## Five-place Logarithmic and Trigonometric Tables |

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adjacent altitude angle of elevation azimuth base Bearing called celestial centre changing circle colog Compute corresponding cos x cosine declination determine difference distance dividing east equal equator EXAMPLE Exercise Express feet figure Find the area formulas functions Given greater height Hence horizon hour angle included increases known latitude length less log cos log cos 9 log sin log tan log logarithm longitude mantissa measured meridian miles negative NOTE observer obtain opposite Page passing places plane pole polygon positive PROBLEM Quadrant radius regular right triangle Rules sails Sect ship sides sin b sin sin x sin² sine solution solve sphere square star tan² tangent tower Trigonometry unit vertical whence yards

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Page 64 - The square of any side of a triamjle is equal to the sum of the squares of the other two sides diminished by twice their product into the cosine of the included angle. • SECTION XXXVI LAW OF TANGENTS By Sect. XXXIV, p. 64, a : b = sin A : sin B...

Page 143 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts. II. The sine of the middle part is equal to the product of the cosines of the opposite parts.

Page 65 - The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides.

Page 63 - The sides of a triangle are proportional to the sines of the opposite angles.

Page i - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.

Page 90 - A pole is fixed on the top of a mound, and the angles of elevation of the top and the bottom of the pole are 60° and 30° respectively. Prove that the length of the pole is twice the height of the mound.

Page 116 - X a" = am+". .'. log. (MX N) = m + n — log. M + log. N. Similarly for the product of three or more factors. (5) The logarithm of the quotient of two positive numbers is found by subtracting the logarithm of the divisor from the logarithm of the dividend. (6) The logarithm of a power of a positive number is found by multiplying the logarithm of the number by the exponent of the power. For, N" = (oT)

Page 29 - 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°.

Page 137 - If, from the vertices of a spherical triangle as poles, arcs of great circles are described, another spherical triangle is formed, called the polar triangle of the first.

Page 180 - Circles are great circles passing through the zenith of an observer, and perpendicular to his horizon. The vertical circle passing through the east and west points of the horizon is called the Prime Vertical ¡ that passing through the north and south points coincides with the celestial meridian.