### Popular passages

Page 55 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 131 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. 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. By Theorem II. we have a : b : : sin. A : sin. B.
Page 268 - ... an indispensable instrument in the treatment of nearly every recondite question in modern physics. To mention only sonorous vibrations, the propagation of electric signals along a telegraph wire, and the conduction of heat by the earth's crust, as subjects in their generality intractable without it, is to give but a feeble idea of its importance.
Page 219 - B) = cos A cos B - sin A sin B. cos (A - B) = cos A cos B + sin A sin B.
Page 54 - The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 35 - 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 those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
Page 126 - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Page 49 - 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 59 - FRACTION is a negative number, and is one more than the number of ciphers between the decimal point and the first significant Jigure.
Page 18 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.