### Popular passages

Page 59 - The sides of a triangle are proportional to the sines of the opposite angles. If...
Page 139 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 343 - A Solar Day is the interval of time between two successive transits of the sun over the same meridian; and the hour-angle of the sun is called Solar Time.
Page 60 - 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 24 - It is shown in Geometry that the area of a triangle is equal to one-half the product of the base by the altitude. Therefore, if a and b denote the legs of a right triangle, and F the area...
Page 61 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides.
Page 149 - Substituting these values of cosp cos m and cosp sin m in the value of cos a, we obtain cos a = cos b cos с + sin b sin с cos A ') and similarly, cos b = cos a cos с -f- sin a sin с cos В >  cos с = cos a cos b -\- sin a sin b cos С J 3.
Page 116 - For, 2Р = (а")' = а"г. . • . loga (N") = np=plog„N. 7. The logarithm of the real positive value of a root of a positive number is found by dividing the logarithm of the number by the index of the root.
Page 172 - Azimuth of a point in the celestial sphere is the angle at the zenith between the meridian of the observer and the vertical circle passing through the point; it may also be regarded as the arc of the horizon intercepted between those circles.
Page 28 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5� and 15�.