Elements of Geometry and Trigonometry |
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Page 68
... altitude of the parallelo- Á gram DB . 7. The altitude of a trapezoid is the per- pendicular drawn between its two parallel sides . Thus , EF is the altitude of the trape- zoid DB . D DE F B DE C A F B 8. The area and surface of a ...
... altitude of the parallelo- Á gram DB . 7. The altitude of a trapezoid is the per- pendicular drawn between its two parallel sides . Thus , EF is the altitude of the trape- zoid DB . D DE F B DE C A F B 8. The area and surface of a ...
Page 69
... altitudes , are equivalent . Let AB be the common base of D CF EDF CE the two parallelograms ABCD , ABEF : and since they are sup- posed to have the same altitude , A B A B their upper bases DC , FE , will be both situated in one ...
... altitudes , are equivalent . Let AB be the common base of D CF EDF CE the two parallelograms ABCD , ABEF : and since they are sup- posed to have the same altitude , A B A B their upper bases DC , FE , will be both situated in one ...
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 same ...
... 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 same ...
Page 71
... altitude AD : they are to each other as their bases AB , AE . E B If AB be divided into 7 Suppose , first , that the bases are A commensurable , and are to each other , for example , as the numbers 7 and 4 . equal parts , AE will ...
... altitude AD : they are to each other as their bases AB , AE . E B If AB be divided into 7 Suppose , first , that the bases are A commensurable , and are to each other , for example , as the numbers 7 and 4 . 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 altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine cotangent cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex