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 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 D H C GH 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 D H C GH same line DG , parallel to AB ...
Page 95
... altitude . Let the triangle ABC , and the parallelogram ABFD , 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 C the triangle ...
... altitude . Let the triangle ABC , and the parallelogram ABFD , 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 C 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
... 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 7 BOOK IV . 97.
... 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 7 BOOK IV . 97.
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Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence