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 251
but AFis the sine of the arch AB, and AE the tangent oi the arch AC ; andthe angle AFE is the inclination of the planes CBD, ABD, (4. def. 2.Sup.), or is equal to the spherical angle ABC ; Therefore the sine ofthe arch AB is to the radius as the tangent of the arch AC to thetangent of the opposite… … PROP. XIX. In right angled spherical triangles the sine of the hy-potenuse is to the radius as the sine of either side is to thesine of the angle opposite to that side. Let the triangle ABC be right angled at A, and let AC be either ofthe sides; the sine of the hypotenuse BC will be to the radius…
Euclid's Elements · Geometry · Trigonometry
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