontal_dials-sublist" class="vector-toc-list"> <li id="toc-Early_Scottish_method_(1440)_Dürer_(1525)_Rohr_(1965)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Early_Scottish_method_(1440)_Dürer_(1525)_Rohr_(1965)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Early Scottish method (1440) Dürer (1525) Rohr (1965)</span> </div> </a> <ul id="toc-Early_Scottish_method_(1440)_Dürer_(1525)_Rohr_(1965)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Benedetti_(1574)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Benedetti_(1574)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Benedetti (1574)</span> </div> </a> <ul id="toc-Benedetti_(1574)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Clavius_method_(1586)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Clavius_method_(1586)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Clavius method (1586)</span> </div> </a> <ul id="toc-Clavius_method_(1586)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stirrup's_method_(1652)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stirrup's_method_(1652)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Stirrup's method (1652)</span> </div> </a> <ul id="toc-Stirrup's_method_(1652)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bettini_method_(1660)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bettini_method_(1660)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Bettini method (1660)</span> </div> </a> <ul id="toc-Bettini_method_(1660)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Leybourn_(1669)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Leybourn_(1669)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Leybourn (1669)</span> </div> </a> <ul id="toc-Leybourn_(1669)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ozanam's_method_(1673)_Mayall_(1938)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Ozanam's_method_(1673)_Mayall_(1938)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.7</span> <span>Ozanam's method (1673) Mayall (1938)</span> </div> </a> <ul id="toc-Ozanam's_method_(1673)_Mayall_(1938)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Encyclopedia_method_(1771)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Encyclopedia_method_(1771)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.8</span> <span>Encyclopedia method (1771)</span> </div> </a> <ul id="toc-Encyclopedia_method_(1771)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-de_Celles_(1760)_(1790)_Waugh_method_(1973)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#de_Celles_(1760)_(1790)_Waugh_method_(1973)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.9</span> <span>de Celles (1760) (1790) Waugh method (1973)</span> </div> </a> <ul id="toc-de_Celles_(1760)_(1790)_Waugh_method_(1973)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Nicholson's_method_(1825)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Nicholson's_method_(1825)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.10</span> <span>Nicholson's method (1825)</span> </div> </a> <ul id="toc-Nicholson's_method_(1825)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Foster_Serles_Dialling_Scales_(1638)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Foster_Serles_Dialling_Scales_(1638)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.11</span> <span>Foster Serles Dialling Scales (1638)</span> </div> </a> <ul id="toc-Foster_Serles_Dialling_Scales_(1638)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Saphea_(As-Saphiah)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Saphea_(As-Saphiah)"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.12</span> <span>Saphea (As-Saphiah)</span> </div> </a> <ul id="toc-Saphea_(As-Saphiah)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notes</span> </div> </a> <ul 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<div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Set of instructions used to construct horizontal sundials</div> <p>A <b>schema for horizontal dials</b> is a set of instructions used to construct horizontal <a href="/wiki/Sundial" title="Sundial">sundials</a> using <a href="/wiki/Compass_and_straightedge_construction" class="mw-redirect" title="Compass and straightedge construction">compass and straightedge construction</a> techniques, which were widely used in Europe from the late fifteenth century to the late nineteenth century. The common <a href="/wiki/London_dial" title="London dial">horizontal sundial</a> is a geometric <a href="/wiki/Graphical_projection" class="mw-redirect" title="Graphical projection">projection</a> of an <a href="/wiki/Equatorial_sundial" class="mw-redirect" title="Equatorial sundial">equatorial sundial</a> onto a horizontal plane. </p><p>The special properties of the <a href="/w/index.php?title=Polar-pointing_gnomon&action=edit&redlink=1" class="new" title="Polar-pointing gnomon (page does not exist)">polar-pointing gnomon</a> (axial gnomon) were first known to the Moorish astronomer <a href="/w/index.php?title=Abdul_Hassan_Ali&action=edit&redlink=1" class="new" title="Abdul Hassan Ali (page does not exist)">Abdul Hassan Ali</a> in the early thirteenth century<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and this led the way to the dial-plates, with which we are familiar, dial plates where the style and hour lines have a common root. </p><p>Through the centuries artisans have used different methods to markup the hour lines sundials using the methods that were familiar to them, in addition the topic has fascinated mathematicians and become a topic of study. Graphical projection was once commonly taught, though this has been superseded by <a href="/wiki/Trigonometry" title="Trigonometry">trigonometry</a>, <a href="/wiki/Logarithms" class="mw-redirect" title="Logarithms">logarithms</a>, <a href="/wiki/Sliderule" class="mw-redirect" title="Sliderule">sliderules</a> and <a href="/wiki/Computer_applications" class="mw-redirect" title="Computer applications">computers</a> which made <a href="/wiki/Arithmetic" title="Arithmetic">arithmetical calculations</a> increasingly trivial/ Graphical projection was once the mainstream method for laying out a sundial but has been sidelined and is now only of academic interest. </p><p>The first known document in English describing a schema for graphical projection was published in Scotland in 1440, leading to a series of distinct schema for horizontal dials each with characteristics that suited the target <a href="/wiki/Latitude" title="Latitude">latitude</a> and construction method of the time. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Context">Context</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=1" title="Edit section: Context"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:The_Ummayad_Mosque_also_known_as_the_Grand_Mosque_of_Damascus.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/The_Ummayad_Mosque_also_known_as_the_Grand_Mosque_of_Damascus.jpg/220px-The_Ummayad_Mosque_also_known_as_the_Grand_Mosque_of_Damascus.jpg" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/The_Ummayad_Mosque_also_known_as_the_Grand_Mosque_of_Damascus.jpg/330px-The_Ummayad_Mosque_also_known_as_the_Grand_Mosque_of_Damascus.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/The_Ummayad_Mosque_also_known_as_the_Grand_Mosque_of_Damascus.jpg/440px-The_Ummayad_Mosque_also_known_as_the_Grand_Mosque_of_Damascus.jpg 2x" data-file-width="1024" data-file-height="819" /></a><figcaption>Umayyad Mosque, also known as the Grand Mosque of Damascus</figcaption></figure> <p>The art of sundial design is to produce a dial that accurately displays local time. Sundial designers have also been fascinated by the mathematics of the dial and possible new ways of displaying the information. Modern dialling started in the tenth century when Arab astronomers made the great discovery that a gnomon parallel to the Earth's axis will produce sundials whose hour lines show <a href="/wiki/Equinoctial_hours" title="Equinoctial hours">equal hours</a> or <i>legal hours</i> on any day of the year: the dial of <a href="/wiki/Ibn_al-Shatir" title="Ibn al-Shatir">Ibn al-Shatir</a> in the <a href="/wiki/Umayyad_Mosque" title="Umayyad Mosque">Umayyad Mosque</a> in <a href="/wiki/Damascus" title="Damascus">Damascus</a> is the oldest dial of this type. <sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> Dials of this type appeared in Austria and Germany in the 1440s.<sup id="cite_ref-FOOTNOTEJones19806_3-0" class="reference"><a href="#cite_note-FOOTNOTEJones19806-3"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>A dial plate can be laid out, by a pragmatic approach, observing and marking a shadow at regular intervals throughout the day on each day of the year. If the <a href="/wiki/Latitude" title="Latitude">latitude</a> is known the dial plate can be laid out using <a href="/wiki/Compass-and-straightedge_construction" class="mw-redirect" title="Compass-and-straightedge construction">geometrical construction techniques</a> which rely on <a href="/wiki/Graphical_projection" class="mw-redirect" title="Graphical projection">projection geometry</a>, or by calculation using the known formulas and <a href="/wiki/Trigonometric_tables" title="Trigonometric tables">trigonometric tables</a> usually using <a href="/wiki/Logarithms" class="mw-redirect" title="Logarithms">logarithms</a>, or <a href="/wiki/Slide_rule" title="Slide rule">slide rules</a> or more recently <a href="/wiki/Computer_application" class="mw-redirect" title="Computer application">computers</a> or <a href="/wiki/Mobile_phone_application" class="mw-redirect" title="Mobile phone application">mobile phones</a>. <a href="/wiki/Linear_algebra" title="Linear algebra">Linear algebra</a> has provided a useful language to describe the <a href="/wiki/Mathematical_transformation" class="mw-redirect" title="Mathematical transformation">transformations</a>. </p><p>A sundial schema uses a <a href="/wiki/Compass-and-straightedge_construction" class="mw-redirect" title="Compass-and-straightedge construction">compass and a straight edge</a> to firstly to derive the essential angles for that latitude, then to use this to draw the hourlines on the dial plate. In modern terminology this would mean that graphical techniques were used to derive <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09b4b55580d6a821a07ad9fe35be88976917b10b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.572ex; height:2.176ex;" alt="{\displaystyle \sin x}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m\tan y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mi>tan</mi> <mo>⁡</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m\tan y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b97b451954f1d8c0109e43f9229912375a0c18db" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.33ex; height:2.343ex;" alt="{\displaystyle m\tan y}"></span> and from it <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin x.\tan y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>x</mi> <mo>.</mo> <mi>tan</mi> <mo>⁡</mo> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin x.\tan y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6f30416a99d372582c6a0b77b55136f3c170a35a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.509ex; height:2.509ex;" alt="{\displaystyle \sin x.\tan y}"></span>. <sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Basic_calculation">Basic calculation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=2" title="Edit section: Basic calculation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Using a large sheet of paper.</li> <li>Starting at the bottom a horizontal line is drawn, and a vertical one up the centre. Where they cross is becomes the origin O, the foot of the Gnomon.</li> <li>A horizontal line draw a line which fixes the size of the dial. Where it crosses the centre line is an important construction point F</li> <li>A construction line is drawn upwards from O at the angle of latitude.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>c<span class="cite-bracket">]</span></a></sup></li> <li>Using a square, (drop a line) a line from F through the construction line is drawn so they cross at right angles. That point E, is an important construction point. To be precise it is the line FE that is important as it is length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc867c18657f81cf14e9381bb8603ea969d63566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.628ex; height:2.509ex;" alt="{\displaystyle \sin \phi }"></span>.</li> <li>Using compasses, or dividers the length FE was copied upwards in the centre line from F. The new construction point is called G The construction lines and FE are erased.</li></ul> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bedos_de_Celles_method_(1790)-(1).svg" class="mw-file-description" title="Setting out a dial for 52°N. The three initial lines."><img alt="Setting out a dial for 52°N. The three initial lines." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Bedos_de_Celles_method_%281790%29-%281%29.svg/85px-Bedos_de_Celles_method_%281790%29-%281%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Bedos_de_Celles_method_%281790%29-%281%29.svg/127px-Bedos_de_Celles_method_%281790%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Bedos_de_Celles_method_%281790%29-%281%29.svg/170px-Bedos_de_Celles_method_%281790%29-%281%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Setting out a dial for 52°N. The three initial lines.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bedos_de_Celles_method_(1790)-(2).svg" class="mw-file-description" title="Marking the latitude, laying out length '"`UNIQ--postMath-00000006-QINU`"', and copying to G on the vertical."><img alt="Marking the latitude, laying out length '"`UNIQ--postMath-00000006-QINU`"', and copying to G on the vertical." src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Bedos_de_Celles_method_%281790%29-%282%29.svg/85px-Bedos_de_Celles_method_%281790%29-%282%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Bedos_de_Celles_method_%281790%29-%282%29.svg/127px-Bedos_de_Celles_method_%281790%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Bedos_de_Celles_method_%281790%29-%282%29.svg/170px-Bedos_de_Celles_method_%281790%29-%282%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Marking the latitude, laying out length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc867c18657f81cf14e9381bb8603ea969d63566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.628ex; height:2.509ex;" alt="{\displaystyle \sin \phi }"></span>, and copying to G on the vertical.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:D%C3%BCrer_method_(1525)-(3).svg" class="mw-file-description" title="A tangent:Laying out the length '"`UNIQ--postMath-00000007-QINU`"'"><img alt="A tangent:Laying out the length '"`UNIQ--postMath-00000007-QINU`"'" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/D%C3%BCrer_method_%281525%29-%283%29.svg/120px-D%C3%BCrer_method_%281525%29-%283%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/D%C3%BCrer_method_%281525%29-%283%29.svg/180px-D%C3%BCrer_method_%281525%29-%283%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/D%C3%BCrer_method_%281525%29-%283%29.svg/240px-D%C3%BCrer_method_%281525%29-%283%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext">A tangent:Laying out the length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08e7b66c250a5021a4deddf3b614c24db6c86ab3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.837ex; height:2.176ex;" alt="{\displaystyle \tan \theta }"></span></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:D%C3%BCrer_method_(1525)-(3).svg" class="mw-file-description" title="A tangent of a sine: Laying out lines of length '"`UNIQ--postMath-00000008-QINU`"', where h is an integer 0 .. 5"><img alt="A tangent of a sine: Laying out lines of length '"`UNIQ--postMath-00000008-QINU`"', where h is an integer 0 .. 5" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/D%C3%BCrer_method_%281525%29-%283%29.svg/120px-D%C3%BCrer_method_%281525%29-%283%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/D%C3%BCrer_method_%281525%29-%283%29.svg/180px-D%C3%BCrer_method_%281525%29-%283%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/D%C3%BCrer_method_%281525%29-%283%29.svg/240px-D%C3%BCrer_method_%281525%29-%283%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext">A tangent of a sine: Laying out lines of length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \phi \tan h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> <mi>tan</mi> <mo>⁡</mo> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \phi \tan h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1b6fb9e7f396462fb356ad60fdffe28cb397cddc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.101ex; height:2.509ex;" alt="{\displaystyle \sin \phi \tan h}"></span>, where h is an integer 0 .. 5</div> </li> </ul> <p>Such geometric constructions were well known and remained part of the high school (UK grammar school) curriculum until the <a href="/wiki/New_Math" title="New Math">New Maths</a> revolution in the 1970s.<sup id="cite_ref-FOOTNOTEDurell1921_6-0" class="reference"><a href="#cite_note-FOOTNOTEDurell1921-6"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p><p>The schema shown above was used in 1525 (from an earlier work 1440) by <a href="/wiki/D%C3%BCrer" class="mw-redirect" title="Dürer">Dürer</a> is still used today. The simpler schema were more suitable for dials designed for the lower latitudes, requiring a narrow sheet of paper for the construction, than those intended for the higher latitudes. This prompted the quest for other constructions. </p> <div class="mw-heading mw-heading2"><h2 id="Horizontal_dials">Horizontal dials</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=3" title="Edit section: Horizontal dials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The first part of the process is common to many methods. It establishes a point on the north south line that is sin φ from the meridian line. </p> <div class="mw-heading mw-heading3"><h3 id="Early_Scottish_method_(1440)_Dürer_(1525)_Rohr_(1965)"><span id="Early_Scottish_method_.281440.29_D.C3.BCrer_.281525.29_Rohr_.281965.29"></span>Early Scottish method (1440) Dürer (1525) Rohr (1965)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=4" title="Edit section: Early Scottish method (1440) Dürer (1525) Rohr (1965)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Start with the basic method shown above</li> <li>From G a series of lines, 15° apart are drawn, long enough so they cross the line through F. These mark the hour points 1, 2, 3 4, 5 and 7, 8, 9, 10, 11.</li> <li>The centre of the dial is at the bottom, point O. The line drawn from each of these hour point to O will be the hour line on the finished dial.<sup id="cite_ref-FOOTNOTEWaugh197338–39_7-0" class="reference"><a href="#cite_note-FOOTNOTEWaugh197338–39-7"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li></ul> <p>The significant problem is the width of the paper needed in the higher latitudes. <sup id="cite_ref-FOOTNOTESawyer191_8-0" class="reference"><a href="#cite_note-FOOTNOTESawyer191-8"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:D%C3%BCrer_method_(1525)-(1).svg" class="mw-file-description" title="Setting out a dial for 52°N. The three initial lines."><img alt="Setting out a dial for 52°N. The three initial lines." src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/D%C3%BCrer_method_%281525%29-%281%29.svg/120px-D%C3%BCrer_method_%281525%29-%281%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/D%C3%BCrer_method_%281525%29-%281%29.svg/180px-D%C3%BCrer_method_%281525%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/D%C3%BCrer_method_%281525%29-%281%29.svg/240px-D%C3%BCrer_method_%281525%29-%281%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext">Setting out a dial for 52°N. The three initial lines.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:D%C3%BCrer_method_(1525)-(2).svg" class="mw-file-description" title="Marking the latitude, laying out length '"`UNIQ--postMath-00000009-QINU`"', and copying to G on the vertical."><img alt="Marking the latitude, laying out length '"`UNIQ--postMath-00000009-QINU`"', and copying to G on the vertical." src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/D%C3%BCrer_method_%281525%29-%282%29.svg/120px-D%C3%BCrer_method_%281525%29-%282%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bb/D%C3%BCrer_method_%281525%29-%282%29.svg/180px-D%C3%BCrer_method_%281525%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/bb/D%C3%BCrer_method_%281525%29-%282%29.svg/240px-D%C3%BCrer_method_%281525%29-%282%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext">Marking the latitude, laying out length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc867c18657f81cf14e9381bb8603ea969d63566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.628ex; height:2.509ex;" alt="{\displaystyle \sin \phi }"></span>, and copying to G on the vertical.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:D%C3%BCrer_method_(1525)-(3).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/D%C3%BCrer_method_%281525%29-%283%29.svg/120px-D%C3%BCrer_method_%281525%29-%283%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/D%C3%BCrer_method_%281525%29-%283%29.svg/180px-D%C3%BCrer_method_%281525%29-%283%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/D%C3%BCrer_method_%281525%29-%283%29.svg/240px-D%C3%BCrer_method_%281525%29-%283%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:D%C3%BCrer_method_(1525)-(4).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/D%C3%BCrer_method_%281525%29-%284%29.svg/120px-D%C3%BCrer_method_%281525%29-%284%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ad/D%C3%BCrer_method_%281525%29-%284%29.svg/180px-D%C3%BCrer_method_%281525%29-%284%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ad/D%C3%BCrer_method_%281525%29-%284%29.svg/240px-D%C3%BCrer_method_%281525%29-%284%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:D%C3%BCrer_method_(1525)-(full).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/D%C3%BCrer_method_%281525%29-%28full%29.svg/120px-D%C3%BCrer_method_%281525%29-%28full%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9a/D%C3%BCrer_method_%281525%29-%28full%29.svg/180px-D%C3%BCrer_method_%281525%29-%28full%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9a/D%C3%BCrer_method_%281525%29-%28full%29.svg/240px-D%C3%BCrer_method_%281525%29-%28full%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext"></div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Benedetti_(1574)"><span id="Benedetti_.281574.29"></span>Benedetti (1574)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=5" title="Edit section: Benedetti (1574)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:De_gnomonum_umbrarumq._solarium_usu_liber.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/De_gnomonum_umbrarumq._solarium_usu_liber.jpg/220px-De_gnomonum_umbrarumq._solarium_usu_liber.jpg" decoding="async" width="220" height="317" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/De_gnomonum_umbrarumq._solarium_usu_liber.jpg/330px-De_gnomonum_umbrarumq._solarium_usu_liber.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/De_gnomonum_umbrarumq._solarium_usu_liber.jpg/440px-De_gnomonum_umbrarumq._solarium_usu_liber.jpg 2x" data-file-width="555" data-file-height="799" /></a><figcaption>De gnomonum umbrarumque solarium usu</figcaption></figure> <p><a href="/wiki/Giambattista_Benedetti" title="Giambattista Benedetti">Giambattista Benedetti</a>, an impoverished nobleman worked as a mathematician at the court of Savola. His book which describes this method was <i>De gnomonum umbrarumque solarium usu</i> published in 1574. It describes a method for displaying the legal hours, that is equal hours as we use today, while most people still used unequal hours which divided the hours of daylight into 12 equal hours- but they would change as the year progressed. Benedettis method divides the quadrant into 15° segments. Two construction are made: a parallel horizontal line that defines the tan h distances, and a gnomonic polar line GT which represents sin φ. </p> <ul><li>Draw a quadrant GRB, with 15° segments. GR is horizontal.</li> <li>A parallel horizontal line is drawn from PE, and ticks made where it bisects the 15° rays.</li> <li>GX is the latitude. T is the crossing point with PE. GTE is the gnomonic triangle.</li> <li>The length GT is copied to the bottom of E giving the point F.</li> <li>The hour lines are drawn from F, and the dial is complete.</li></ul> <p>Benedetti included instructions for drawing a point gnomon so unequal hours could be plotted. <sup id="cite_ref-FOOTNOTEGunella2013b_9-0" class="reference"><a href="#cite_note-FOOTNOTEGunella2013b-9"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Benedetti(1575)-(1).svg" class="mw-file-description" title="Quadrant with 15° segments."><img alt="Quadrant with 15° segments." src="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Benedetti%281575%29-%281%29.svg/120px-Benedetti%281575%29-%281%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/52/Benedetti%281575%29-%281%29.svg/180px-Benedetti%281575%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/52/Benedetti%281575%29-%281%29.svg/240px-Benedetti%281575%29-%281%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">Quadrant with 15° segments.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Benedetti(1575)-(2).svg" class="mw-file-description" title="constructing the rays."><img alt="constructing the rays." src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Benedetti%281575%29-%282%29.svg/120px-Benedetti%281575%29-%282%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Benedetti%281575%29-%282%29.svg/180px-Benedetti%281575%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Benedetti%281575%29-%282%29.svg/240px-Benedetti%281575%29-%282%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">constructing the rays.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Benedetti(1575)-(3).svg" class="mw-file-description" title="Finding the origin."><img alt="Finding the origin." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Benedetti%281575%29-%283%29.svg/120px-Benedetti%281575%29-%283%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Benedetti%281575%29-%283%29.svg/180px-Benedetti%281575%29-%283%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Benedetti%281575%29-%283%29.svg/240px-Benedetti%281575%29-%283%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">Finding the origin.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Benedetti(1575)-(4).svg" class="mw-file-description" title="Adding the hour lines."><img alt="Adding the hour lines." src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Benedetti%281575%29-%284%29.svg/120px-Benedetti%281575%29-%284%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Benedetti%281575%29-%284%29.svg/180px-Benedetti%281575%29-%284%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Benedetti%281575%29-%284%29.svg/240px-Benedetti%281575%29-%284%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">Adding the hour lines.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Benedetti(1575)-(dial).svg" class="mw-file-description" title="Dial face."><img alt="Dial face." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Benedetti%281575%29-%28dial%29.svg/120px-Benedetti%281575%29-%28dial%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Benedetti%281575%29-%28dial%29.svg/180px-Benedetti%281575%29-%28dial%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/23/Benedetti%281575%29-%28dial%29.svg/240px-Benedetti%281575%29-%28dial%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">Dial face.</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Clavius_method_(1586)"><span id="Clavius_method_.281586.29"></span>Clavius method (1586)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=6" title="Edit section: Clavius method (1586)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>(<i>Fabica et usus instrumenti ad horologiorum descriptionem.</i>) Rome Italy. </p><p>The Clavius method looks at a quarter of the dial. It views the horizontal and the perpendicular plane to the polar axis as two rectangles hinged around the top edge of both dials. the polar axis will be at φ degrees to the polar axis, and the hour lines will be equispaced on the polar plane an equatorial dial. (15°). Hour points on the polar plane will connect to the matching point on the horizontal plane. The horizontal hour lines are plotted to the origin. </p><p><sup id="cite_ref-FOOTNOTEGunella2013_10-0" class="reference"><a href="#cite_note-FOOTNOTEGunella2013-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Draw the gnomomic triangle, lying on its hypotenuse.</li> <li>On the small side, draw a (equatorial) square, with 15° hour markings.</li> <li>The dial plate is constructed with compasses taking it sizes from the triangle.</li> <li>The hour lines 12, 3, and 6 are known. The hour lines 1 and 2 are taken from the side of the square.</li> <li>A diagonal is taken from 12 to 6, and lines parallel to this drawn through 1 and 2, giving 5 and 4</li> <li>The morning dial is a reflection of this.</li></ul> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Clavius(1586)-(1._GT).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Clavius%281586%29-%281._GT%29.svg/102px-Clavius%281586%29-%281._GT%29.svg.png" decoding="async" width="102" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Clavius%281586%29-%281._GT%29.svg/153px-Clavius%281586%29-%281._GT%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Clavius%281586%29-%281._GT%29.svg/203px-Clavius%281586%29-%281._GT%29.svg.png 2x" data-file-width="825" data-file-height="973" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Clavius(1586)-(2.TB).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Clavius%281586%29-%282.TB%29.svg/102px-Clavius%281586%29-%282.TB%29.svg.png" decoding="async" width="102" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Clavius%281586%29-%282.TB%29.svg/153px-Clavius%281586%29-%282.TB%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Clavius%281586%29-%282.TB%29.svg/203px-Clavius%281586%29-%282.TB%29.svg.png 2x" data-file-width="825" data-file-height="973" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Clavius(1586)-(3.TB).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Clavius%281586%29-%283.TB%29.svg/102px-Clavius%281586%29-%283.TB%29.svg.png" decoding="async" width="102" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Clavius%281586%29-%283.TB%29.svg/153px-Clavius%281586%29-%283.TB%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Clavius%281586%29-%283.TB%29.svg/203px-Clavius%281586%29-%283.TB%29.svg.png 2x" data-file-width="825" data-file-height="973" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Clavius(1586)-(4.DP).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Clavius%281586%29-%284.DP%29.svg/102px-Clavius%281586%29-%284.DP%29.svg.png" decoding="async" width="102" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Clavius%281586%29-%284.DP%29.svg/153px-Clavius%281586%29-%284.DP%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Clavius%281586%29-%284.DP%29.svg/203px-Clavius%281586%29-%284.DP%29.svg.png 2x" data-file-width="825" data-file-height="973" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Clavius(1586)-(5.DP).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Clavius%281586%29-%285.DP%29.svg/102px-Clavius%281586%29-%285.DP%29.svg.png" decoding="async" width="102" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Clavius%281586%29-%285.DP%29.svg/153px-Clavius%281586%29-%285.DP%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Clavius%281586%29-%285.DP%29.svg/203px-Clavius%281586%29-%285.DP%29.svg.png 2x" data-file-width="825" data-file-height="973" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Clavius(1586)-(full).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Clavius%281586%29-%28full%29.svg/102px-Clavius%281586%29-%28full%29.svg.png" decoding="async" width="102" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Clavius%281586%29-%28full%29.svg/153px-Clavius%281586%29-%28full%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Clavius%281586%29-%28full%29.svg/203px-Clavius%281586%29-%28full%29.svg.png 2x" data-file-width="825" data-file-height="973" /></a></span></div> <div class="gallerytext"></div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Stirrup's_method_(1652)"><span id="Stirrup.27s_method_.281652.29"></span>Stirrup's method (1652)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=7" title="Edit section: Stirrup's method (1652)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>From G a series of lines, 15° apart are drawn, long enough so they cross the line through F. These mark the hour points 9, 10, 11, 12, 1, 2, 3.</li> <li>The centre of the dial is at the bottom, point O. The line drawn from each of these hour point to O will be the hour line on the finished dial.</li></ul> <p><sup id="cite_ref-FOOTNOTESawyer191_8-1" class="reference"><a href="#cite_note-FOOTNOTESawyer191-8"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Stirrup_method_(1652)-(1).svg" class="mw-file-description" title="Setting out a dial for 52°N. The three initial lines."><img alt="Setting out a dial for 52°N. The three initial lines." src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Stirrup_method_%281652%29-%281%29.svg/85px-Stirrup_method_%281652%29-%281%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Stirrup_method_%281652%29-%281%29.svg/127px-Stirrup_method_%281652%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Stirrup_method_%281652%29-%281%29.svg/170px-Stirrup_method_%281652%29-%281%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Setting out a dial for 52°N. The three initial lines.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Stirrup_method_(1652)-(2).svg" class="mw-file-description" title="Marking the latitude, laying out length '"`UNIQ--postMath-0000000A-QINU`"', and copying to G on the vertical."><img alt="Marking the latitude, laying out length '"`UNIQ--postMath-0000000A-QINU`"', and copying to G on the vertical." src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Stirrup_method_%281652%29-%282%29.svg/85px-Stirrup_method_%281652%29-%282%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Stirrup_method_%281652%29-%282%29.svg/127px-Stirrup_method_%281652%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Stirrup_method_%281652%29-%282%29.svg/170px-Stirrup_method_%281652%29-%282%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Marking the latitude, laying out length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc867c18657f81cf14e9381bb8603ea969d63566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.628ex; height:2.509ex;" alt="{\displaystyle \sin \phi }"></span>, and copying to G on the vertical.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Stirrup_method_(1652)-(3).svg" class="mw-file-description" title="From G casting '"`UNIQ--postMath-0000000B-QINU`"' on the horizontal."><img alt="From G casting '"`UNIQ--postMath-0000000B-QINU`"' on the horizontal." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Stirrup_method_%281652%29-%283%29.svg/85px-Stirrup_method_%281652%29-%283%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/33/Stirrup_method_%281652%29-%283%29.svg/127px-Stirrup_method_%281652%29-%283%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/33/Stirrup_method_%281652%29-%283%29.svg/170px-Stirrup_method_%281652%29-%283%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">From G casting <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan h\sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>h</mi> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan h\sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c36afcd9804bad917f765b2a27fe8ca8a6c9e2ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.101ex; height:2.509ex;" alt="{\displaystyle \tan h\sin \phi }"></span> on the horizontal.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Stirrup_method_(1652)-(4).svg" class="mw-file-description" title="The actual hour lines 9, 10, 11, 12, 1, 2, 3."><img alt="The actual hour lines 9, 10, 11, 12, 1, 2, 3." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Stirrup_method_%281652%29-%284%29.svg/85px-Stirrup_method_%281652%29-%284%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Stirrup_method_%281652%29-%284%29.svg/127px-Stirrup_method_%281652%29-%284%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Stirrup_method_%281652%29-%284%29.svg/170px-Stirrup_method_%281652%29-%284%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">The actual hour lines 9, 10, 11, 12, 1, 2, 3.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Stirrup_method_(1652)-(5).svg" class="mw-file-description" title="Construction lines removed."><img alt="Construction lines removed." src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Stirrup_method_%281652%29-%285%29.svg/85px-Stirrup_method_%281652%29-%285%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Stirrup_method_%281652%29-%285%29.svg/127px-Stirrup_method_%281652%29-%285%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Stirrup_method_%281652%29-%285%29.svg/170px-Stirrup_method_%281652%29-%285%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Construction lines removed.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Stirrup_method_(1652)-(6).svg" class="mw-file-description" title="Finding the angle for 4 and 5."><img alt="Finding the angle for 4 and 5." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Stirrup_method_%281652%29-%286%29.svg/85px-Stirrup_method_%281652%29-%286%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Stirrup_method_%281652%29-%286%29.svg/127px-Stirrup_method_%281652%29-%286%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Stirrup_method_%281652%29-%286%29.svg/170px-Stirrup_method_%281652%29-%286%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Finding the angle for 4 and 5.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Stirrup_method_(1652)-(7).svg" class="mw-file-description" title="Drawing 4 and 5."><img alt="Drawing 4 and 5." src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Stirrup_method_%281652%29-%287%29.svg/85px-Stirrup_method_%281652%29-%287%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Stirrup_method_%281652%29-%287%29.svg/127px-Stirrup_method_%281652%29-%287%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Stirrup_method_%281652%29-%287%29.svg/170px-Stirrup_method_%281652%29-%287%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Drawing 4 and 5.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Stirrup_method_(1652)-(8).svg" class="mw-file-description" title="Construction lines removed. The completed dial plate for 52°N. Stirrup (1652)"><img alt="Construction lines removed. The completed dial plate for 52°N. Stirrup (1652)" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Stirrup_method_%281652%29-%288%29.svg/85px-Stirrup_method_%281652%29-%288%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/49/Stirrup_method_%281652%29-%288%29.svg/127px-Stirrup_method_%281652%29-%288%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/49/Stirrup_method_%281652%29-%288%29.svg/170px-Stirrup_method_%281652%29-%288%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Construction lines removed. The completed dial plate for 52°N. Stirrup (1652)</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Bettini_method_(1660)"><span id="Bettini_method_.281660.29"></span>Bettini method (1660)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=8" title="Edit section: Bettini method (1660)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Jesuit" class="mw-redirect" title="Jesuit">Jesuit</a> <a href="/wiki/Bettinus" class="mw-redirect" title="Bettinus">Mario Bettini</a> penned a method which was posthumously published in the book <i>Recreationum Mathematicarum Apiaria Novissima</i> 1660. </p> <ul><li>Draw the gnomonic triangle with the hypotenuse against the <i>meridian</i> line, and φ to the bottom, C. The other point call M, the right angle call G.</li> <li>A horizontal line is drawn through M, this is the <i>equinoctial</i></li> <li>A circle centred an M with a radius MG is drawn. G2 and G3 are the intersections of the circle and meridian.</li> <li>In the top quadrants, points are marked each 30°. Two are named P, Q.</li> <li>Construction lines are drawn from G2 and G3 through P and Q- the intersections with the equinoctial are marked.</li> <li>To finish the hourlines are drawn through these points from C, and the dial squared off.</li></ul> <p><sup id="cite_ref-FOOTNOTEGunella201413_11-0" class="reference"><a href="#cite_note-FOOTNOTEGunella201413-11"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerycaption">Bettini's Method 1660</li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 110px;"><span typeof="mw:File"><a href="/wiki/File:Bettini(1660)-(1).svg" class="mw-file-description" title="Gnomonic triangle"><img alt="Gnomonic triangle" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Bettini%281660%29-%281%29.svg/120px-Bettini%281660%29-%281%29.svg.png" decoding="async" width="120" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Bettini%281660%29-%281%29.svg/180px-Bettini%281660%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Bettini%281660%29-%281%29.svg/240px-Bettini%281660%29-%281%29.svg.png 2x" data-file-width="1576" data-file-height="975" /></a></span></div> <div class="gallerytext">Gnomonic triangle</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 110px;"><span typeof="mw:File"><a href="/wiki/File:Bettini(1660)-(2).svg" class="mw-file-description" title="Circle marked each 30°"><img alt="Circle marked each 30°" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Bettini%281660%29-%282%29.svg/120px-Bettini%281660%29-%282%29.svg.png" decoding="async" width="120" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/66/Bettini%281660%29-%282%29.svg/180px-Bettini%281660%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/66/Bettini%281660%29-%282%29.svg/240px-Bettini%281660%29-%282%29.svg.png 2x" data-file-width="1576" data-file-height="975" /></a></span></div> <div class="gallerytext">Circle marked each 30°</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 110px;"><span typeof="mw:File"><a href="/wiki/File:Bettini(1660)-(3).svg" class="mw-file-description" title="Construction Lines"><img alt="Construction Lines" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Bettini%281660%29-%283%29.svg/120px-Bettini%281660%29-%283%29.svg.png" decoding="async" width="120" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Bettini%281660%29-%283%29.svg/180px-Bettini%281660%29-%283%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3d/Bettini%281660%29-%283%29.svg/240px-Bettini%281660%29-%283%29.svg.png 2x" data-file-width="1576" data-file-height="975" /></a></span></div> <div class="gallerytext">Construction Lines</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 110px;"><span typeof="mw:File"><a href="/wiki/File:Bettini(1660)-(4).svg" class="mw-file-description" title="Hour lines drawn to the origin"><img alt="Hour lines drawn to the origin" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Bettini%281660%29-%284%29.svg/120px-Bettini%281660%29-%284%29.svg.png" decoding="async" width="120" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Bettini%281660%29-%284%29.svg/180px-Bettini%281660%29-%284%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Bettini%281660%29-%284%29.svg/240px-Bettini%281660%29-%284%29.svg.png 2x" data-file-width="1576" data-file-height="975" /></a></span></div> <div class="gallerytext">Hour lines drawn to the origin</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 110px;"><span typeof="mw:File"><a href="/wiki/File:Bettini(1660)-(5).svg" class="mw-file-description" title="The dial plate"><img alt="The dial plate" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Bettini%281660%29-%285%29.svg/120px-Bettini%281660%29-%285%29.svg.png" decoding="async" width="120" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Bettini%281660%29-%285%29.svg/180px-Bettini%281660%29-%285%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Bettini%281660%29-%285%29.svg/240px-Bettini%281660%29-%285%29.svg.png 2x" data-file-width="1576" data-file-height="975" /></a></span></div> <div class="gallerytext">The dial plate</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Leybourn_(1669)"><span id="Leybourn_.281669.29"></span>Leybourn (1669)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=9" title="Edit section: Leybourn (1669)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/William_Leybourn" title="William Leybourn">William Leybourn</a> published his "<i>Art of Dialling</i>"<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>d<span class="cite-bracket">]</span></a></sup> in 1669, a with it a six-stage method. His description relies heavily on the term <i><a href="/wiki/Scale_of_chords" title="Scale of chords">line of chords</a></i>, for which a modern diallist substitutes a <a href="/wiki/Protractor" class="mw-redirect" title="Protractor">protractor</a>. The line of chords was a scale found on the <a href="/wiki/Sector_(instrument)" title="Sector (instrument)">sector</a> which was used in conjunction with a set of dividers or compasses. It was still used by navigators up to the end of the 19th century.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>e<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Draw a circle, and its two cardinal diameters: E–W, and S–N (top to bottom). O is their crossing point or origin.</li> <li>Using a <a href="/wiki/Scale_of_chords" title="Scale of chords">scale of chords</a> or protractor, lay off two lines, <i>"0a"</i> that is 52° from OS, and <i>"0b"</i> that is 52° from OW. (they will be at right angles. The points "a" and "b" are important.</li> <li>With a straight edge draw a line connect E with "a", it cuts SN (the meridian line) at P, which is called the <i>pole of the world</i>. Now connect E to "a", it connects AE. This point is important as it is where the <i>meridian crosses the equinoctial circle</i>. The points E, AE, and W lie on the equinoctial circle. The next task is to use this information to locate the centre and to draw the circle. Use a construction line to join AE and W. At the centre point, raise a line at right angles. Where it cuts the SN (the meridian) will be C, the centre of the equinoctial circle. Use C to draw an arc from E to W, it will pass through AE.</li> <li>There is now a semicircle passing through E and W, and the equinoctial arc passing through E and W. Divide the semicircle into 12 equal parts, i.e. 15° angles. Mark with a "construction point". <sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>f<span class="cite-bracket">]</span></a></sup></li> <li>A ruler joins O with the points on the semicircle. These lines cut the equinoctial arc: a series of unequal points ("markers) are created.</li> <li>A ruler from P (the pole of the world) takes a line from these markers back over the semicircle. Where it cuts it will be the "hour point"; these hour points are unequally spaced.</li> <li>The hour lines are drawn from each of these "hour points" to O the origin. The origin is the foot of the style which is cut at 52°. <sup id="cite_ref-FOOTNOTELeybourn1700_16-0" class="reference"><a href="#cite_note-FOOTNOTELeybourn1700-16"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTESawyer191_8-2" class="reference"><a href="#cite_note-FOOTNOTESawyer191-8"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li></ul> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Leybourn(1700)-(1).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Leybourn%281700%29-%281%29.svg/85px-Leybourn%281700%29-%281%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/Leybourn%281700%29-%281%29.svg/127px-Leybourn%281700%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/Leybourn%281700%29-%281%29.svg/170px-Leybourn%281700%29-%281%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Leybourn(1700)-(2).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Leybourn%281700%29-%282%29.svg/85px-Leybourn%281700%29-%282%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Leybourn%281700%29-%282%29.svg/127px-Leybourn%281700%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/50/Leybourn%281700%29-%282%29.svg/170px-Leybourn%281700%29-%282%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Leybourn(1700)-(3).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Leybourn%281700%29-%283%29.svg/85px-Leybourn%281700%29-%283%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Leybourn%281700%29-%283%29.svg/127px-Leybourn%281700%29-%283%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Leybourn%281700%29-%283%29.svg/170px-Leybourn%281700%29-%283%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Leybourn(1700)-(4).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Leybourn%281700%29-%284%29.svg/85px-Leybourn%281700%29-%284%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/02/Leybourn%281700%29-%284%29.svg/127px-Leybourn%281700%29-%284%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/02/Leybourn%281700%29-%284%29.svg/170px-Leybourn%281700%29-%284%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Leybourn(1700)-(5).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Leybourn%281700%29-%285%29.svg/85px-Leybourn%281700%29-%285%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/de/Leybourn%281700%29-%285%29.svg/127px-Leybourn%281700%29-%285%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/de/Leybourn%281700%29-%285%29.svg/170px-Leybourn%281700%29-%285%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Leybourn(1700)-(6).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Leybourn%281700%29-%286%29.svg/85px-Leybourn%281700%29-%286%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Leybourn%281700%29-%286%29.svg/127px-Leybourn%281700%29-%286%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Leybourn%281700%29-%286%29.svg/170px-Leybourn%281700%29-%286%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Leybourn(1700)-(7).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Leybourn%281700%29-%287%29.svg/85px-Leybourn%281700%29-%287%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Leybourn%281700%29-%287%29.svg/127px-Leybourn%281700%29-%287%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3a/Leybourn%281700%29-%287%29.svg/170px-Leybourn%281700%29-%287%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Leybourn(1700)-(8).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Leybourn%281700%29-%288%29.svg/85px-Leybourn%281700%29-%288%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Leybourn%281700%29-%288%29.svg/127px-Leybourn%281700%29-%288%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Leybourn%281700%29-%288%29.svg/170px-Leybourn%281700%29-%288%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext"></div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Ozanam's_method_(1673)_Mayall_(1938)"><span id="Ozanam.27s_method_.281673.29_Mayall_.281938.29"></span>Ozanam's method (1673) Mayall (1938)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=10" title="Edit section: Ozanam's method (1673) Mayall (1938)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This method requires a far smaller piece of paper,<sup id="cite_ref-FOOTNOTESawyer191_8-3" class="reference"><a href="#cite_note-FOOTNOTESawyer191-8"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> a great advantage for higher latitudes. </p> <ul><li>From G a series of lines, 15° apart are drawn, long enough so they cross the line through F. These mark the hour points 9, 10, 11, 12, 1, 2, 3 and represent the points <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan h\sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>h</mi> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan h\sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c36afcd9804bad917f765b2a27fe8ca8a6c9e2ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.101ex; height:2.509ex;" alt="{\displaystyle \tan h\sin \phi }"></span>.</li> <li>The centre of the dial is at the bottom, point O. The line drawn from each of these hour point to O will be the hour line on the finished dial.<sup id="cite_ref-FOOTNOTEWaugh197338–39_7-1" class="reference"><a href="#cite_note-FOOTNOTEWaugh197338–39-7"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li>The lines through 9 and 3 are extended to the WE line and a line dropped orthogonally from 9 and 3 to the WE line, call the crossing points W' and E'. From W and E two more lines are drawn 15° apart, these cut the verticals creating the hour points 7, 8 and 4, 5. Lines taken from 0 to these hour points are the hour lines on the final dial.</li></ul> <p><sup id="cite_ref-FOOTNOTESawyer191_8-4" class="reference"><a href="#cite_note-FOOTNOTESawyer191-8"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Ozanam%27s_method_(1673)-(1).svg" class="mw-file-description" title="Setting out a dial for 52°N. The three initial lines."><img alt="Setting out a dial for 52°N. The three initial lines." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Ozanam%27s_method_%281673%29-%281%29.svg/120px-Ozanam%27s_method_%281673%29-%281%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Ozanam%27s_method_%281673%29-%281%29.svg/180px-Ozanam%27s_method_%281673%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Ozanam%27s_method_%281673%29-%281%29.svg/240px-Ozanam%27s_method_%281673%29-%281%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext">Setting out a dial for 52°N. The three initial lines.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Ozanam%27s_method_(1673)-(2).svg" class="mw-file-description" title="Marking the latitude, laying out length '"`UNIQ--postMath-0000000D-QINU`"', and copying to G on the vertical."><img alt="Marking the latitude, laying out length '"`UNIQ--postMath-0000000D-QINU`"', and copying to G on the vertical." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Ozanam%27s_method_%281673%29-%282%29.svg/120px-Ozanam%27s_method_%281673%29-%282%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Ozanam%27s_method_%281673%29-%282%29.svg/180px-Ozanam%27s_method_%281673%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Ozanam%27s_method_%281673%29-%282%29.svg/240px-Ozanam%27s_method_%281673%29-%282%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext">Marking the latitude, laying out length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc867c18657f81cf14e9381bb8603ea969d63566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.628ex; height:2.509ex;" alt="{\displaystyle \sin \phi }"></span>, and copying to G on the vertical.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Ozanam%27s_method_(1673)-(3).svg" class="mw-file-description" title="From G casting '"`UNIQ--postMath-0000000E-QINU`"' on the horizontal."><img alt="From G casting '"`UNIQ--postMath-0000000E-QINU`"' on the horizontal." src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Ozanam%27s_method_%281673%29-%283%29.svg/120px-Ozanam%27s_method_%281673%29-%283%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Ozanam%27s_method_%281673%29-%283%29.svg/180px-Ozanam%27s_method_%281673%29-%283%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Ozanam%27s_method_%281673%29-%283%29.svg/240px-Ozanam%27s_method_%281673%29-%283%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext">From G casting <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan h\sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>h</mi> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan h\sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c36afcd9804bad917f765b2a27fe8ca8a6c9e2ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.101ex; height:2.509ex;" alt="{\displaystyle \tan h\sin \phi }"></span> on the horizontal.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Ozanam%27s_method_(1673)-(4).svg" class="mw-file-description" title="The actual hour lines 9, 10, 11, 12, 1, 2, 3."><img alt="The actual hour lines 9, 10, 11, 12, 1, 2, 3." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Ozanam%27s_method_%281673%29-%284%29.svg/120px-Ozanam%27s_method_%281673%29-%284%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/29/Ozanam%27s_method_%281673%29-%284%29.svg/180px-Ozanam%27s_method_%281673%29-%284%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/29/Ozanam%27s_method_%281673%29-%284%29.svg/240px-Ozanam%27s_method_%281673%29-%284%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext">The actual hour lines 9, 10, 11, 12, 1, 2, 3.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Ozanam%27s_method_(1673)-(5).svg" class="mw-file-description" title="Construction lines removed."><img alt="Construction lines removed." src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Ozanam%27s_method_%281673%29-%285%29.svg/120px-Ozanam%27s_method_%281673%29-%285%29.svg.png" decoding="async" width="120" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Ozanam%27s_method_%281673%29-%285%29.svg/180px-Ozanam%27s_method_%281673%29-%285%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5c/Ozanam%27s_method_%281673%29-%285%29.svg/240px-Ozanam%27s_method_%281673%29-%285%29.svg.png 2x" data-file-width="1052" data-file-height="744" /></a></span></div> <div class="gallerytext">Construction lines removed.</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Encyclopedia_method_(1771)"><span id="Encyclopedia_method_.281771.29"></span>Encyclopedia method (1771)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=11" title="Edit section: Encyclopedia method (1771)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This method uses the properties of chords to establish distance <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m.\sin \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>.</mo> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m.\sin \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdf4f30c1ff2979f42b69c9e2f445342f050dd9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.408ex; height:2.176ex;" alt="{\displaystyle m.\sin \theta }"></span> in the top quadrant, and then transfers this distance into the bottom quadrant so that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \phi \sin \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \phi \sin \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc52db15772c3e9aa73b1e4bfc910628eaca710f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.348ex; height:2.509ex;" alt="{\displaystyle \sin \phi \sin \theta }"></span> is established. Again, a transfer of this measure to the chords in the top quadrant. The final lines establish the formula <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan \kappa =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>κ</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \kappa =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/667bd0bd06bbac45de749cd58ee570a67c7fa620" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.539ex; height:2.009ex;" alt="{\displaystyle \tan \kappa =}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \theta \sin \phi \over \cos \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mrow> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \theta \sin \phi \over \cos \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b209c651ed4e55a257dc77946b0fcc67da4b0302" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.185ex; height:5.509ex;" alt="{\displaystyle \sin \theta \sin \phi \over \cos \theta }"></span> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan \theta \sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>θ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \theta \sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90f9d67e28da1056f1c6870243e07c258110bc56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.852ex; height:2.509ex;" alt="{\displaystyle \tan \theta \sin \phi }"></span> </p><p>This is then transferred by symmetry to all quadrants. It was used in the <a href="/wiki/Encyclop%C3%A6dia_Britannica_First_Edition" title="Encyclopædia Britannica First Edition">Encyclopædia Britannica First Edition</a> 1771, Sixth Edition 1823<sup id="cite_ref-FOOTNOTESawyer19336_17-0" class="reference"><a href="#cite_note-FOOTNOTESawyer19336-17"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <ul><li>The gnomon is drawn first against the north–south line. In doing so, a diameter at <i>φ</i> degrees to the vertical is drawn; its reflection will also be needed.</li> <li>The circumference is marked off at 15° intervals in the top quadrants. Chords parallel to the horizontal are drawn (the length of these chords will be sin Θ.</li> <li>The measurement of each chord is transferred to form a scale along the lower radiuses. When joined these points form a series of parallel lines that are sin θ. sin φ in length.</li> <li>These measurements are transferred up to the chord.</li> <li>The final hour lines are drawn from the origins through these crossing points. ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan \kappa =}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>κ</mi> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \kappa =}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/667bd0bd06bbac45de749cd58ee570a67c7fa620" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.539ex; height:2.009ex;" alt="{\displaystyle \tan \kappa =}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \theta \sin \phi \over \cos \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>θ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mrow> </mfrac> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \theta \sin \phi \over \cos \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b209c651ed4e55a257dc77946b0fcc67da4b0302" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:10.185ex; height:5.509ex;" alt="{\displaystyle \sin \theta \sin \phi \over \cos \theta }"></span> = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan \theta \sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>θ</mi> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan \theta \sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90f9d67e28da1056f1c6870243e07c258110bc56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.852ex; height:2.509ex;" alt="{\displaystyle \tan \theta \sin \phi }"></span> )<sup id="cite_ref-FOOTNOTESawyer19337_18-0" class="reference"><a href="#cite_note-FOOTNOTESawyer19337-18"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li></ul> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Britannica(1771)-(1).svg" class="mw-file-description" title="Draw the gnomon and diameters at the target angle."><img alt="Draw the gnomon and diameters at the target angle." src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Britannica%281771%29-%281%29.svg/120px-Britannica%281771%29-%281%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Britannica%281771%29-%281%29.svg/180px-Britannica%281771%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Britannica%281771%29-%281%29.svg/240px-Britannica%281771%29-%281%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">Draw the gnomon and diameters at the target angle.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Britannica(1771)-(2).svg" class="mw-file-description" title="Mark the top quadrants at 15° angles, and connect with chords"><img alt="Mark the top quadrants at 15° angles, and connect with chords" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Britannica%281771%29-%282%29.svg/120px-Britannica%281771%29-%282%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Britannica%281771%29-%282%29.svg/180px-Britannica%281771%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1d/Britannica%281771%29-%282%29.svg/240px-Britannica%281771%29-%282%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">Mark the top quadrants at 15° angles, and connect with chords</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Britannica(1771)-(3a).svg" class="mw-file-description" title="Transfer the half-chord length to the lower radius, and draw across."><img alt="Transfer the half-chord length to the lower radius, and draw across." src="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Britannica%281771%29-%283a%29.svg/120px-Britannica%281771%29-%283a%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/80/Britannica%281771%29-%283a%29.svg/180px-Britannica%281771%29-%283a%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/80/Britannica%281771%29-%283a%29.svg/240px-Britannica%281771%29-%283a%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">Transfer the half-chord length to the lower radius, and draw across.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Britannica(1771)-(4).svg" class="mw-file-description" title="Raise verticals"><img alt="Raise verticals" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Britannica%281771%29-%284%29.svg/120px-Britannica%281771%29-%284%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Britannica%281771%29-%284%29.svg/180px-Britannica%281771%29-%284%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Britannica%281771%29-%284%29.svg/240px-Britannica%281771%29-%284%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">Raise verticals</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Britannica(1771)-(5).svg" class="mw-file-description" title="Draw hour line through the intersections."><img alt="Draw hour line through the intersections." src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Britannica%281771%29-%285%29.svg/120px-Britannica%281771%29-%285%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Britannica%281771%29-%285%29.svg/180px-Britannica%281771%29-%285%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Britannica%281771%29-%285%29.svg/240px-Britannica%281771%29-%285%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">Draw hour line through the intersections.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Britannica(1771)-(dial).svg" class="mw-file-description" title="Resulting dial for 52°."><img alt="Resulting dial for 52°." src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Britannica%281771%29-%28dial%29.svg/120px-Britannica%281771%29-%28dial%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Britannica%281771%29-%28dial%29.svg/180px-Britannica%281771%29-%28dial%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Britannica%281771%29-%28dial%29.svg/240px-Britannica%281771%29-%28dial%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">Resulting dial for 52°.</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="de_Celles_(1760)_(1790)_Waugh_method_(1973)"><span id="de_Celles_.281760.29_.281790.29_Waugh_method_.281973.29"></span>de Celles (1760) (1790) Waugh method (1973)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=12" title="Edit section: de Celles (1760) (1790) Waugh method (1973)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Dom_B%C3%A9dos_de_Celles" title="Dom Bédos de Celles">Dom Francois Bedos de Celles</a> method (1760) <sup id="cite_ref-FOOTNOTEBédos_de_Celles176058_19-0" class="reference"><a href="#cite_note-FOOTNOTEBédos_de_Celles176058-19"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> otherwise known as the Waugh method (1973) <sup id="cite_ref-FOOTNOTEWaugh197338_20-0" class="reference"><a href="#cite_note-FOOTNOTEWaugh197338-20"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTESawyer191_8-5" class="reference"><a href="#cite_note-FOOTNOTESawyer191-8"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <ul><li>From G a series of lines, 15° apart are drawn, long enough so they cross the line through F. These mark the hour points 9, 10, 11, 12, 1, 2, 3 if you take just 3 and represent the points <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan h\sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>h</mi> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan h\sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c36afcd9804bad917f765b2a27fe8ca8a6c9e2ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.101ex; height:2.509ex;" alt="{\displaystyle \tan h\sin \phi }"></span>.</li> <li>The centre of the dial is at the bottom, point O. The line drawn from each of these hour point to O will be the hour line on the finished dial.<sup id="cite_ref-FOOTNOTEWaugh197338–39_7-2" class="reference"><a href="#cite_note-FOOTNOTEWaugh197338–39-7"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li>If the paper is large enough, the method above works from 7 until 12, and 12 until 5 and the values before and after 6 are calculated through symmetry. However, there is another way of marking up 7 and 8, and 4 and 5. Call the point where 3 crosses the line R, and a drop a line at right-angles to the base line. Call that point W. Use a construction line to join W and F. Waugh calls the crossing points with the hours lines K, L, M.</li> <li>Using compasses or dividers, add two more points to this line N and P, so that the distances MN = ML, and MP = MK. The missing hour lines are drawn from O through N and through P. The construction lines are erased.<sup id="cite_ref-FOOTNOTEWaugh197338–39_7-3" class="reference"><a href="#cite_note-FOOTNOTEWaugh197338–39-7"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> <sup id="cite_ref-FOOTNOTESawyer191_8-6" class="reference"><a href="#cite_note-FOOTNOTESawyer191-8"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></li></ul> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bedos_de_Celles_method_(1790)-(1).svg" class="mw-file-description" title="Setting out a dial for 52°N. The three initial lines."><img alt="Setting out a dial for 52°N. The three initial lines." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Bedos_de_Celles_method_%281790%29-%281%29.svg/85px-Bedos_de_Celles_method_%281790%29-%281%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Bedos_de_Celles_method_%281790%29-%281%29.svg/127px-Bedos_de_Celles_method_%281790%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/Bedos_de_Celles_method_%281790%29-%281%29.svg/170px-Bedos_de_Celles_method_%281790%29-%281%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Setting out a dial for 52°N. The three initial lines.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bedos_de_Celles_method_(1790)-(2).svg" class="mw-file-description" title="Marking the latitude, laying out length '"`UNIQ--postMath-00000018-QINU`"', and copying to G on the vertical."><img alt="Marking the latitude, laying out length '"`UNIQ--postMath-00000018-QINU`"', and copying to G on the vertical." src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Bedos_de_Celles_method_%281790%29-%282%29.svg/85px-Bedos_de_Celles_method_%281790%29-%282%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Bedos_de_Celles_method_%281790%29-%282%29.svg/127px-Bedos_de_Celles_method_%281790%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Bedos_de_Celles_method_%281790%29-%282%29.svg/170px-Bedos_de_Celles_method_%281790%29-%282%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Marking the latitude, laying out length <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc867c18657f81cf14e9381bb8603ea969d63566" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.628ex; height:2.509ex;" alt="{\displaystyle \sin \phi }"></span>, and copying to G on the vertical.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bedos_de_Celles_method_(1790)-(3).svg" class="mw-file-description" title="From G casting '"`UNIQ--postMath-00000019-QINU`"' on the horizontal."><img alt="From G casting '"`UNIQ--postMath-00000019-QINU`"' on the horizontal." src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Bedos_de_Celles_method_%281790%29-%283%29.svg/85px-Bedos_de_Celles_method_%281790%29-%283%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Bedos_de_Celles_method_%281790%29-%283%29.svg/127px-Bedos_de_Celles_method_%281790%29-%283%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ed/Bedos_de_Celles_method_%281790%29-%283%29.svg/170px-Bedos_de_Celles_method_%281790%29-%283%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">From G casting <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \tan h\sin \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>tan</mi> <mo>⁡</mo> <mi>h</mi> <mi>sin</mi> <mo>⁡</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \tan h\sin \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c36afcd9804bad917f765b2a27fe8ca8a6c9e2ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.101ex; height:2.509ex;" alt="{\displaystyle \tan h\sin \phi }"></span> on the horizontal.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bedos_de_Celles_method_(1790)-(4).svg" class="mw-file-description" title="The actual hour lines 9, 10, 11, 12, 1, 2, 3."><img alt="The actual hour lines 9, 10, 11, 12, 1, 2, 3." src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Bedos_de_Celles_method_%281790%29-%284%29.svg/85px-Bedos_de_Celles_method_%281790%29-%284%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Bedos_de_Celles_method_%281790%29-%284%29.svg/127px-Bedos_de_Celles_method_%281790%29-%284%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Bedos_de_Celles_method_%281790%29-%284%29.svg/170px-Bedos_de_Celles_method_%281790%29-%284%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">The actual hour lines 9, 10, 11, 12, 1, 2, 3.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bedos_de_Celles_method_(1790)-(5).svg" class="mw-file-description" title="Construction lines removed."><img alt="Construction lines removed." src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Bedos_de_Celles_method_%281790%29-%285%29.svg/85px-Bedos_de_Celles_method_%281790%29-%285%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Bedos_de_Celles_method_%281790%29-%285%29.svg/127px-Bedos_de_Celles_method_%281790%29-%285%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Bedos_de_Celles_method_%281790%29-%285%29.svg/170px-Bedos_de_Celles_method_%281790%29-%285%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Construction lines removed.</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bedos_de_Celles_method_(1790)-(6).svg" class="mw-file-description" title="Constructing the 7, 8, 4, 5 lines"><img alt="Constructing the 7, 8, 4, 5 lines" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Bedos_de_Celles_method_%281790%29-%286%29.svg/85px-Bedos_de_Celles_method_%281790%29-%286%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Bedos_de_Celles_method_%281790%29-%286%29.svg/127px-Bedos_de_Celles_method_%281790%29-%286%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Bedos_de_Celles_method_%281790%29-%286%29.svg/170px-Bedos_de_Celles_method_%281790%29-%286%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Constructing the 7, 8, 4, 5 lines</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bedos_de_Celles_method_(1790)-(7).svg" class="mw-file-description" title="Marking the 7, 8, 4, 5 lines"><img alt="Marking the 7, 8, 4, 5 lines" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Bedos_de_Celles_method_%281790%29-%287%29.svg/85px-Bedos_de_Celles_method_%281790%29-%287%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/Bedos_de_Celles_method_%281790%29-%287%29.svg/127px-Bedos_de_Celles_method_%281790%29-%287%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/Bedos_de_Celles_method_%281790%29-%287%29.svg/170px-Bedos_de_Celles_method_%281790%29-%287%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">Marking the 7, 8, 4, 5 lines</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Bedos_de_Celles_method_(1790)-(8).svg" class="mw-file-description" title="The completed dial plate for 52°N. Bedos de Celles (1790)"><img alt="The completed dial plate for 52°N. Bedos de Celles (1790)" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Bedos_de_Celles_method_%281790%29-%288%29.svg/85px-Bedos_de_Celles_method_%281790%29-%288%29.svg.png" decoding="async" width="85" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Bedos_de_Celles_method_%281790%29-%288%29.svg/127px-Bedos_de_Celles_method_%281790%29-%288%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Bedos_de_Celles_method_%281790%29-%288%29.svg/170px-Bedos_de_Celles_method_%281790%29-%288%29.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div> <div class="gallerytext">The completed dial plate for 52°N. Bedos de Celles (1790)</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Nicholson's_method_(1825)"><span id="Nicholson.27s_method_.281825.29"></span>Nicholson's method (1825)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=13" title="Edit section: Nicholson's method (1825)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This method first appeared in Peter Nicholsons <i>A popular Course of Pure and Mixed Mathematics</i> in 1825. It was copied by School World in Jun 1903, then in Kenneth Lynch's, Sundial and Spheres 1971. <sup id="cite_ref-FOOTNOTESawyer194_21-0" class="reference"><a href="#cite_note-FOOTNOTESawyer194-21"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> It starts by drawing the well known triangle, and takes the vertices to draw two circles at radius (OB) sin φ and (AB) tan φ. The 15° lines are drawn, intersecting these circles. Lines are taken horizontally, and vertically from these circles and their intersection point (OB sin t,AB cos t) is on the hour line. That is tan κ = OB sin t/ AB cos t which resolves to sin φ. tan t. </p> <ul><li>Draw the NS line, and the EW line crossing at the origin O. At a convenient point in the first quadrant join the axes with a line set at the target angle. This forms the basic triangle OAB.</li> <li>Set the compasses at length OB and inscribe a circle. Set the compasses on AB and inscribe a concentric circle. On both of these circles mark out the 15° angles.</li> <li>Taking the lines vertically from the inner circle, and horizontally from the outer circle, Mark each of the intersections. These are on the hour lines.</li> <li>Connect the intersection points to the origin.</li></ul> <p><sup id="cite_ref-FOOTNOTESawyer194_21-1" class="reference"><a href="#cite_note-FOOTNOTESawyer194-21"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Nicholson(1825)-(1).svg" class="mw-file-description" title="The basic triangle"><img alt="The basic triangle" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Nicholson%281825%29-%281%29.svg/120px-Nicholson%281825%29-%281%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Nicholson%281825%29-%281%29.svg/180px-Nicholson%281825%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Nicholson%281825%29-%281%29.svg/240px-Nicholson%281825%29-%281%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">The basic triangle</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Nicholson(1825)-(2).svg" class="mw-file-description" title="The circles"><img alt="The circles" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Nicholson%281825%29-%282%29.svg/120px-Nicholson%281825%29-%282%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Nicholson%281825%29-%282%29.svg/180px-Nicholson%281825%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Nicholson%281825%29-%282%29.svg/240px-Nicholson%281825%29-%282%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">The circles</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Nicholson(1825)-(3a).svg" class="mw-file-description" title="The 15° measure"><img alt="The 15° measure" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Nicholson%281825%29-%283a%29.svg/120px-Nicholson%281825%29-%283a%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Nicholson%281825%29-%283a%29.svg/180px-Nicholson%281825%29-%283a%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Nicholson%281825%29-%283a%29.svg/240px-Nicholson%281825%29-%283a%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">The 15° measure</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Nicholson(1825)-(4).svg" class="mw-file-description" title="The intersection points"><img alt="The intersection points" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Nicholson%281825%29-%284%29.svg/120px-Nicholson%281825%29-%284%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Nicholson%281825%29-%284%29.svg/180px-Nicholson%281825%29-%284%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Nicholson%281825%29-%284%29.svg/240px-Nicholson%281825%29-%284%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">The intersection points</div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Nicholson(1825)-(5).svg" class="mw-file-description" title="The completed dial"><img alt="The completed dial" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Nicholson%281825%29-%285%29.svg/120px-Nicholson%281825%29-%285%29.svg.png" decoding="async" width="120" height="120" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Nicholson%281825%29-%285%29.svg/180px-Nicholson%281825%29-%285%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/90/Nicholson%281825%29-%285%29.svg/240px-Nicholson%281825%29-%285%29.svg.png 2x" data-file-width="744" data-file-height="744" /></a></span></div> <div class="gallerytext">The completed dial</div> </li> </ul> <div class="mw-heading mw-heading3"><h3 id="Foster_Serles_Dialling_Scales_(1638)"><span id="Foster_Serles_Dialling_Scales_.281638.29"></span>Foster Serles Dialling Scales (1638)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=14" title="Edit section: Foster Serles Dialling Scales (1638)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Dialing_scales" title="Dialing scales">Dialing scales</a></div> <ul><li>A right-angle is drawn on the dial-face and the latitude scale is laid against the <i>x</i>-axis.</li> <li>The target latitude point is marked across on to the dial face. The hour scale is placed from this point to the noon line (conventionally, the zero point is on the noon line).</li> <li>Each of the hour points is copied over to the dial face, and this procedure is repeated, giving the hours both sides of noon. A straight edge is used to connect these points to the origin, thus drawing the hour lines for that location.</li> <li>A vertical line from the target latitude point, and a horizontal line through the noon point will bisect at the three-hour (9am–3pm) marker.</li> <li>The style will be at the same angle as the latitude.</li></ul> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Serle_scales_method_(1657)-(1).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Serle_scales_method_%281657%29-%281%29.svg/120px-Serle_scales_method_%281657%29-%281%29.svg.png" decoding="async" width="120" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Serle_scales_method_%281657%29-%281%29.svg/180px-Serle_scales_method_%281657%29-%281%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Serle_scales_method_%281657%29-%281%29.svg/240px-Serle_scales_method_%281657%29-%281%29.svg.png 2x" data-file-width="689" data-file-height="549" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Serle_scales_method_(1657)-(2).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Serle_scales_method_%281657%29-%282%29.svg/120px-Serle_scales_method_%281657%29-%282%29.svg.png" decoding="async" width="120" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/40/Serle_scales_method_%281657%29-%282%29.svg/180px-Serle_scales_method_%281657%29-%282%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/40/Serle_scales_method_%281657%29-%282%29.svg/240px-Serle_scales_method_%281657%29-%282%29.svg.png 2x" data-file-width="689" data-file-height="549" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Serle_scales_method_(1657)-(full).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Serle_scales_method_%281657%29-%28full%29.svg/120px-Serle_scales_method_%281657%29-%28full%29.svg.png" decoding="async" width="120" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Serle_scales_method_%281657%29-%28full%29.svg/180px-Serle_scales_method_%281657%29-%28full%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ab/Serle_scales_method_%281657%29-%28full%29.svg/240px-Serle_scales_method_%281657%29-%28full%29.svg.png 2x" data-file-width="689" data-file-height="549" /></a></span></div> <div class="gallerytext"></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/File:Serle_scales_method_(1657)-(result).svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Serle_scales_method_%281657%29-%28result%29.svg/120px-Serle_scales_method_%281657%29-%28result%29.svg.png" decoding="async" width="120" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Serle_scales_method_%281657%29-%28result%29.svg/180px-Serle_scales_method_%281657%29-%28result%29.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Serle_scales_method_%281657%29-%28result%29.svg/240px-Serle_scales_method_%281657%29-%28result%29.svg.png 2x" data-file-width="689" data-file-height="549" /></a></span></div> <div class="gallerytext"></div> </li> </ul> <p><sup id="cite_ref-NASS-2-2_22-0" class="reference"><a href="#cite_note-NASS-2-2-22"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Saphea_(As-Saphiah)"><span id="Saphea_.28As-Saphiah.29"></span>Saphea (As-Saphiah)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=15" title="Edit section: Saphea (As-Saphiah)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>This was an early and convenient method to use if you had access to an <a href="/wiki/Astrolabe" title="Astrolabe">astrolabe</a> as many <a href="/wiki/Astrologer" class="mw-redirect" title="Astrologer">astrologers</a> and <a href="/wiki/Mathematician" title="Mathematician">mathematicians</a> of the time would have had. The method involved copying the projections of the <a href="/wiki/Celestial_sphere" title="Celestial sphere">celestial sphere</a> onto a plane surface. A vertical line was drawn with a line at the angle of the latitude drawn on the bisection of the vertical with the celestial sphere. <sup id="cite_ref-FOOTNOTEGunella2013c_23-0" class="reference"><a href="#cite_note-FOOTNOTEGunella2013c-23"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=16" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/London_dial" title="London dial">London dial</a></li> <li><a href="/wiki/Schema_for_vertical_declining_dials" title="Schema for vertical declining dials">Schema for vertical declining dials</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=17" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Time had been measured by dividing the daylight hours by twelve using <i>unequal hours</i>, known as <a href="/wiki/Italian_hours" class="mw-redirect" title="Italian hours">Italian hours</a> or <a href="/wiki/Babylonian_hours" class="mw-redirect" title="Babylonian hours">Babylonian hours</a>.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">The British Sundial Society publishes a glossary of computer terms and the symbols that are commonly used to represent them. Latitude is represented by <i>phi</i>,<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> or <i>φ</i> or Φ.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">All dials in these illustrations use a latitude of 52°, it was chosen randomly but is roughly that of <a href="/wiki/Bletchley_Park" title="Bletchley Park">Bletchley Park</a>, <a href="/wiki/The_Hague" title="The Hague">The Hague</a> or <a href="/wiki/Bielefeld" title="Bielefeld">Bielefeld</a>.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">The Art of Dialling : Performed Geometrically, by Scale and Compasses: Arithmetically, by the Canons of Sines and Tangents: Instrumentally, by a Trigonal Instrument ...; To which is added A Supplement; Shewing, How by Scale and Compasses to inscribe such Circles of the Sphere into Sun-Dial-Plans, that shall shew (besides the hour of the day) the Diurnal Motion of the Sun ...</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">The line of chords is available on a builders metal rule (Stanley 60R Line of Chords Rule) in 2015.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">This can be done using the line of chords set at 60° and subdividing.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=18" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Citations">Citations</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=19" title="Edit section: Citations"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20071010085501/http://www.sundialsoc.org.uk/glossary/alpha.htm#S">"BSS Glossary"</a>. British Sundial Society. Archived from <a rel="nofollow" class="external text" href="http://www.sundialsoc.org.uk/index.htm">the original</a> on 10 October 2007<span class="reference-accessdate">. Retrieved <span class="nowrap">2 May</span> 2011</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=BSS+Glossary&rft.pub=British+Sundial+Society&rft_id=http%3A%2F%2Fwww.sundialsoc.org.uk%2Findex.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEJones19806-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEJones19806_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFJones1980">Jones 1980</a>, p. 6.<span class="error harv-error" style="display: none; font-size:100%"> sfn error: no target: CITEREFJones1980 (<a href="/wiki/Category:Harv_and_Sfn_template_errors" title="Category:Harv and Sfn template errors">help</a>)</span></span> </li> <li id="cite_note-FOOTNOTEDurell1921-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDurell1921_6-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDurell1921">Durell 1921</a>.</span> </li> <li id="cite_note-FOOTNOTEWaugh197338–39-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEWaugh197338–39_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTEWaugh197338–39_7-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTEWaugh197338–39_7-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTEWaugh197338–39_7-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFWaugh1973">Waugh 1973</a>, pp. 38–39.</span> </li> <li id="cite_note-FOOTNOTESawyer191-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTESawyer191_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTESawyer191_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-FOOTNOTESawyer191_8-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-FOOTNOTESawyer191_8-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-FOOTNOTESawyer191_8-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-FOOTNOTESawyer191_8-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-FOOTNOTESawyer191_8-6"><sup><i><b>g</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFSawyer191">Sawyer 191</a>.</span> </li> <li id="cite_note-FOOTNOTEGunella2013b-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGunella2013b_9-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGunella2013b">Gunella 2013b</a>.</span> </li> <li id="cite_note-FOOTNOTEGunella2013-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGunella2013_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGunella2013">Gunella 2013</a>.</span> </li> <li id="cite_note-FOOTNOTEGunella201413-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGunella201413_11-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGunella2014">Gunella 2014</a>, p. 13.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20150920194250/http://metal.brightcookie.com/shared/toolbook/tool_46.htm">"Toolbook"</a>. Archived from <a rel="nofollow" class="external text" href="http://metal.brightcookie.com/shared/toolbook/tool_46.htm">the original</a> on 20 September 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">11 September</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Toolbook&rft_id=http%3A%2F%2Fmetal.brightcookie.com%2Fshared%2Ftoolbook%2Ftool_46.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTELeybourn1700-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTELeybourn1700_16-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFLeybourn1700">Leybourn 1700</a>.</span> </li> <li id="cite_note-FOOTNOTESawyer19336-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESawyer19336_17-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSawyer193">Sawyer 193</a>, p. 36.</span> </li> <li id="cite_note-FOOTNOTESawyer19337-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTESawyer19337_18-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFSawyer193">Sawyer 193</a>, p. 37.</span> </li> <li id="cite_note-FOOTNOTEBédos_de_Celles176058-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBédos_de_Celles176058_19-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBédos_de_Celles1760">Bédos de Celles 1760</a>, p. 58.</span> </li> <li id="cite_note-FOOTNOTEWaugh197338-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWaugh197338_20-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWaugh1973">Waugh 1973</a>, p. 38.</span> </li> <li id="cite_note-FOOTNOTESawyer194-21"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTESawyer194_21-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-FOOTNOTESawyer194_21-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="#CITEREFSawyer194">Sawyer 194</a>.</span> </li> <li id="cite_note-NASS-2-2-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-NASS-2-2_22-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSawyer1995" class="citation journal cs1">Sawyer, Fred (1995). "Serle's Dialing Scales". <i>Compendium</i>. <b>2</b> (2). Glastonbury, CT, USA: North American Sundial Society: 5.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Compendium&rft.atitle=Serle%27s+Dialing+Scales&rft.volume=2&rft.issue=2&rft.pages=5&rft.date=1995&rft.aulast=Sawyer&rft.aufirst=Fred&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></span> </li> <li id="cite_note-FOOTNOTEGunella2013c-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEGunella2013c_23-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFGunella2013c">Gunella 2013c</a>.</span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Schema_for_horizontal_dials&action=edit&section=20" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDurell1921" class="citation book cs1">Durell, Clement V (1921). <a rel="nofollow" class="external text" href="https://archive.org/details/concisegeometry032982mbp"><i>Geometry</i></a>. Publisher G.Bell And Sons Limited.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geometry&rft.pub=Publisher+G.Bell+And+Sons+Limited&rft.date=1921&rft.aulast=Durell&rft.aufirst=Clement+V&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fconcisegeometry032982mbp&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBédos_de_Celles1760" class="citation book cs1 cs1-prop-foreign-lang-source">Bédos de Celles, Francois (1760). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=_BY4AAAAMAAJ&q=La+Gnomonique+pratique+ou+l%27Art+de+tracer+les+cadrans+solaires+avec+la+plus+grande+pr%C3%A9cision.&pg=PA405">"4-3"</a>. <i>La Gnomonique pratique ou l'Art de tracer les cadrans solaires avec la plus grande précision</i> (in French) (3 ed.). Paris. p. 459<span class="reference-accessdate">. Retrieved <span class="nowrap">12 July</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=4-3&rft.btitle=La+Gnomonique+pratique+ou+l%27Art+de+tracer+les+cadrans+solaires+avec+la+plus+grande+pr%C3%A9cision&rft.place=Paris&rft.pages=459&rft.edition=3&rft.date=1760&rft.aulast=B%C3%A9dos+de+Celles&rft.aufirst=Francois&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D_BY4AAAAMAAJ%26q%3DLa%2BGnomonique%2Bpratique%2Bou%2Bl%2527Art%2Bde%2Btracer%2Bles%2Bcadrans%2Bsolaires%2Bavec%2Bla%2Bplus%2Bgrande%2Bpr%25C3%25A9cision.%26pg%3DPA405&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavis2014" class="citation journal cs1 cs1-prop-long-vol">Davis, John (June 2014). <a rel="nofollow" class="external text" href="http://www.flowton-dials.co.uk/wp-content/uploads/2015/02/Engraved-decoration-English-Horizontal-dials-Bull-26ii.pdf">"Engraved decoration English-Horizontal dials"</a> <span class="cs1-format">(PDF)</span>. <i>Bulletin</i>. 26 (ii). British Sundial Society: <span class="nowrap">48–</span>52. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0958-4315">0958-4315</a><span class="reference-accessdate">. Retrieved <span class="nowrap">3 July</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin&rft.atitle=Engraved+decoration+English-Horizontal+dials&rft.volume=26+%28ii%29&rft.pages=%3Cspan+class%3D%22nowrap%22%3E48-%3C%2Fspan%3E52&rft.date=2014-06&rft.issn=0958-4315&rft.aulast=Davis&rft.aufirst=John&rft_id=http%3A%2F%2Fwww.flowton-dials.co.uk%2Fwp-content%2Fuploads%2F2015%2F02%2FEngraved-decoration-English-Horizontal-dials-Bull-26ii.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRohr1996" class="citation book cs1">Rohr, René R.J.; with a foreword by Henri Michel; translated by Gabriel Godin (1996). <a rel="nofollow" class="external text" href="https://archive.org/details/sundialshistoryt0000rohr/page/142"><i>Sundials : history, theory, and practice</i></a> (Paperback ed.). New York: <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/sundialshistoryt0000rohr/page/142">142</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-29139-1" title="Special:BookSources/0-486-29139-1"><bdi>0-486-29139-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sundials+%3A+history%2C+theory%2C+and+practice&rft.place=New+York&rft.pages=142&rft.edition=Paperback&rft.pub=Dover+Publications&rft.date=1996&rft.isbn=0-486-29139-1&rft.aulast=Rohr&rft.aufirst=Ren%C3%A9+R.J.%3B+with+a+foreword+by+Henri+Michel%3B+translated+by+Gabriel+Godin&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsundialshistoryt0000rohr%2Fpage%2F142&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSawyer1995" class="citation journal cs1">Sawyer, Fred (1995). "Serle's Dialing Scales". <i>Compendium</i>. <b>2</b> (2). Glastonbury, CT, USA: North American Sundial Society: 5.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Compendium&rft.atitle=Serle%27s+Dialing+Scales&rft.volume=2&rft.issue=2&rft.pages=5&rft.date=1995&rft.aulast=Sawyer&rft.aufirst=Fred&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSawyer191" class="citation journal cs1">Sawyer, Fred (2012). "Horizontal Layouts 1–4". <i>Compendium</i>. <b>19</b> (1). Glastonbury, CT, USA: North American Sundial Society: 33.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Compendium&rft.atitle=Horizontal+Layouts+1%E2%80%934&rft.volume=19&rft.issue=1&rft.pages=33&rft.date=2012&rft.aulast=Sawyer&rft.aufirst=Fred&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSawyer193" class="citation journal cs1">Sawyer, Fred (2012). "Horizontal Layouts 6". <i>Compendium</i>. <b>19</b> (3). Glastonbury, CT, USA: North American Sundial Society: <span class="nowrap">36–</span>7.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Compendium&rft.atitle=Horizontal+Layouts+6&rft.volume=19&rft.issue=3&rft.pages=%3Cspan+class%3D%22nowrap%22%3E36-%3C%2Fspan%3E7&rft.date=2012&rft.aulast=Sawyer&rft.aufirst=Fred&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSawyer194" class="citation journal cs1">Sawyer, Fred (2012). "Horizontal Layouts 7". <i>Compendium</i>. <b>19</b> (4). Glastonbury, CT, USA: North American Sundial Society: 39.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Compendium&rft.atitle=Horizontal+Layouts+7&rft.volume=19&rft.issue=4&rft.pages=39&rft.date=2012&rft.aulast=Sawyer&rft.aufirst=Fred&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGunella2013" class="citation journal cs1">Gunella, Alessandro (2013). Sawyer, Fred (ed.). "Horizontal Layouts 8 – Clavius Method". <i>Compendium</i>. <b>20</b> (1). Glastonbury, CT, USA: North American Sundial Society: 31.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Compendium&rft.atitle=Horizontal+Layouts+8+%E2%80%93+Clavius+Method&rft.volume=20&rft.issue=1&rft.pages=31&rft.date=2013&rft.aulast=Gunella&rft.aufirst=Alessandro&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGunella2013b" class="citation journal cs1">Gunella, Alessandro (2013). Sawyer, Fred (ed.). "Horizontal Layouts 9 – Benedetti Method". <i>Compendium</i>. <b>20</b> (2). Glastonbury, CT, USA: North American Sundial Society: 37.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Compendium&rft.atitle=Horizontal+Layouts+9+%E2%80%93+Benedetti+Method&rft.volume=20&rft.issue=2&rft.pages=37&rft.date=2013&rft.aulast=Gunella&rft.aufirst=Alessandro&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGunella2013c" class="citation journal cs1">Gunella, Alessandro (2013). Sawyer, Fred (ed.). "Horizontal Layouts 10 – Saphea Method". <i>Compendium</i>. <b>20</b> (3). Glastonbury, CT, USA: North American Sundial Society: 39.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Compendium&rft.atitle=Horizontal+Layouts+10+%E2%80%93+Saphea+Method&rft.volume=20&rft.issue=3&rft.pages=39&rft.date=2013&rft.aulast=Gunella&rft.aufirst=Alessandro&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGunella2014" class="citation journal cs1">Gunella, Alessandro (2013). Sawyer, Fred (ed.). "Horizontal Layouts 11 – Still a method for the Horizontal Sundial". <i>Compendium</i>. <b>21</b> (3). Glastonbury, CT, USA: North American Sundial Society: 13.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Compendium&rft.atitle=Horizontal+Layouts+11+%E2%80%93+Still+a+method+for+the+Horizontal+Sundial&rft.volume=21&rft.issue=3&rft.pages=13&rft.date=2013&rft.aulast=Gunella&rft.aufirst=Alessandro&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeybourn1700" class="citation journal cs1">Powers, Patrick (2012). Sawyer, Fred (ed.). "Horizontal Layouts 5 – Leybourns Method". <i>Compendium</i>. <b>19</b> (2). Glastonbury, CT, USA: North American Sundial Society: 4.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Compendium&rft.atitle=Horizontal+Layouts+5+%E2%80%93+Leybourns+Method&rft.volume=19&rft.issue=2&rft.pages=4&rft.date=2012&rft.aulast=Powers&rft.aufirst=Patrick&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWaugh1973" class="citation book cs1">Waugh, Albert E. (1973). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/sundialstheirthe00albe/page/38"><i>Sundials : their theory and construction</i></a></span>. New York: Dover. pp. <a rel="nofollow" class="external text" href="https://archive.org/details/sundialstheirthe00albe/page/38">38–39</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0486229475" title="Special:BookSources/0486229475"><bdi>0486229475</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Sundials+%3A+their+theory+and+construction.&rft.place=New+York&rft.pages=38-39&rft.pub=Dover&rft.date=1973&rft.isbn=0486229475&rft.aulast=Waugh&rft.aufirst=Albert+E.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsundialstheirthe00albe%2Fpage%2F38&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASchema+for+horizontal+dials" class="Z3988"></span></li></ul> <div style="clear:both;" class=""></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output 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six-hour clock">Thai six-hour clock</a></li> <li><a href="/wiki/12-hour_clock" title="12-hour clock">12-hour clock</a></li> <li><a href="/wiki/24-hour_clock" title="24-hour clock">24-hour clock</a></li> <li><a href="/wiki/Relative_hour" title="Relative hour">Relative hour</a></li> <li><a href="/wiki/Daylight_saving_time" title="Daylight saving time">Daylight saving time</a></li> <li><a href="/wiki/Traditional_Chinese_timekeeping" title="Traditional Chinese timekeeping">Chinese</a></li> <li><a href="/wiki/Decimal_time" title="Decimal time">Decimal</a></li> <li><a href="/wiki/Hexadecimal_time" title="Hexadecimal time">Hexadecimal</a></li> <li><a href="/wiki/Hindu_units_of_time" title="Hindu units of time">Hindu</a></li> <li><a href="/wiki/Metric_time" title="Metric time">Metric</a></li> <li><a href="/wiki/Roman_timekeeping" title="Roman timekeeping">Roman</a></li> <li><a href="/wiki/Sidereal_time" title="Sidereal time">Sidereal</a></li> <li><a href="/wiki/Solar_time" title="Solar time">Solar</a></li> <li><a href="/wiki/Time_zone" title="Time zone">Time zone</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;"><a href="/wiki/Calendar" title="Calendar">Calendars</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Calendar#Systems" title="Calendar">Main types</a> <ul><li><a href="/wiki/Solar_calendar" title="Solar calendar">Solar</a></li> <li><a href="/wiki/Lunar_calendar" title="Lunar calendar">Lunar</a></li> <li><a href="/wiki/Lunisolar_calendar" title="Lunisolar calendar">Lunisolar</a></li></ul></li> <li><a href="/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian</a></li> <li><a href="/wiki/Julian_calendar" title="Julian calendar">Julian</a></li> <li><a href="/wiki/Hebrew_calendar" title="Hebrew calendar">Hebrew</a></li> <li><a href="/wiki/Islamic_calendar" title="Islamic calendar">Islamic</a></li> <li><a href="/wiki/Solar_Hijri_calendar" title="Solar Hijri calendar">Solar Hijri</a></li> <li><a href="/wiki/Chinese_calendar" title="Chinese calendar">Chinese</a></li> <li><a href="/wiki/Hindu_calendar" title="Hindu calendar">Hindu Panchang</a></li> <li><a href="/wiki/Maya_calendar" title="Maya calendar">Maya</a></li> <li><i><a href="/wiki/List_of_calendars" title="List of calendars">List</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;"><a href="/wiki/Clock" title="Clock">Clocks</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Clock#Types" title="Clock">Main types</a> <ul><li><a href="/wiki/Astronomical_clock" title="Astronomical clock">astronomical</a> <ul><li><a href="/wiki/Astrarium" title="Astrarium">astrarium</a></li></ul></li> <li><a href="/wiki/Atomic_clock" title="Atomic clock">atomic</a> <ul><li><a href="/wiki/Quantum_clock" class="mw-redirect" title="Quantum clock">quantum</a></li></ul></li> <li><a href="/wiki/Hourglass" title="Hourglass">hourglass</a></li> <li><a href="/wiki/Marine_chronometer" title="Marine chronometer">marine</a></li> <li><a href="/wiki/Sundial" title="Sundial">sundial</a></li> <li><a href="/wiki/Watch" title="Watch">watch</a> <ul><li><a href="/wiki/Mechanical_watch" title="Mechanical watch">mechanical</a></li> <li><a href="/wiki/Stopwatch" title="Stopwatch">stopwatch</a></li></ul></li> <li><a href="/wiki/Water_clock" title="Water clock">water-based</a></li></ul></li> <li><a href="/wiki/Cuckoo_clock" title="Cuckoo clock">Cuckoo clock</a></li> <li><a href="/wiki/Digital_clock" title="Digital clock">Digital clock</a></li> <li><a href="/wiki/Grandfather_clock" title="Grandfather clock">Grandfather clock</a></li> <li><i><a href="/wiki/History_of_timekeeping_devices" title="History of timekeeping devices">History</a></i> <ul><li><i><a href="/wiki/Timeline_of_time_measurement_inventions" title="Timeline of time measurement inventions">Timeline</a></i></li></ul></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist"><ul><li><a href="/wiki/Chronology" title="Chronology">Chronology</a></li><li><a href="/wiki/History" title="History">History</a></li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astronomical_chronology" title="Astronomical chronology">Astronomical chronology</a></li> <li><a href="/wiki/Big_History" title="Big History">Big History</a></li> <li><a href="/wiki/Calendar_era" title="Calendar era">Calendar era</a></li> <li><a href="/wiki/Deep_time" title="Deep time">Deep time</a></li> <li><a href="/wiki/Periodization" title="Periodization">Periodization</a></li> <li><a href="/wiki/Regnal_year" title="Regnal year">Regnal year</a></li> <li><a href="/wiki/Timeline" title="Timeline">Timeline</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Philosophy_of_space_and_time" title="Philosophy of space and time">Philosophy of time</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/A_series_and_B_series" title="A series and B series">A series and B series</a></li> <li><a href="/wiki/B-theory_of_time" title="B-theory of time">B-theory of time</a></li> <li><a href="/wiki/Chronocentrism" title="Chronocentrism">Chronocentrism</a></li> <li><a href="/wiki/Duration_(philosophy)" title="Duration (philosophy)">Duration</a></li> <li><a href="/wiki/Endurantism" title="Endurantism">Endurantism</a></li> <li><a href="/wiki/Eternal_return" title="Eternal return">Eternal return</a></li> <li><a href="/wiki/Eternalism_(philosophy_of_time)" title="Eternalism (philosophy of time)">Eternalism</a></li> <li><a href="/wiki/Event_(philosophy)" title="Event (philosophy)">Event</a></li> <li><a href="/wiki/Perdurantism" title="Perdurantism">Perdurantism</a></li> <li><a href="/wiki/Philosophical_presentism" title="Philosophical presentism">Presentism</a></li> <li><a href="/wiki/Temporal_finitism" title="Temporal finitism">Temporal finitism</a></li> <li><a href="/wiki/Temporal_parts" title="Temporal parts">Temporal parts</a></li> <li><i><a href="/wiki/The_Unreality_of_Time" title="The Unreality of Time">The Unreality of Time</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div class="hlist"><ul><li><a href="/wiki/Category:Time_in_religion" title="Category:Time in religion">Religion</a></li><li><a href="/wiki/Template:Time_in_religion_and_mythology" title="Template:Time in religion and mythology">Mythology</a></li></ul></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ages_of_Man" title="Ages of Man">Ages of Man</a></li> <li><a href="/wiki/Destiny" title="Destiny">Destiny</a></li> <li><a href="/wiki/Immortality" title="Immortality">Immortality</a></li> <li><a href="/wiki/The_Dreaming" title="The Dreaming">Dreamtime</a></li> <li><a href="/wiki/K%C4%81la" title="Kāla">Kāla</a></li> <li><a href="/wiki/Time_and_fate_deities" title="Time and fate deities">Time and fate deities</a> <ul><li><a href="/wiki/Father_Time" title="Father Time">Father Time</a></li></ul></li> <li><a href="/wiki/Wheel_of_time" title="Wheel of time">Wheel of time</a> <ul><li><a href="/wiki/Kalachakra" title="Kalachakra">Kalachakra</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Time_perception" title="Time perception">Human experience</a><br />and <a href="/wiki/Time-use_research" title="Time-use research">use of time</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chronemics" title="Chronemics">Chronemics</a></li> <li><a href="/wiki/Generation_time" title="Generation time">Generation time</a></li> <li><a href="/wiki/Mental_chronometry" title="Mental chronometry">Mental chronometry</a></li> <li><a href="/wiki/Duration_(music)" title="Duration (music)">Music</a> <ul><li><a href="/wiki/Tempo" title="Tempo">tempo</a></li> <li><a href="/wiki/Time_signature" title="Time signature">time signature</a></li></ul></li> <li><a href="/wiki/Rosy_retrospection" title="Rosy retrospection">Rosy retrospection</a></li> <li><a href="/wiki/Tense%E2%80%93aspect%E2%80%93mood" title="Tense–aspect–mood">Tense–aspect–mood</a></li> <li><a href="/wiki/Time_management" title="Time management">Time management</a></li> <li><a href="/wiki/Yesterday_(time)" title="Yesterday (time)">Yesterday</a> – <a href="/wiki/Present" title="Present">Today</a> – <a href="/wiki/Tomorrow_(time)" title="Tomorrow (time)">Tomorrow</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Time in <a href="/wiki/Science" title="Science">science</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;"><a href="/wiki/Geology" title="Geology">Geology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geologic_time_scale" title="Geologic time scale">Geological time</a> <ul><li><a href="/wiki/Age_(geology)" class="mw-redirect" title="Age (geology)">age</a></li> <li><a href="/wiki/Chronozone" title="Chronozone">chron</a></li> <li><a href="/wiki/Eon_(geology)" class="mw-redirect" title="Eon (geology)">eon</a></li> <li><a href="/wiki/Epoch_(geology)" class="mw-redirect" title="Epoch (geology)">epoch</a></li> <li><a href="/wiki/Era_(geology)" class="mw-redirect" title="Era (geology)">era</a></li> <li><a href="/wiki/Geological_period" class="mw-redirect" title="Geological period">period</a></li></ul></li> <li><a href="/wiki/Geochronology" title="Geochronology">Geochronology</a></li> <li><a href="/wiki/Geological_history_of_Earth" title="Geological history of Earth">Geological history of Earth</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;"><a href="/wiki/Time_in_physics" title="Time in physics">Physics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Absolute_space_and_time" title="Absolute space and time">Absolute space and time</a></li> <li><a href="/wiki/Arrow_of_time" title="Arrow of time">Arrow of time</a></li> <li><a href="/wiki/Chronon" title="Chronon">Chronon</a></li> <li><a href="/wiki/Coordinate_time" title="Coordinate time">Coordinate time</a></li> <li><a href="/wiki/Instant" title="Instant">Instant</a></li> <li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></li> <li><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Theory of relativity</a></li> <li><a href="/wiki/Time_domain" title="Time domain">Time domain</a></li> <li><a href="/wiki/Time_translation_symmetry" class="mw-redirect" title="Time translation symmetry">Time translation symmetry</a></li> <li><a href="/wiki/T-symmetry" title="T-symmetry">Time reversal symmetry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:6.5em;font-weight:normal; text-align:center;">Other fields</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chronological_dating" title="Chronological dating">Chronological dating</a></li> <li><a href="/wiki/Chronobiology" title="Chronobiology">Chronobiology</a> <ul><li><a href="/wiki/Circadian_rhythm" title="Circadian rhythm">Circadian rhythms</a></li></ul></li> <li><a href="/wiki/Chemical_clock" title="Chemical clock">Clock reaction</a></li> <li><a href="/wiki/Glottochronology" title="Glottochronology">Glottochronology</a></li> <li><a href="/wiki/Time_geography" title="Time geography">Time geography</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Leap_year" title="Leap year">Leap year</a></li> <li><a href="/wiki/Memory" title="Memory">Memory</a></li> <li><a href="/wiki/Moment_(unit)" title="Moment (unit)">Moment</a></li> <li><a href="/wiki/Space" title="Space">Space</a></li> <li><a href="/wiki/System_time" title="System time">System time</a></li> <li><i><a href="/wiki/Tempus_fugit" title="Tempus fugit">Tempus fugit</a></i></li> <li><a href="/wiki/Time_capsule" title="Time capsule">Time capsule</a></li> <li><a href="/wiki/Time_immemorial" title="Time immemorial">Time immemorial</a></li> <li><a href="/wiki/Time_travel" title="Time travel">Time travel</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:Time" title="Category:Time">Category</a></li> <li><span class="noviewer" typeof="mw:File"><span title="Commons page"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> <a href="https://commons.wikimedia.org/wiki/Category:Time" class="extiw" title="commons:Category:Time">Commons</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Time_measurement_and_standards342" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Time_measurement_and_standards" title="Template:Time measurement and standards"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Time_measurement_and_standards" title="Template talk:Time measurement and standards"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Time_measurement_and_standards" title="Special:EditPage/Template:Time measurement and standards"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Time_measurement_and_standards342" style="font-size:114%;margin:0 4em"><a href="/wiki/Time" title="Time">Time measurement</a> and <a href="/wiki/Time_standard" title="Time standard">standards</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><a href="/wiki/Chronometry" title="Chronometry">Chronometry</a></li> <li><a href="/wiki/Orders_of_magnitude_(time)" title="Orders of magnitude (time)">Orders of magnitude</a></li> <li><a href="/wiki/Time_metrology" class="mw-redirect" title="Time metrology">Metrology</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">International standards</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coordinated_Universal_Time" title="Coordinated Universal Time">Coordinated Universal Time</a> <ul><li><a href="/wiki/UTC_offset" title="UTC offset">offset</a></li></ul></li> <li><a href="/wiki/Universal_Time" title="Universal Time">UT</a></li> <li><a href="/wiki/%CE%94T_(timekeeping)" title="ΔT (timekeeping)">ΔT</a></li> <li><a href="/wiki/DUT1" title="DUT1">DUT1</a></li> <li><a href="/wiki/International_Earth_Rotation_and_Reference_Systems_Service" title="International Earth Rotation and Reference Systems Service">International Earth Rotation and Reference Systems Service</a></li> <li><a href="/wiki/ISO_31-1" title="ISO 31-1">ISO 31-1</a></li> <li><a href="/wiki/ISO_8601" title="ISO 8601">ISO 8601</a></li> <li><a href="/wiki/International_Atomic_Time" title="International Atomic Time">International Atomic Time</a></li> <li><a href="/wiki/12-hour_clock" title="12-hour clock">12-hour clock</a></li> <li><a href="/wiki/24-hour_clock" title="24-hour clock">24-hour clock</a></li> <li><a href="/wiki/Barycentric_Coordinate_Time" title="Barycentric Coordinate Time">Barycentric Coordinate Time</a></li> <li><a href="/wiki/Barycentric_Dynamical_Time" title="Barycentric Dynamical Time">Barycentric Dynamical Time</a></li> <li><a href="/wiki/Civil_time" title="Civil time">Civil time</a></li> <li><a href="/wiki/Daylight_saving_time" title="Daylight saving time">Daylight saving time</a></li> <li><a href="/wiki/Geocentric_Coordinate_Time" title="Geocentric Coordinate Time">Geocentric Coordinate Time</a></li> <li><a href="/wiki/International_Date_Line" title="International Date Line">International Date Line</a></li> <li><a href="/wiki/IERS_Reference_Meridian" title="IERS Reference Meridian">IERS Reference Meridian</a></li> <li><a href="/wiki/Leap_second" title="Leap second">Leap second</a></li> <li><a href="/wiki/Solar_time" title="Solar time">Solar time</a></li> <li><a href="/wiki/Terrestrial_Time" title="Terrestrial Time">Terrestrial Time</a></li> <li><a href="/wiki/Time_zone" title="Time zone">Time zone</a></li> <li><a href="/wiki/180th_meridian" title="180th meridian">180th meridian</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="9" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/Hourglass" title="Hourglass"><img alt="template illustration" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Marine_sandglass_MMM.jpg/75px-Marine_sandglass_MMM.jpg" decoding="async" width="75" height="175" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Marine_sandglass_MMM.jpg/113px-Marine_sandglass_MMM.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Marine_sandglass_MMM.jpg/150px-Marine_sandglass_MMM.jpg 2x" data-file-width="1637" data-file-height="3819" /></a></span><br /><span typeof="mw:File"><a href="/wiki/Time_zone" title="Time zone"><img alt="template illustration" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png/75px-Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png" decoding="async" width="75" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/63/Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png/113px-Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/63/Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png/150px-Aleutian_Islands_with_180th_meridian_and_International_Date_Line_%28cropped%29.png 2x" data-file-width="496" data-file-height="1007" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Obsolete standards</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ephemeris_time" title="Ephemeris time">Ephemeris time</a></li> <li><a href="/wiki/Greenwich_Mean_Time" title="Greenwich Mean Time">Greenwich Mean Time</a></li> <li><a href="/wiki/Prime_meridian" title="Prime meridian">Prime meridian</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Time_in_physics" title="Time in physics">Time in physics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Absolute_space_and_time" title="Absolute space and time">Absolute space and time</a></li> <li><a href="/wiki/Spacetime" title="Spacetime">Spacetime</a></li> <li><a href="/wiki/Chronon" title="Chronon">Chronon</a></li> <li><a href="/wiki/Continuous_signal" class="mw-redirect" title="Continuous signal">Continuous signal</a></li> <li><a href="/wiki/Coordinate_time" title="Coordinate time">Coordinate time</a></li> <li><a href="/wiki/Cosmological_decade" class="mw-redirect" title="Cosmological decade">Cosmological decade</a></li> <li><a href="/wiki/Discrete_time_and_continuous_time" title="Discrete time and continuous time">Discrete time and continuous time</a></li> <li><a href="/wiki/Proper_time" title="Proper time">Proper time</a></li> <li><a href="/wiki/Theory_of_relativity" title="Theory of relativity">Theory of relativity</a></li> <li><a href="/wiki/Time_dilation" title="Time dilation">Time dilation</a></li> <li><a href="/wiki/Gravitational_time_dilation" title="Gravitational time dilation">Gravitational time dilation</a></li> <li><a href="/wiki/Time_domain" title="Time domain">Time domain</a></li> <li><a href="/wiki/Time-translation_symmetry" title="Time-translation symmetry">Time-translation symmetry</a></li> <li><a href="/wiki/T-symmetry" title="T-symmetry">T-symmetry</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Horology" class="mw-redirect" title="Horology">Horology</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Clock" title="Clock">Clock</a></li> <li><a href="/wiki/Astrarium" title="Astrarium">Astrarium</a></li> <li><a href="/wiki/Atomic_clock" title="Atomic clock">Atomic clock</a></li> <li><a href="/wiki/Complication_(horology)" title="Complication (horology)">Complication</a></li> <li><a href="/wiki/History_of_timekeeping_devices" title="History of timekeeping devices">History of timekeeping devices</a></li> <li><a href="/wiki/Hourglass" title="Hourglass">Hourglass</a></li> <li><a href="/wiki/Marine_chronometer" title="Marine chronometer">Marine chronometer</a></li> <li><a href="/wiki/Marine_sandglass" title="Marine sandglass">Marine sandglass</a></li> <li><a href="/wiki/Radio_clock" title="Radio clock">Radio clock</a></li> <li><a href="/wiki/Watch" title="Watch">Watch</a> <ul><li><a href="/wiki/Stopwatch" title="Stopwatch">stopwatch</a></li></ul></li> <li><a href="/wiki/Water_clock" title="Water clock">Water clock</a></li> <li><a href="/wiki/Sundial" title="Sundial">Sundial</a></li> <li><a href="/wiki/Dialing_scales" title="Dialing scales">Dialing scales</a></li> <li><a href="/wiki/Equation_of_time" title="Equation of time">Equation of time</a></li> <li><a href="/wiki/History_of_sundials" title="History of sundials">History of sundials</a></li> <li><a class="mw-selflink selflink">Sundial markup schema</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Calendar" title="Calendar">Calendar</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Gregorian_calendar" title="Gregorian calendar">Gregorian</a></li> <li><a href="/wiki/Hebrew_calendar" title="Hebrew calendar">Hebrew</a></li> <li><a href="/wiki/Hindu_calendar" title="Hindu calendar">Hindu</a></li> <li><a href="/wiki/Holocene_calendar" title="Holocene calendar">Holocene</a></li> <li><a href="/wiki/Islamic_calendar" title="Islamic calendar">Islamic</a> (lunar Hijri)</li> <li><a href="/wiki/Julian_calendar" title="Julian calendar">Julian</a></li> <li><a href="/wiki/Solar_Hijri_calendar" title="Solar Hijri calendar">Solar Hijri</a></li> <li><a href="/wiki/Astronomical_year_numbering" title="Astronomical year numbering">Astronomical</a></li> <li><a href="/wiki/Dominical_letter" title="Dominical letter">Dominical letter</a></li> <li><a href="/wiki/Epact" title="Epact">Epact</a></li> <li><a href="/wiki/Equinox" title="Equinox">Equinox</a></li> <li><a href="/wiki/Intercalation_(timekeeping)" title="Intercalation (timekeeping)">Intercalation</a></li> <li><a href="/wiki/Julian_day" title="Julian day">Julian day</a></li> <li><a href="/wiki/Leap_year" title="Leap year">Leap year</a></li> <li><a href="/wiki/Lunar_calendar" title="Lunar calendar">Lunar</a></li> <li><a href="/wiki/Lunisolar_calendar" title="Lunisolar calendar">Lunisolar</a></li> <li><a href="/wiki/Solar_calendar" title="Solar calendar">Solar</a></li> <li><a href="/wiki/Solstice" title="Solstice">Solstice</a></li> <li><a href="/wiki/Tropical_year" title="Tropical year">Tropical year</a></li> <li><a href="/wiki/Determination_of_the_day_of_the_week" title="Determination of the day of the week">Weekday determination</a></li> <li><a href="/wiki/Names_of_the_days_of_the_week" title="Names of the days of the week">Weekday names</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Archaeology and geology</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chronological_dating" title="Chronological dating">Chronological dating</a></li> <li><a href="/wiki/Geologic_time_scale" title="Geologic time scale">Geologic time scale</a></li> <li><a href="/wiki/International_Commission_on_Stratigraphy" title="International Commission on Stratigraphy">International Commission on Stratigraphy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Astronomical_chronology" title="Astronomical chronology">Astronomical chronology</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Galactic_year" title="Galactic year">Galactic year</a></li> <li><a href="/wiki/Nuclear_timescale" title="Nuclear timescale">Nuclear timescale</a></li> <li><a href="/wiki/Precession" title="Precession">Precession</a></li> <li><a href="/wiki/Sidereal_time" title="Sidereal time">Sidereal time</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other <a href="/wiki/Unit_of_time" title="Unit of time">units of time</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Instant" title="Instant">Instant</a></li> <li><a href="/wiki/Flick_(time)" title="Flick (time)">Flick</a></li> <li><a href="/wiki/Shake_(unit)" title="Shake (unit)">Shake</a></li> <li><a href="/wiki/Jiffy_(time)" title="Jiffy (time)">Jiffy</a></li> <li><a href="/wiki/Second" title="Second">Second</a></li> <li><a href="/wiki/Minute" title="Minute">Minute</a></li> <li><a href="/wiki/Moment_(unit)" title="Moment (unit)">Moment</a></li> <li><a href="/wiki/Hour" title="Hour">Hour</a></li> <li><a href="/wiki/Day" title="Day">Day</a></li> <li><a href="/wiki/Week" title="Week">Week</a></li> <li><a href="/wiki/Fortnight" title="Fortnight">Fortnight</a></li> <li><a href="/wiki/Month" title="Month">Month</a></li> <li><a href="/wiki/Year" title="Year">Year</a></li> <li><a href="/wiki/Olympiad" title="Olympiad">Olympiad</a></li> <li><a href="/wiki/Lustrum" title="Lustrum">Lustrum</a></li> <li><a href="/wiki/Decade" title="Decade">Decade</a></li> <li><a href="/wiki/Century" title="Century">Century</a></li> <li><a href="/wiki/Saeculum" title="Saeculum">Saeculum</a></li> <li><a href="/wiki/Millennium" title="Millennium">Millennium</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chronology" title="Chronology">Chronology</a></li> <li><a href="/wiki/Duration_(philosophy)" title="Duration (philosophy)">Duration</a> <ul><li><a href="/wiki/Duration_(music)" title="Duration (music)">music</a></li></ul></li> <li><a href="/wiki/Mental_chronometry" title="Mental chronometry">Mental chronometry</a></li> <li><a href="/wiki/Decimal_time" title="Decimal time">Decimal time</a></li> <li><a href="/wiki/Metric_time" title="Metric time">Metric time</a></li> <li><a href="/wiki/System_time" title="System time">System time</a></li> <li><a href="/wiki/Time_metrology" class="mw-redirect" title="Time metrology">Time metrology</a></li> <li><a href="/wiki/Time_value_of_money" title="Time value of money">Time value of money</a></li> <li><a href="/wiki/Timekeeper" title="Timekeeper">Timekeeper</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Astronomy_in_the_medieval_Islamic_world43" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Astronomy_in_medieval_Islam" title="Template:Astronomy in medieval Islam"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Astronomy_in_medieval_Islam" title="Template talk:Astronomy in medieval Islam"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Astronomy_in_medieval_Islam" title="Special:EditPage/Template:Astronomy in medieval Islam"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Astronomy_in_the_medieval_Islamic_world43" style="font-size:114%;margin:0 4em"><a href="/wiki/Astronomy_in_the_medieval_Islamic_world" title="Astronomy in the medieval Islamic world">Astronomy in the medieval Islamic world</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible uncollapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Astronomers43" style="font-size:114%;margin:0 4em"><a href="/wiki/List_of_Muslim_astronomers" class="mw-redirect" title="List of Muslim astronomers">Astronomers</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td class="navbox-abovebelow" colspan="2"><div id="*_by_century51"> <ul><li>by century</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">8th</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ahmad_Nahavandi" title="Ahmad Nahavandi">Ahmad Nahavandi</a></li> <li><a href="/wiki/Al-Fadl_ibn_Naubakht" title="Al-Fadl ibn Naubakht">Al-Fadl ibn Naubakht</a></li> <li><a href="/wiki/Mu%E1%B8%A5ammad_ibn_Ibr%C4%81h%C4%ABm_al-Faz%C4%81r%C4%AB" title="Muḥammad ibn Ibrāhīm al-Fazārī">Muḥammad ibn Ibrāhīm al-Fazārī</a></li> <li><a href="/wiki/Ibr%C4%81h%C4%ABm_al-Faz%C4%81r%C4%AB" class="mw-redirect" title="Ibrāhīm al-Fazārī">Ibrāhīm al-Fazārī</a></li> <li><a href="/wiki/Mashallah_ibn_Athari" title="Mashallah ibn Athari">Mashallah ibn Athari</a></li> <li><a href="/wiki/Ya%CA%BFq%C5%ABb_ibn_%E1%B9%AC%C4%81riq" class="mw-redirect" title="Yaʿqūb ibn Ṭāriq">Yaʿqūb ibn Ṭāriq</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">9th</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abu_Ali_al-Khayyat" title="Abu Ali al-Khayyat">Abu Ali al-Khayyat</a></li> <li><a href="/wiki/Abu_Ma%27shar_al-Balkhi" title="Abu Ma'shar al-Balkhi">Abu Ma'shar al-Balkhi</a></li> <li><a href="/wiki/Abu_Said_Gorgani" title="Abu Said Gorgani">Abu Said Gorgani</a></li> <li><a href="/wiki/Al-Farghani" title="Al-Farghani">Al-Farghani</a></li> <li><a href="/wiki/Al-Kindi" title="Al-Kindi">Al-Kindi</a></li> <li><a href="/wiki/Al-Mahani" title="Al-Mahani">Al-Mahani</a></li> <li><a href="/wiki/Abu_Hanifa_Dinawari" title="Abu Hanifa Dinawari">Abu Hanifa Dinawari</a></li> <li><a href="/wiki/Al-%E1%B8%A4ajj%C4%81j_ibn_Y%C5%ABsuf_ibn_Ma%E1%B9%ADar" title="Al-Ḥajjāj ibn Yūsuf ibn Maṭar">Al-Ḥajjāj ibn Yūsuf</a></li> <li><a href="/wiki/Habash_al-Hasib_al-Marwazi" class="mw-redirect" title="Habash al-Hasib al-Marwazi">Al-Marwazi</a></li> <li><a href="/wiki/Ali_ibn_Isa_al-Asturlabi" title="Ali ibn Isa al-Asturlabi">Ali ibn Isa al-Asturlabi</a></li> <li><a href="/wiki/Ban%C5%AB_M%C5%ABs%C4%81_brothers" title="Banū Mūsā brothers">Banū Mūsā brothers</a></li> <li><a href="/wiki/Abu_al-Abbas_Iranshahri" title="Abu al-Abbas Iranshahri">Iranshahri</a></li> <li><a href="/wiki/Khalid_ibn_Abd_al%E2%80%90Malik_al%E2%80%90Marwarrudhi" class="mw-redirect" title="Khalid ibn Abd al‐Malik al‐Marwarrudhi">Khalid ibn Abd al‐Malik al‐Marwarrudhi</a></li> <li><a href="/wiki/Al-Khwarizmi" title="Al-Khwarizmi">Al-Khwarizmi</a></li> <li><a href="/wiki/Sahl_ibn_Bishr" title="Sahl ibn Bishr">Sahl ibn Bishr</a></li> <li><a href="/wiki/Th%C4%81bit_ibn_Qurra" title="Thābit ibn Qurra">Thābit ibn Qurra</a></li> <li><a href="/wiki/Yahya_ibn_Abi_Mansur" title="Yahya ibn Abi Mansur">Yahya ibn Abi Mansur</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">10th</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abd_al-Rahman_al-Sufi" title="Abd al-Rahman al-Sufi">al-Sufi</a></li> <li><a href="/wiki/Ibn_al-Adami" title="Ibn al-Adami">Ibn</a></li> <li><a href="/wiki/Al-Adami" title="Al-Adami">Al-Adami</a></li> <li><a href="/wiki/Abu-Mahmud_Khojandi" class="mw-redirect" title="Abu-Mahmud Khojandi">al-Khojandi</a></li> <li><a href="/wiki/Abu_Ja%27far_al-Khazin" title="Abu Ja'far al-Khazin">al-Khazin</a></li> <li><a href="/wiki/Abu_Sahl_al-Quhi" title="Abu Sahl al-Quhi">al-Qūhī</a></li> <li><a href="/wiki/Abu_al-Wafa%27_Buzjani" class="mw-redirect" title="Abu al-Wafa' Buzjani">Abu al-Wafa</a></li> <li><a href="/wiki/Ahmad_ibn_Yusuf" title="Ahmad ibn Yusuf">Ahmad ibn Yusuf</a></li> <li><a href="/wiki/Al-Battani" title="Al-Battani">al-Battani</a></li> <li><a href="/wiki/Al-Qabisi" title="Al-Qabisi">Al-Qabisi</a></li> <li><a href="/wiki/Ibn_al-A%27lam" title="Ibn al-A'lam">Ibn al-A'lam</a></li> <li><a href="/wiki/Al-Nayrizi" title="Al-Nayrizi">Al-Nayrizi</a></li> <li><a href="/wiki/Al-Saghani" class="mw-redirect" title="Al-Saghani">Al-Saghani</a></li> <li><a href="/wiki/A%E1%B9%A3-%E1%B9%A2aidan%C4%81n%C4%AB" title="Aṣ-Ṣaidanānī">Aṣ-Ṣaidanānī</a></li> <li><a href="/wiki/Ibn_Yunus" title="Ibn Yunus">Ibn Yunus</a></li> <li><a href="/wiki/Ibrahim_ibn_Sinan" title="Ibrahim ibn Sinan">Ibrahim ibn Sinan</a></li> <li><a href="/wiki/Ma_Yize" title="Ma Yize">Ma Yize</a></li> <li><a href="/wiki/Al-Sijzi" title="Al-Sijzi">al-Sijzi</a></li> <li><a href="/wiki/Al-%CA%BBIjliyyah" title="Al-ʻIjliyyah">Al-ʻIjliyyah</a></li> <li><a href="/wiki/Nastulus" title="Nastulus">Nastulus</a></li> <li><a href="/wiki/Abolfadl_Harawi" title="Abolfadl Harawi">Abolfadl Harawi</a></li> <li><a href="/wiki/Haseb-i_Tabari" title="Haseb-i Tabari">Haseb-i Tabari</a></li> <li><a href="/wiki/Maslama_al-Majriti" title="Maslama al-Majriti">al-Majriti</a></li> <li><a href="/wiki/Abu_al-Hasan_al-Ahwazi" title="Abu al-Hasan al-Ahwazi">Abu al-Hasan al-Ahwazi</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">11th</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Abu_Nasr_Mansur" title="Abu Nasr Mansur">Abu Nasr Mansur</a></li> <li><a href="/wiki/Al-Biruni" title="Al-Biruni">al-Biruni</a></li> <li><a href="/wiki/Ali_ibn_Ridwan" title="Ali ibn Ridwan">Ali ibn Ridwan</a></li> <li><a href="/wiki/Ab%C5%AB_Is%E1%B8%A5%C4%81q_Ibr%C4%81h%C4%ABm_al-Zarq%C4%81l%C4%AB" class="mw-redirect" title="Abū Isḥāq Ibrāhīm al-Zarqālī">Al-Zarqālī</a></li> <li><a href="/wiki/Ibn_al-Samh" title="Ibn al-Samh">Ibn al-Samh</a></li> <li><a href="/wiki/Ibn_al-Haytham" title="Ibn al-Haytham">Alhazen</a></li> <li><a href="/wiki/Avicenna" title="Avicenna">Avicenna</a></li> <li><a href="/wiki/Ibn_al-Saffar" class="mw-redirect" title="Ibn al-Saffar">Ibn al-Saffar</a></li> <li><a href="/wiki/Kushyar_Gilani" title="Kushyar Gilani">Kushyar Gilani</a></li> <li><a href="/wiki/Said_al-Andalusi" title="Said al-Andalusi">Said al-Andalusi</a></li> <li><a href="/wiki/Ibrahim_ibn_Said_al-Sahli" title="Ibrahim ibn Said al-Sahli">Ibrahim ibn Said al-Sahli</a></li> <li><a href="/wiki/Ibn_Mu%27adh_al-Jayyani" title="Ibn Mu'adh al-Jayyani">Ibn Mu'adh al-Jayyani </a></li> <li><a href="/wiki/Al-Isfizari" title="Al-Isfizari">Al-Isfizari</a></li> <li><a href="/wiki/Ali_ibn_Khalaf" title="Ali ibn Khalaf">Ali ibn Khalaf</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">12th</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nur_ad-Din_al-Bitruji" title="Nur ad-Din al-Bitruji">Al-Bitruji</a></li> <li><a href="/wiki/Avempace" title="Avempace">Avempace</a></li> <li><a href="/wiki/Ibn_Tufail" class="mw-redirect" title="Ibn Tufail">Ibn Tufail</a></li> <li><a href="/wiki/Al-Kharaq%C4%AB" title="Al-Kharaqī">Al-Kharaqī</a></li> <li><a href="/wiki/Al-Khazini" title="Al-Khazini">Al-Khazini</a></li> <li><a href="/wiki/Al-Samawal_al-Maghribi" title="Al-Samawal al-Maghribi">Al-Samawal al-Maghribi</a></li> <li><a href="/wiki/Abu_al-Salt" class="mw-redirect" title="Abu al-Salt">Abu al-Salt</a></li> <li><a href="/wiki/Averroes" title="Averroes">Averroes</a></li> <li><a href="/wiki/Ibn_al-Kammad" title="Ibn al-Kammad">Ibn al-Kammad</a></li> <li><a href="/wiki/Jabir_ibn_Aflah" title="Jabir ibn Aflah">Jabir ibn Aflah</a></li> <li><a href="/wiki/Omar_Khayyam" title="Omar Khayyam">Omar Khayyam</a></li> <li><a href="/wiki/Sharaf_al-Din_al-Tusi" title="Sharaf al-Din al-Tusi">Sharaf al-Din al-Tusi</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">13th</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ibn_al-Banna%27_al-Marrakushi" title="Ibn al-Banna' al-Marrakushi">Ibn al-Banna' al-Marrakushi</a></li> <li><a href="/wiki/Ibn_al%E2%80%90Ha%27im_al%E2%80%90Ishbili" class="mw-redirect" title="Ibn al‐Ha'im al‐Ishbili">Ibn al‐Ha'im al‐Ishbili</a></li> <li><a href="/wiki/Jamal_ad-Din_Bukhari" title="Jamal ad-Din Bukhari">Jamal ad-Din</a></li> <li><a href="/wiki/Alam_al-Din_al-Hanafi" title="Alam al-Din al-Hanafi">Alam al-Din al-Hanafi</a></li> <li><a href="/wiki/Najm_al%E2%80%90Din_al%E2%80%90Misri" class="mw-redirect" title="Najm al‐Din al‐Misri">Najm al‐Din al‐Misri</a></li> <li><a href="/wiki/Muhyi_al-Din_al-Maghribi" title="Muhyi al-Din al-Maghribi">Muhyi al-Din al-Maghribi</a></li> <li><a href="/wiki/Nasir_al-Din_al-Tusi" title="Nasir al-Din al-Tusi">Nasir al-Din al-Tusi</a></li> <li><a href="/wiki/Qutb_al-Din_al-Shirazi" title="Qutb al-Din al-Shirazi">Qutb al-Din al-Shirazi</a></li> <li><a href="/wiki/Shams_al-Din_al-Samarqandi" title="Shams al-Din al-Samarqandi">Shams al-Din al-Samarqandi</a></li> <li><a href="/wiki/Zakariya_al-Qazwini" title="Zakariya al-Qazwini">Zakariya al-Qazwini</a></li> <li><a href="/wiki/Mu%27ayyad_al-Din_al-Urdi" title="Mu'ayyad al-Din al-Urdi">al-Urdi</a></li> <li><a href="/wiki/Athir_al-Din_al-Abhari" title="Athir al-Din al-Abhari">al-Abhari</a></li> <li><a href="/wiki/Muhammad_ibn_Abi_Bakr_al%E2%80%90Farisi" class="mw-redirect" title="Muhammad ibn Abi Bakr al‐Farisi">Muhammad ibn Abi Bakr al‐Farisi</a></li> <li><a href="/wiki/Abu_Ali_al-Hasan_al-Marrakushi" title="Abu Ali al-Hasan al-Marrakushi">Abu Ali al-Hasan al-Marrakushi</a></li> <li><a href="/wiki/Ibn_Ishaq_al-Tunisi" title="Ibn Ishaq al-Tunisi">Ibn Ishaq al-Tunisi</a></li> <li><a href="/wiki/Ibn_al%E2%80%90Raqqam" class="mw-redirect" title="Ibn al‐Raqqam">Ibn al‐Raqqam</a></li> <li><a href="/wiki/Al-Ashraf_Umar_II" title="Al-Ashraf Umar II">Al-Ashraf Umar II</a></li> <li><a href="/wiki/Fakhr_al-Din_al-Akhlati" title="Fakhr al-Din al-Akhlati">Fakhr al-Din al-Akhlati</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">14th</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ibn_al-Shatir" title="Ibn al-Shatir">Ibn al-Shatir</a></li> <li><a href="/wiki/Shams_al-Din_Abu_Abd_Allah_al-Khalili" title="Shams al-Din Abu Abd Allah al-Khalili">Al-Khalili</a></li> <li><a href="/wiki/Ibn_Shuayb" title="Ibn Shuayb">Ibn Shuayb</a></li> <li><a href="/wiki/Abu_Muqri_Mohammed_al-Battiwi" title="Abu Muqri Mohammed al-Battiwi"> al-Battiwi</a></li> <li><a href="/wiki/Ab%C5%AB_al%E2%80%90%CA%BFUq%C5%ABl" class="mw-redirect" title="Abū al‐ʿUqūl">Abū al‐ʿUqūl</a></li> <li><a href="/wiki/Al-Wabkanawi" title="Al-Wabkanawi">Al-Wabkanawi</a></li> <li><a href="/wiki/Nizam_al-Din_al-Nisapuri" class="mw-redirect" title="Nizam al-Din al-Nisapuri">Nizam al-Din al-Nisapuri</a></li> <li><a href="/wiki/Abd_al-Rahman_al-Jadiri" title="Abd al-Rahman al-Jadiri"> al-Jadiri</a></li> <li><a href="/wiki/Sadr_al-Shari%27a_al-Asghar" title="Sadr al-Shari'a al-Asghar">Sadr al-Shari'a al-Asghar</a></li> <li><a href="/wiki/Fathullah_Shirazi" title="Fathullah Shirazi">Fathullah Shirazi</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">15th</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ali_Qushji" title="Ali Qushji">Ali Kuşçu</a></li> <li><a href="/wiki/Abd_al%E2%80%90Wajid" class="mw-redirect" title="Abd al‐Wajid">Abd al‐Wajid</a></li> <li><a href="/wiki/Jamshid_al-Kashi" title="Jamshid al-Kashi">Jamshid al-Kashi</a></li> <li><a href="/wiki/Q%C4%81%E1%B8%8D%C4%AB_Z%C4%81da_al-R%C5%ABm%C4%AB" title="Qāḍī Zāda al-Rūmī">Kadızade Rumi</a></li> <li><a href="/wiki/Ulugh_Beg" title="Ulugh Beg">Ulugh Beg</a></li> <li><a href="/wiki/Sibt_al-Maridini" title="Sibt al-Maridini">Sibt al-Maridini</a></li> <li><a href="/wiki/Ibn_al-Majdi" title="Ibn al-Majdi">Ibn al-Majdi</a></li> <li><a href="/wiki/%27Abd_al-%27Aziz_al-Wafa%27i" title="'Abd al-'Aziz al-Wafa'i">al-Wafa'i</a></li> <li><a href="/wiki/Abu_Ishaq_al-Kubunani" title="Abu Ishaq al-Kubunani">al-Kubunani</a></li> <li><a href="/wiki/%27Abd_al-%27Aziz_al-Wafa%27i" title="'Abd al-'Aziz al-Wafa'i">'Abd al-'Aziz al-Wafa'i</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">16th</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Al-Birjandi" title="Al-Birjandi">Al-Birjandi</a></li> <li><a href="/wiki/Shams_al-Din_al-Khafri" title="Shams al-Din al-Khafri">al-Khafri</a></li> <li><a href="/wiki/Baha%27_al-din_al-%27Amili" class="mw-redirect" title="Baha' al-din al-'Amili">Baha' al-din al-'Amili </a></li> <li><a href="/wiki/Piri_Reis" title="Piri Reis">Piri Reis</a></li> <li><a href="/wiki/Taqi_ad-Din_Muhammad_ibn_Ma%27ruf" title="Taqi ad-Din Muhammad ibn Ma'ruf">Takiyüddin</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">17th</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Yang_Guangxian" title="Yang Guangxian">Yang Guangxian</a></li> <li><a href="/wiki/Ehmed%C3%AA_Xan%C3%AE" title="Ehmedê Xanî">Ehmedê Xanî</a></li> <li><a href="/wiki/Al_Achsasi_al_Mouakket" title="Al Achsasi al Mouakket">Al Achsasi al Mouakket</a></li> <li><a href="/wiki/Muhammad_al-Rudani" title="Muhammad al-Rudani">Muhammad al-Rudani</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks mw-collapsible uncollapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Topics43" style="font-size:114%;margin:0 4em">Topics</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Works112" scope="row" class="navbox-group" style="width:1%">Works</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_Arabic_star_names" title="List of Arabic star names">Arabic star names</a></li> <li><a href="/wiki/Islamic_calendar" title="Islamic calendar">Islamic calendar</a></li> <li><i><a href="/wiki/Aja%27ib_al-Makhluqat" title="Aja'ib al-Makhluqat">Aja'ib al-Makhluqat</a></i></li> <li><i><a href="/wiki/Encyclopedia_of_the_Brethren_of_Purity" title="Encyclopedia of the Brethren of Purity">Encyclopedia of the Brethren of Purity</a></i></li> <li><i><a href="/wiki/Tabula_Rogeriana" title="Tabula Rogeriana">Tabula Rogeriana</a></i></li> <li><i><a href="/wiki/The_Book_of_Healing" title="The Book of Healing">The Book of Healing</a></i></li> <li><i><a href="/wiki/The_Remaining_Signs_of_Past_Centuries" title="The Remaining Signs of Past Centuries">The Remaining Signs of Past Centuries</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><i><a href="/wiki/Zij" title="Zij">Zij</a></i></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alfonsine_tables" title="Alfonsine tables">Alfonsine tables</a></li> <li><i><a href="/wiki/Huihui_Lifa" title="Huihui Lifa">Huihui Lifa</a></i></li> <li><i><a href="/wiki/Book_of_Fixed_Stars" class="mw-redirect" title="Book of Fixed Stars">Book of Fixed Stars</a></i></li> <li><a href="/wiki/Toledan_Tables" title="Toledan Tables">Toledan Tables</a></li> <li><i><a href="/wiki/Zij-i_Ilkhani" title="Zij-i Ilkhani">Zij-i Ilkhani</a></i></li> <li><i><a href="/wiki/Zij-i_Sultani" title="Zij-i Sultani">Zij-i Sultani</a></i></li> <li><i><a href="/wiki/Sullam_al-sama%27" title="Sullam al-sama'">Sullam al-sama'</a></i></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Astronomy_in_the_medieval_Islamic_world#Instruments" title="Astronomy in the medieval Islamic world">Instruments</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alidade" title="Alidade">Alidade</a></li> <li><a href="/wiki/Analog_computer" title="Analog computer">Analog computer</a></li> <li><a href="/wiki/Aperture" title="Aperture">Aperture</a></li> <li><a href="/wiki/Armillary_sphere" title="Armillary sphere">Armillary sphere</a></li> <li><a href="/wiki/Astrolabe" title="Astrolabe">Astrolabe</a></li> <li><a href="/wiki/Astronomical_clock" title="Astronomical clock">Astronomical clock</a></li> <li><a href="/wiki/Armillary_sphere" title="Armillary sphere">Celestial globe</a></li> <li><a href="/wiki/Compass" title="Compass">Compass</a></li> <li><a href="/wiki/Compass_rose" title="Compass rose">Compass rose</a></li> <li><a href="/wiki/Dioptra" title="Dioptra">Dioptra</a></li> <li><a href="/wiki/Equatorial_ring" title="Equatorial ring">Equatorial ring</a></li> <li><a href="/wiki/Equatorium" title="Equatorium">Equatorium</a></li> <li><a href="/wiki/Globe" title="Globe">Globe</a></li> <li><a href="/wiki/Graph_paper" title="Graph paper">Graph paper</a></li> <li><a href="/wiki/Mural_instrument" title="Mural instrument">Mural instrument</a></li> <li><a href="/wiki/Mariner%27s_astrolabe" title="Mariner's astrolabe">Navigational astrolabe</a></li> <li><a href="/wiki/Octant_(instrument)" title="Octant (instrument)">Octant</a></li> <li><a href="/wiki/Planisphere" title="Planisphere">Planisphere</a></li> <li><a href="/wiki/Quadrant_(instrument)" title="Quadrant (instrument)">Quadrant</a></li> <li><a href="/wiki/Sextant_(astronomy)" title="Sextant (astronomy)">Sextant</a></li> <li><a href="/wiki/Shadow_square" title="Shadow square">Shadow square</a></li> <li><a href="/wiki/Sundial" title="Sundial">Sundial</a></li> <li><a class="mw-selflink selflink">Schema for horizontal sundials</a></li> <li><a href="/wiki/Triquetrum_(astronomy)" title="Triquetrum (astronomy)">Triquetrum</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Almucantar" title="Almucantar">Almucantar</a></li> <li><a href="/wiki/Apsis" title="Apsis">Apogee</a></li> <li><a href="/wiki/Astrology_in_the_medieval_Islamic_world" title="Astrology in the medieval Islamic world">Astrology</a></li> <li><a href="/wiki/Astrophysics" title="Astrophysics">Astrophysics</a></li> <li><a href="/wiki/Axial_tilt" title="Axial tilt">Axial tilt</a></li> <li><a href="/wiki/Azimuth" title="Azimuth">Azimuth</a></li> <li><a href="/wiki/Celestial_mechanics" title="Celestial mechanics">Celestial mechanics</a></li> <li><a href="/wiki/Celestial_spheres" title="Celestial spheres">Celestial spheres</a></li> <li><a href="/wiki/Circular_orbit" title="Circular orbit">Circular orbit</a></li> <li><a href="/wiki/Deferent_and_epicycle" title="Deferent and epicycle">Deferent and epicycle</a></li> <li><a href="/wiki/Earth%27s_rotation" title="Earth's rotation">Earth's rotation</a></li> <li><a href="/wiki/Orbital_eccentricity" title="Orbital eccentricity">Eccentricity</a></li> <li><a href="/wiki/Ecliptic" title="Ecliptic">Ecliptic</a></li> <li><a href="/wiki/Elliptic_orbit" title="Elliptic orbit">Elliptic orbit</a></li> <li><a href="/wiki/Equant" title="Equant">Equant</a></li> <li><a href="/wiki/Galaxy" title="Galaxy">Galaxy</a></li> <li><a href="/wiki/Geocentric_model" title="Geocentric model">Geocentrism</a></li> <li><a href="/wiki/Gravitational_energy" title="Gravitational energy">Gravitational energy</a></li> <li><a href="/wiki/Gravity" title="Gravity">Gravity</a></li> <li><a href="/wiki/Heliocentrism" title="Heliocentrism">Heliocentrism</a></li> <li><a href="/wiki/Inertia" title="Inertia">Inertia</a></li> <li><a href="/wiki/Cosmology_in_medieval_Islam" class="mw-redirect" title="Cosmology in medieval Islam">Islamic cosmology</a></li> <li><a href="/wiki/Moonlight" title="Moonlight">Moonlight</a></li> <li><a href="/wiki/Multiverse" title="Multiverse">Multiverse</a></li> <li><a href="/wiki/Muwaqqit" title="Muwaqqit">Muwaqqit</a></li> <li><a href="/wiki/Axial_tilt" title="Axial tilt">Obliquity</a></li> <li><a href="/wiki/Parallax" title="Parallax">Parallax</a></li> <li><a href="/wiki/Precession" title="Precession">Precession</a></li> <li><a href="/wiki/Qibla" title="Qibla">Qibla</a></li> <li><a href="/wiki/Salah_times" title="Salah times">Salah times</a></li> <li><a href="/wiki/Specific_gravity" class="mw-redirect" title="Specific gravity">Specific gravity</a></li> <li><a href="/wiki/Spherical_Earth" title="Spherical Earth">Spherical Earth</a></li> <li><a href="/wiki/Sublunary_sphere" title="Sublunary sphere">Sublunary sphere</a></li> <li><a href="/wiki/Sunlight" title="Sunlight">Sunlight</a></li> <li><a href="/wiki/Supernova" title="Supernova">Supernova</a></li> <li><a href="/wiki/Temporal_finitism" title="Temporal finitism">Temporal finitism</a></li> <li><a href="/wiki/Trepidation" title="Trepidation">Trepidation</a></li> <li><a href="/wiki/Triangulation" title="Triangulation">Triangulation</a></li> <li><a href="/wiki/Tusi_couple" title="Tusi couple">Tusi couple</a></li> <li><a href="/wiki/Universe" title="Universe">Universe</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Institutions</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Al-Azhar_University" title="Al-Azhar University">Al-Azhar University</a></li> <li><a href="/wiki/House_of_Knowledge" title="House of Knowledge">House of Knowledge</a></li> <li><a href="/wiki/House_of_Wisdom" title="House of Wisdom">House of Wisdom</a></li> <li><a href="/wiki/University_of_al-Qarawiyyin" title="University of al-Qarawiyyin">University of al-Qarawiyyin</a></li> <li><a href="/wiki/Astronomy_in_the_medieval_Islamic_world#Observatories" title="Astronomy in the medieval Islamic world">Observatories</a> <ul><li><span style="font-size:85%;"><a href="/wiki/Constantinople_observatory_of_Taqi_ad-Din" title="Constantinople observatory of Taqi ad-Din">Constantinople (Taqi al-Din)</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Maragheh_observatory" title="Maragheh observatory">Maragheh</a></span></li> <li><span style="font-size:85%;"><a href="/wiki/Ulugh_Beg_Observatory" title="Ulugh Beg Observatory">Samarkand (Ulugh Beg)</a></span></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Influences</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Babylonian_astronomy" title="Babylonian astronomy">Babylonian astronomy</a></li> <li><a href="/wiki/Egyptian_astronomy" title="Egyptian astronomy">Egyptian astronomy</a></li> <li><a href="/wiki/Ancient_Greek_astronomy#Hellenistic_astronomy" title="Ancient Greek astronomy">Hellenistic astronomy</a></li> <li><a href="/wiki/Indian_astronomy" title="Indian astronomy">Indian astronomy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Influenced</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Byzantine_science" title="Byzantine science">Byzantine science</a></li> <li><a href="/wiki/Chinese_astronomy" title="Chinese astronomy">Chinese astronomy</a></li> <li><a href="/wiki/European_science_in_the_Middle_Ages" title="European science in the Middle Ages">Medieval European science</a></li> <li><a href="/wiki/Indian_astronomy" title="Indian astronomy">Indian astronomy</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr></tbody></table></div> <p><br /> </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Schema_for_horizontal_dials&oldid=1248668715">https://en.wikipedia.org/w/index.php?title=Schema_for_horizontal_dials&oldid=1248668715</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div 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