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 17
... rectangles and rhomboids . 1st . A RECTANGLE is is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . 2d . A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral ...
... rectangles and rhomboids . 1st . A RECTANGLE is is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . 2d . A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral ...
Page 99
... 7 ) ; which was to be proved . Cor . Triangles having equal bases and equal altitudes are equal , for they are halves of equal parallelograms . PROPOSITION III . THEOREM . Rectangles having equal altitudes , BOOK IV . 99.
... 7 ) ; which was to be proved . Cor . Triangles having equal bases and equal altitudes are equal , for they are halves of equal parallelograms . PROPOSITION III . THEOREM . Rectangles having equal altitudes , BOOK IV . 99.
Page 100
... Rectangles having equal 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 ...
... Rectangles having equal 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 ...
Page 101
... rectangles be incommensura- ble then the rectangles are 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 proportional to ...
... rectangles be incommensura- ble then the rectangles are 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 proportional to ...
Page 102
... rectangles are to each other as the products of their bases and altitudes . Let ABCD and AEGF be two rectangles : then ABCD is to AEGF , as ABX AD is to AE x AF . For , place the rectangles so that ... rectangle is equal to 102 GEOMETRY .
... rectangles are to each other as the products of their bases and altitudes . Let ABCD and AEGF be two rectangles : then ABCD is to AEGF , as ABX AD is to AE x AF . For , place the rectangles so that ... rectangle is equal to 102 GEOMETRY .
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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