Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 93
... ALTITUDE OF A TRIANGLE , is the perpendicular distance from the vertex of either an- gle to the opposite side , or the opposite side produced . The vertex of the angle from which the distance is measured , is called the vertex of the ...
... ALTITUDE OF A TRIANGLE , is the perpendicular distance from the vertex of either an- gle to the opposite side , or the opposite side produced . The vertex of the angle from which the distance is measured , is called the vertex of the ...
Page 94
... altitudes : then will the parallelograms be equal . For , let them be so placed that their lower bases shall coincide ; then , because they have the same altitude , their upper bases will be in the same line DG , parallel to AB ...
... altitudes : then will the parallelograms be equal . For , let them be so placed that their lower bases shall coincide ; then , because they have the same altitude , their upper bases will be in the same line DG , parallel to AB ...
Page 95
... altitude . Let the triangle ABC , and the parallelogram ABFÐ , have equal bases and equal altitudes : then will the triangle be equal to one - half of the parallelogram . For , let them be so placed that the base of D E F the triangle ...
... altitude . Let the triangle ABC , and the parallelogram ABFÐ , have equal bases and equal altitudes : then will the triangle be equal to one - half of the parallelogram . For , let them be so placed that the base of D E F the triangle ...
Page 96
... altitudes , are proportional to their 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 ...
... altitudes , are proportional to their 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 ...
Page 97
... be equal to AE : hence , ABCD : AEFD :: AB AE ; which was to be proved . Cor . If rectangles have equal bases , they are to each other as their altitudes . PROPOSITION IV . THEOREM . Any two rectangles are to 7 BOOK IV . 97.
... be equal to AE : hence , ABCD : AEFD :: AB AE ; which was to be proved . Cor . If rectangles have equal bases , they are to each other as their altitudes . PROPOSITION IV . THEOREM . Any two rectangles are to 7 BOOK IV . 97.
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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