Elements of Geometry and Trigonometry |
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Page 68
... altitude of the parallelo- gram DB . B 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 FB DE C A F B 8. The area and surface of a figure ...
... altitude of the parallelo- gram DB . B 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 FB DE C A F B 8. The area and surface of a figure ...
Page 69
... altitudes , are equivalent . 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 D CF EDF CE X A B A both situated in one ...
... altitudes , are equivalent . 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 D CF EDF CE X A B A 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 ...
... 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 a 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 contain ...
... altitude AD : they are to each other as their bases AB , AE . A a 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 contain ...
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 centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex