### Popular passages

Page 50 - ... fourth, if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Page 106 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 94 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 51 - DEF, having two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, are themselves equal (Prop.
Page 96 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides...
Page 8 - Axis of a great circle of a sphere is that diameter of the sphere which is perpendicular to the plane of the circle.
Page 27 - Therefore, if two triangles have two sides and the included angle of one, equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Page 96 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 27 - If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. In the spherical triangle ABC, let the angle B equal the angle C. To prove that AC = AB. Proof. Let the A A'B'C