Elements of Geometry and Trigonometry |
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Page 68
... altitude of the triangle BAC A B D DE 6. The altitude of a parallelogram is the perpendicular which measures the distance between two opposite sides taken as bases . Thus , EF is the altitude of the parallelo- A gram DB . 7. The ...
... altitude of the triangle BAC A B D DE 6. The altitude of a parallelogram is the perpendicular which measures the distance between two opposite sides taken as bases . Thus , EF is the altitude of the parallelo- A gram DB . 7. The ...
Page 69
... altitudes , are equivalent . D CF EDF CE Let AB be the common base of the two parallelograms ABCD , ABEF : and since they are sup- posed to have the same altitude , their upper bases DC , FE , will be both situated in one straight line ...
... altitudes , are equivalent . D CF EDF CE Let AB be the common base of the two parallelograms ABCD , ABEF : and since they are sup- posed to have the same altitude , their upper bases DC , FE , will be both situated in one straight line ...
Page 70
... altitude , are equivalent . Cor . Every parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II . THEOREM . Every triangle is half the parallelogram which has the same base and the ...
... altitude , are equivalent . Cor . Every parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II . THEOREM . Every triangle is half the parallelogram which has the same base and the ...
Page 71
... altitude AD : they are to each other as their bases AB , AE . A F C E B Suppose , first , that the bases are commensurable , and are to each other , for example , as the numbers 7 and 4. If AB be divided into 7 equal parts , AE will ...
... altitude AD : they are to each other as their bases AB , AE . A F C E B Suppose , first , that the bases are commensurable , and are to each other , for example , as the numbers 7 and 4. If AB be divided into 7 equal parts , AE will ...
Page 72
... altitude , are to each other as their bases AB , AE . PROPOSITION IV . THEOREM . Any two rectangles are to each other as the products of their bases multiplied by their altitudes . Let ABCD , AEGF , be two rectangles ; then will the ...
... altitude , are to each other as their bases AB , AE . PROPOSITION IV . THEOREM . Any two rectangles are to each other as the products of their bases multiplied by their altitudes . Let ABCD , AEGF , be two rectangles ; then will the ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex