# Military examinations. Mathematical examination papers set at an open competition for admission to the Royal military college, Sandhurst, and for first appointments in the Royal marine light infantry, held under the directions of the Civil service commissioners, 1883, with solutions by J.F. and T. Heather

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Página 12 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Página 10 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página 14 - In equal circles, angles, whether at the centres or circumferences, have the same ratio which the circumferences on which they stand have to one another ; so also have the sectors.
Página 13 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle.
Página 15 - In the ordinary or sexagesimal system, a right-angle, which is used as the measure of all plane angles, is divided into 90 equal parts, called degrees; a degree is divided into 60 equal parts, called minutes ; and a minute into 60 equal parts, called seconds.
Página 18 - Ans. ty. 7. Prove that the sides of any plane triangle are proportional to the sines of the angles opposite to these sides. If 2s = the sum of the three sides (a, b, c) of a triangle, and if A be the angle opposite to the side a, prove that sin A = ^ Vs (s -a)(s — b) (s — c).
Página 14 - ... being 10 in. ; (2) 1.5 radians, radius 2 ft. ; (3) 4.3 radians, radius 21 yd. ; (4) 1.25 radians, radius 8 in. 4. The value of the division on the outer rim of a graduated circle is 5', and the distance between the two successive divisions is .1 of an inch. Find the radius of the circle. 5. Show that the distance in miles between two places on the equator, which differ in longitude by 3° 9', assuming the earth's equatorial diameter to be 7925.6 mi., is 217.954 mi. 6. (a) The difference of two...
Página 13 - TRIANGLES. 33. Given the vertical angle, one of the sides containing it, and the length of the perpendicular from the vertex on the base : construct the triangle. 34. Given the feet of the perpendiculars drawn from the vertices on the opposite sides : construct the triangle. 35. Given the base, the altitude, and the radius of the circumscribed circle : construct the triangle. 36. Given the base, the vertical...
Página 12 - IF a straight line be divided into two equal parts, and also into two unequal parts : the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Página 16 - Then show that cos (A + B) = cos A cos В — sin A sin B.