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 257
i (BD-fAD) : tan.HBC+AC) :*. tan.| (BC-^AC): tan. i (BD -AIJ). CoR. 2. Since, when the perpendicular CD falls within the trian-gle, BD+AD = AB, the base; and when CD falls without the tri-angle BD —AD=AB, iherefore in the hrst case, the proportion inthe last corollary becomes tan, ^ (AB) : tan. 5… … SCHOLIUM. The preceding proposition, which is very useful in spherical triajo-rometry, may be easily remembered from its analogy to the proposi-tion in plane trigonometry, that the rectangle under half the sum»and half the difference of the sides of a plane triang^le, is equal tothe rectangle under…
Euclid's Elements · Geometry · Trigonometry
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