Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 96
... bases . There may be two cases : the bases may be commensu- rable , or they may be incommensurable . 1o . Let ABCD and HEFK , be two rectangles whose altitudes AD and HK are equal , and whose bases AB and HE are commensurable : then ...
... bases . There may be two cases : the bases may be commensu- rable , or they may be incommensurable . 1o . Let ABCD and HEFK , be two rectangles whose altitudes AD and HK are equal , and whose bases AB and HE are commensurable : then ...
Page 97
... bases of the rectangles be incommensurable : then will the rectangles be proportional to their bases . For , place the rectangle HEFK upon the rectangle ABCD , so that it shall take the position AEFD . Then , if the rectangles are not ...
... bases of the rectangles be incommensurable : then will the rectangles be proportional to their bases . For , place the rectangle HEFK upon the rectangle ABCD , so that it shall take the position AEFD . Then , if the rectangles are not ...
Page 99
... base by the number of linear units in its altitude . Scholium 2. The product of two lines is sometimes called the ... base and altitude . Let ABCD be a parallelogram , AB its base , and BE its altitude : then will the area of ABCD be ...
... base by the number of linear units in its altitude . Scholium 2. The product of two lines is sometimes called the ... base and altitude . Let ABCD be a parallelogram , AB its base , and BE its altitude : then will the area of ABCD be ...
Page 100
... base , and AD its altitude : then will the area of the triangle be equal to BC × AD . E For , from C , draw СЕ ... bases and altitudes ( B. II . , P. VII . ) . If their alti- tudes are equal , they are to each other as their bases . If ...
... base , and AD its altitude : then will the area of the triangle be equal to BC × AD . E For , from C , draw СЕ ... bases and altitudes ( B. II . , P. VII . ) . If their alti- tudes are equal , they are to each other as their bases . If ...
Page 105
... base BF , and because DE is the prolongation of DA , their altitudes are equal : hence , the triangle ABF is equal to half the rectangle BE ( P. II . ) . The triangle HBC , and the square BL , have the same base BH , and because AC is ...
... base BF , and because DE is the prolongation of DA , their altitudes are equal : hence , the triangle ABF is equal to half the rectangle BE ( P. II . ) . The triangle HBC , and the square BL , have the same base BH , and because AC is ...
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Common terms and phrases
AB² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following