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 a parallelogram whose angles are all right angles . ( A SQUARE is an equilateral rectangle . 21. A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral ...
... rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . ( A SQUARE is an equilateral rectangle . 21. A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral ...
Page 95
... . 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 . 95.
... . 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 . 95.
Page 96
... Rectangles having 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 ...
... Rectangles having 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 ...
Page 97
... rectangles be incommensurable : then will the rectangles be 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 pro- portional ...
... rectangles be incommensurable : then will the rectangles be 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 pro- portional ...
Page 98
... rectangles are to each other as the products of their bases and altitudes . H Let ABCD and AEGF be two rectangles : then ... rectangle AEGF will be the superficial unit , and we shall have , ABCD • 1 :: AB × AD : 1 ; ABCD AB X AD : hence ...
... rectangles are to each other as the products of their bases and altitudes . H Let ABCD and AEGF be two rectangles : then ... rectangle AEGF will be the superficial unit , and we shall have , ABCD • 1 :: AB × AD : 1 ; ABCD AB X AD : hence ...
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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