### Popular passages

Page 66 - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Page 70 - 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 101 - In a spherical triangle the cosine of any side is equal to the product of the cosines of the other two sides plus the product of the sines of these two sides and the cosine of their included angle.
Page 67 - Hence the Law of Tangents : The difference of two sides of a triangle is to their sum as the tangent of half the difference of the opposite angles is to the tangent of half their sum.
Page 97 - The area of a spherical triangle is to the area of the surface of the sphere as the number which expresses its spherical excess is to 720.
Page 101 - sin В sin C' sin С sin A cos a = cos b cos с + sin 6 sin с cos A, with similar formulae for cos b and cos c. cos A = — cos В cos С + sin В sin С cos a, with similar formulae for cos В and cos C.
Page 13 - Cologarithms.* The cologarithm of a number is the logarithm of the reciprocal of the number.
Page 2 - The ratio of the side opposite the angle to the hypotenuse is merely one of six possible ratios which may be formed from the three sides of any right triangle.
Page 66 - The law of cosines states that in any triangle the square of any side equals the sum of the squares of the other two sides minus twice their product multiplied by the cosine of the angle between them.
Page 20 - Equation 3, we see that an angle of 1 rad is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle (see Figure 2).