Elements of Geometry and Trigonometry |
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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 75
... ABCD be a trapezoid , EF its alti- D tude , AB and CD its parallel bases ; then will its area be equal to EF × ( AB + CD ) . H Through I , the middle point of the side BC , draw KL parallel to the opposite side AD ; and produce DC till ...
... ABCD be a trapezoid , EF its alti- D tude , AB and CD its parallel bases ; then will its area be equal to EF × ( AB + CD ) . H Through I , the middle point of the side BC , draw KL parallel to the opposite side AD ; and produce DC till ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
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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 consequently convex surface cosine Cotang 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 number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex