Elements of Geometry and Trigonometry |
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Page 70
... ABCD be a parallelo- gram , and ABE a triangle , having the same base AB , and the same altitude : then will the triangle be half the parallelogram . E H D G с F A B For , since the triangle and the parallelogram have the same altitude ...
... ABCD be a parallelo- gram , and ABE a triangle , having the same base AB , and the same altitude : then will the triangle be half the parallelogram . E H D G с F A B For , since the triangle and the parallelogram have the same altitude ...
Page 71
... ABCD will contain seven partial rectangles , while AEFD will contain four : hence the rectangle ABCD is to AEFD as 7 is to 4 , or as AB is to AE . The same reasoning may be applied to any other ratio equally with that of 7 to 4 : hence ...
... ABCD will contain seven partial rectangles , while AEFD will contain four : hence the rectangle ABCD is to AEFD as 7 is to 4 , or as AB is to AE . The same reasoning may be applied to any other ratio equally with that of 7 to 4 : hence ...
Page 72
... ABCD , AEFD , of the same 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 ...
... ABCD , AEFD , of the same 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 ...
Page 74
... ABCD is equivalent FD to the rectangle ABEF , which has the same base AB , and the same altitude BE ( Prop . I. Cor . ) : but this rectangle is measured by AB × BE ( Prop . IV . Sch . ) ; therefore , AB BE A is equal to the area of the ...
... ABCD is equivalent FD to the rectangle ABEF , which has the same base AB , and the same altitude BE ( Prop . I. Cor . ) : but this rectangle is measured by AB × BE ( Prop . IV . Sch . ) ; therefore , AB BE A is equal to the area of the ...
Page 75
... ABCD be a trapezoid , EF its a'ti- tude , AB and CD its parallel bases ; then will its area be equal to EFx ( AB + CD ) . H Through I , the middle point of the side BC , draw KL parallel to the opposite side AD ; and produce DC till it ...
... ABCD be a trapezoid , EF its a'ti- tude , AB and CD its parallel bases ; then will its area be equal to EFx ( AB + CD ) . H Through I , the middle point of the side BC , draw KL parallel to the opposite side AD ; and produce DC till it ...
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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