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 94
... equal altitudes , are equal . Let the parallelograms ABCD and EFGH have equal bases and equal altitudes : then will the parallelograms be equal . For , let them be so placed that their lower bases shall coincide ; then , because they ...
... equal altitudes , are equal . Let the parallelograms ABCD and EFGH have equal bases and equal altitudes : then will the parallelograms be equal . For , let them be so placed that their lower bases shall coincide ; then , because they ...
Page 95
... equal ( B. I. , P. V. ) . If from the quadrilateral ABGD , we take away the tri- angle DAH , there will remain the parallelogram AG ; if from the same quadrilateral ABGD , we take away the triangle CBG ... equal altitudes , BOOK IV . 95.
... equal ( B. I. , P. V. ) . If from the quadrilateral ABGD , we take away the tri- angle DAH , there will remain the parallelogram AG ; if from the same quadrilateral ABGD , we take away the triangle CBG ... equal altitudes , BOOK IV . 95.
Page 96
... equal 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 ...
... equal 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 ...
Page 97
... equal parts , each less than OE ; division , as I , will fall between E and ... above proportions have their antecedents the same in each ; hence ( B. II ... altitudes . PROPOSITION IV . THEOREM . Any two rectangles are to 7 300K IV . 97.
... equal parts , each less than OE ; division , as I , will fall between E and ... above proportions have their antecedents the same in each ; hence ( B. II ... altitudes . PROPOSITION IV . THEOREM . Any two rectangles are to 7 300K IV . 97.
Page 98
... altitudes . H Let ABCD and AEGF be two rectangles : then wil ABCD be to AEGF ... altitude AD : hence ( P. III . ) , E B A ABCD : ADHE :: AB : AE . The ... equal to the linear unit , the rectangle AEGF will be the superficial unit ...
... altitudes . H Let ABCD and AEGF be two rectangles : then wil ABCD be to AEGF ... altitude AD : hence ( P. III . ) , E B A ABCD : ADHE :: AB : AE . The ... equal to the linear unit , the rectangle AEGF will be the superficial unit ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence