Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 97
... ALTITUDE OF A TRIANGLE is the perpendicular distance from the vertex of any angle to the opposite side , or the opposite side pro- duced . 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 any angle to the opposite side , or the opposite side pro- duced . The vertex of the angle from which the distance is measured , is called the vertex of the ...
Page 98
... altitudes : then the parallelograms are equal . D H BE F 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 the parallelograms are equal . D H BE F 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 99
... altitude . Let the triangle ABC , and the parallelogram ABFD , have equal bases and equal altitudes : then the triangle is equal to one half of the parallelogram . For , let them be SO placed that that the base of the triangle shall ...
... altitude . Let the triangle ABC , and the parallelogram ABFD , have equal bases and equal altitudes : then the triangle is equal to one half of the parallelogram . For , let them be SO placed that that the base of the triangle shall ...
Page 100
... altitudes , are proportional to their bases . There may be two cases : the bases may be commen- surable , or they may be incommensurable . 1 ° . Let ABCD and HEFK , be two rectangles whose alti- tudes AD and HK are equal , and whose ...
... altitudes , are proportional to their bases . There may be two cases : the bases may be commen- surable , or they may be incommensurable . 1 ° . Let ABCD and HEFK , be two rectangles whose alti- tudes AD and HK are equal , and whose ...
Page 101
... 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 BOOK IV . 101.
... 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 BOOK IV . 101.
Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence