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82 Extracting root AABC ABCD ABEL HEYWOOD acres base binomial theorem bisected centre changing the signs chord circle circumference collecting the terms completing the square cosec denominator diameter difference distance dividing divisor equal equiangular extracting the root feet find the area find the differential fraction given equation gives gonal greater segment half the sum hence the area hypotenuse inches integral inverted latitude least common multiple length Let ABC miles Mult Multiply number sought perp perpendicular poles Problem VIII Prop question radius rectangle represent right angles semiperimeter slant height solidity specific gravity square root substituting Subt Subtract surf Tabular area tangent Theorem third side transp transposing transposition Trig value of y vertical angle whence wherefore whole arc whole surface yards
Side 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.
Side 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.
Side 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...
Side 15 - ... 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...
Side 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.
Side 139 - Arc, on the Sine and Cosine of an Arc in terms of the Arc itself, and a new Theorem for the Elliptic Quadrant.
Side 137 - The differential of the logarithm of a function is equal to the differential of the function, divided by the function itself.
Side 149 - The pyramid may be conceived to be made up of an infinite number of planes parallel to ABC.
Side 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