### Contents

 Development of sin x cos x and tanx 82 Equations containing multiple angles 88 Facts derived from geometry 97 Methods of solution 110 The polar triangle 123
 89 17 107 29 RR 91 Copyright

### Popular passages

Page 104 - 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 ii - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 98 - The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the sides and the cosine of the included angle.
Page 137 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 130 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides...
Page vi - ... preceded by a *). The first three figures of the required number will be found in the column headed N, in the same horizontal line with the last three figures of the mantissa, and the fourth figure of the number at the top of the column in which the last three figures of the mantissa are found. Thus (page 398), 0.06221 = log 1.154 ; 0.06558 = log 1.163 ' 0.06893 = log 1.172 ; 0.07004 = log 1.175 ; 0.07188 = log 1.180 ; 0.08063 = log 1.204.
Page 189 - If the declination is negative, the polar distance is equal numerically to 90� + the declination. The Hour Angle of a star is the angle at the pole formed by the meridian of the observer and the hour circle passing through the star. On account of the diurnal rotation, it is constantly changing at the rate of 15� per hour. Hour angles are reckoned from the celestial meridian, positive towards the west, and negative towards the east. III. The equinoctial...
Page 132 - The co-sine of any angle of a spherical triangle is equal to the product of the sines of the other angles into the co-sine of their included side, minus the product of the co-sines of these angles.
Page 189 - A, it follows that (pr), or the height of the pole above the horizon is equal to the latitude of the place.
Page vii - Seconds belonging to a given Sine or Tangent. If the given sine or tangent is found exactly in the table, the corresponding degrees will be found at the top of the page, and the minutes on the left hand. But when the given number is not found exactly in the table, look for the sine or tangent which is next less than the proposed one, and take out the corresponding degrees and minutes. Find, also, the difference between this tabular number and the number proposed, and divide it by the proportional...