File:Britannica(1771)-(4).svg

Summary

This method uses the properties of chords to establish distance Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>sin</mi><mo>⁡<!-- &#8289; --></mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>θ<!-- &theta; --></mi><mn>2</mn></mfrac></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \sin {\frac {\theta }{2}}}</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2606b670d56d534e573bb46276605e8b9427921" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -1.838ex; width:5.283ex; height:5.343ex;" alt="{\displaystyle \sin {\frac {\theta }{2}}}"> in the top quadrant, and then transfers this distance onto the latitude radius in the bottom quadrant so that Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>sin</mi><mo>⁡<!-- &#8289; --></mo><mi>ϕ<!-- &#981; --></mi><mi>sin</mi><mo>⁡<!-- &#8289; --></mo><mi>θ<!-- &theta; --></mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \sin \phi \sin \theta }</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc52db15772c3e9aa73b1e4bfc910628eaca710f" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:9.432ex; height:2.509ex;" alt="{\displaystyle \sin \phi \sin \theta }"> is established. Again, a transfer of this measure to the chords in the top quadrant. The final lines establish the formula Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>tan</mi><mo>⁡<!-- &#8289; --></mo><mi>κ<!-- &kappa; --></mi><mo>=</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \tan \kappa =}</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/667bd0bd06bbac45de749cd58ee570a67c7fa620" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:7.591ex; height:2.009ex;" alt="{\displaystyle \tan \kappa =}"> Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mfrac><mstyle displaystyle="true" scriptlevel="0"><mi>sin</mi><mo>⁡<!-- &#8289; --></mo><mi>θ<!-- &theta; --></mi><mi>sin</mi><mo>⁡<!-- &#8289; --></mo><mi>ϕ<!-- &#981; --></mi></mstyle><mrow><mi>cos</mi><mo>⁡<!-- &#8289; --></mo><mi>θ<!-- &theta; --></mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">{\displaystyle \sin \theta \sin \phi \over \cos \theta }</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b209c651ed4e55a257dc77946b0fcc67da4b0302" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -2.005ex; width:10.268ex; height:5.676ex;" alt="{\displaystyle \sin \theta \sin \phi \over \cos \theta }"> = Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>tan</mi><mo>⁡<!-- &#8289; --></mo><mi>θ<!-- &theta; --></mi><mi>sin</mi><mo>⁡<!-- &#8289; --></mo><mi>ϕ<!-- &#981; --></mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \tan \theta \sin \phi }</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90f9d67e28da1056f1c6870243e07c258110bc56" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:9.936ex; height:2.509ex;" alt="{\displaystyle \tan \theta \sin \phi }">

It was used in the <a href="https://en.wikipedia.org/wiki/Encyclopedia_Britannica#1768.E2.80.931826" class="extiw" title="w:Encyclopedia Britannica">Encyclopedia Britannica</a> First Edition 1771- Sixth Edition 1823

• 1: The Gnomon is drawn first against the North South line. In doing so, a diameter at φ degrees to the vertical is drawn- its reflection is needed.
• 2: 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 2 sin (Θ/2).
• 3: The measurement of each chord is transfered 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.
• 4: These measurements are transferred up to the chord.
• 5: The final hour lines are drawn from the origins through these crossing points.

Licensing

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