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altitude angles or arcs base called celestial circle colog column complement comprised compute cos b cos cos b sin cosc cosec cosines cotangent decimal declination determine difference distance dividing ecliptic equal equations equinoctial EXAMPLES feet figures Find the angle find the logarithmic follows formed formulŠ four functions give Given greater horizon included increase inscribed latitude less limit logarithmic mantissa measured minutes multiplying Napier's natural Note obliquity obtain opposite passing perpendicular plane pole polygon positive problem quadrant quantities radii radius Relations Replacing respectively result right angle seconds sides sin B sin sin C cos sin(s sin(sb sin│ sinc sine sines and cosines sins solution Solve sphere spherical triangle star subtract sun's surface taken tanc tangent triangle ABC trigonometric values vertical бо
Page 34 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 58 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180░ and less than 540░. (gr). If A'B'C' is the polar triangle of ABC...
Page iv - The foregoing method is based on the assumption that the differences of logarithms are proportional to the differences of their corresponding numbers, which, though not strictly accurate, is sufficiently exact for practical purposes.
Page 51 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Page 100 - I. The logarithm of a product equals the sum of the logarithms of the factors.
Page 62 - Rules are . (1) The sine of the middle part equals the product of the tangents of the adjacent parts.
Page vii - In searching for the next less (or greater) logarithm, attention must be paid to the fact that the functions are found in different columns according as the angle is below or above 45░. If, for example, the next less logarithmic sine is found in the column with