The 1440 published method also used by Dürer in 1525, and because of its simplicity, by many others. It works well in Mediterranean latitude but in increasingly difficult further north.
<ul><li>Take a large sheet of paper (Three times wide as high for 52 N).</li>
<li>Starting at the bottom, draw a line across, and a vertical one up the centre. Where they cross is important call it O.</li>
<li>Choose the size of the dial, and draw a line across. Where it crosses the centre line is important call it F</li>
<li>You know your latitude. Draw a line upwards from O at this angle, this is a construction line.</li>
<li>Using a square, (drop a line) draw a line from F through the construction line so they cross at right angles. Call that point E, it is important. 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<!-- 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" 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 is copied upwards in the centre line from F. The new point is called G and yes it is important- the construction lines and FE can now be erased.</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 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5.  <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<!-- 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" 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.</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.</li>
<li>Clip the dial to fit your plate</li></ul>
Photograph by <a href="//commons.wikimedia.org/wiki/User:ClemRutter" title="User:ClemRutter">Clem Rutter, Rochester, Kent.</a> (<a rel="nofollow" class="external text" href="http://www.clemrutter.net/">www.clemrutter.net</a>).
CC BY-SA 3.0
<span class="int-own-work" lang="en">Own work</span>