Geometry : the elements of Euclid and Legendre simplified and arranged to exclude from geomtrical reasoning the reductio ad absurdum : with the elements of plane and spherical trigonometry, and exercises in elementary geometry and trigonometry / /c By Lawrence S. Benson (1868)
Benson, Lawrence S. (Lawrence Sluter), Legendre, A. M. (Adrien Marie), 1752-1833 · New York : Pub. for the author by Davies & Kent · leaf 185
ngle ACD is the radius CD. Cor. 3. If AF bo half of AD, and consequently ACF half aright angle, the tangent AH is equal to the radius. For A be-ing a right angle, II must be half a right angle, and (I. 1, cor.2) AH equal to AC. Cor. 4. Put the angle = A, and the radius=:l. Then (I. 24,cor. 1)… … Cor. 5. In the similar triangles CGF, CAH, CG : CF, orCA : : CA : CH ; that is, the cosine of an angle is to the ra-dius as the radius to its secant. Hence also (V. 9, cor.) CG.CH=:CA^; that is, cosAsecA = l. It would be found in likemanner from the triangles GIF, CDK, that sin A cosecA=l,CI being…
Geometry · Trigonometry
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