Elements of geometry : containing the first six books of Euclid, with a supplement on the quadrature of the circle, and the geometry of solids : to which are added, Elements of plane and spherical geometry (1826)
Playfair, John, 1748-1819, Euclid · Philadelphia : Marot & Walter · leaf 253
of the side adjacent tothat angle is to the tangent of the hypotenuse. The same construction remaining: In the triangle CEF, sin.FE :R :: tan. CE : tan. CFE (IS.); hut sin. EF=cos. ABC; tan. CE =cot. BC, and tan. CFE=cot.AB, therefore cos. ABC : R cot.BC :eot.AB. Now,hecause(Cor. 1. def. Q.Pl.Tr.)… … CoR. 1. From the demonstration it is manifest, that the tangfents ofany two arches AB, BC are reciprocally proportional to their cotan-gents. CoR. 2. Because cos. ABC : R :: tan. AB : tan. BC, and R : cot.BC : : tan. BC : R, by equality, cos. ABC : cot. BC : : tan. AB : R.That is, the cosine of any…
Euclid's Elements · Geometry · Trigonometry
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![An illustration from Nicolai Copernici Torinensis De reuolutionibus orbium coelestium, libri VI : Habes in hoc opere iam recens nato, & aedito, studiose lector, motus stellarum, tam fixarum, quàm erraticarum, cum ex ueteribus, tum etiam ex recentibus obseruationibus restitutos: & nouis insuper ac admirabilibus hypothesibus ornatos. Habes etiam tabulas expeditissimas, ex quibus eosdem ad quoduis tempus quàm facillime caculare poteris. Igitur eme, lege, fruere. [Line in Greek] (1543)](https://img.insideoutlibrary.com/img/200/ia-nicolaicopernici00cope-338-229.webp)
![An illustration from Nicolai Copernici Torinensis De reuolutionibus orbium coelestium, libri VI : Habes in hoc opere iam recens nato, & aedito, studiose lector, motus stellarum, tam fixarum, quàm erraticarum, cum ex ueteribus, tum etiam ex recentibus obseruationibus restitutos: & nouis insuper ac admirabilibus hypothesibus ornatos. Habes etiam tabulas expeditissimas, ex quibus eosdem ad quoduis tempus quàm facillime caculare poteris. Igitur eme, lege, fruere. [Line in Greek] (1543)](https://img.insideoutlibrary.com/img/200/ia-nicolaicopernici00cope-61-37.webp)
