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acres angle base becomes bisected centre changing chord circle circumference coefficients collecting common completing the square contained cosec course denominator diameter difference differential distance dividing ends equal evidently EXERCISES expression Extracting root extracting the root feet figure follows four fourth fraction given equation gives greater half height hence inches integral join latitude length less logarithm Long mean measure middle miles Mult Multiply nearly Note obtain perp perpendicular poles PROBLEM Prop proved quantity question radius remainder represent root Rule segment sides signs sine solidity sought square substituting Subtract surf Table Theorem third transp transposing transposition triangle Trig wherefore whole yards
Page 74 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 75 - If the vertical angle of a triangle be 'bisected 'by a straight line which also cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Page 9 - Let x measure у by the units in n, then it will measure cy by the units in nc. 2d. If a quantity measure two others, it will measure their sum or difference. Let a be contained...
Page 13 - ... sin(a + b + c). Again (a) represents the coarse ROM, and bands b and c are two controls of the fine-tuned ROMs so that a < 90°, b < 90 • 2~a and c < 90 • 2~(a + 6). This is shown in Fig. 7-7. Sunderland showed that the trigonometric identity can be written as sin(a + b + c) = sin(a + 6) cos c + cos a cos b sin...
Page 10 - The truth of this rule depends upon these two principles ; 1". If one quantity measure another, it will also measure any multiple of that quantity. Let x measure y by the units in n, then it will measure cy by the units in nc.
Page 133 - Arc, on the Sine and Cosine of an Arc in terms of the Arc itself, and a new Theorem for the Elliptic Quadrant.
Page 131 - The differential of the logarithm of a function is equal to the differential of the function, divided by the function itself.
Page 143 - The pyramid may be conceived to be made up of an infinite number of planes parallel to ABC.
Page 81 - ... sum of any number of quantities is equal to the sum of the corresponding functions of each of these quantities, will be called distributive