Elements of Geometry and Trigonometry |
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Page 73
... altitude ten , that rectangle will be represented by the number 3 x 10 , or 30 , a number which signifies nothing while thus isolated ; but if there is a second rectangle B , the base of which contains twelve units , and the altitude ...
... altitude ten , that rectangle will be represented by the number 3 x 10 , or 30 , a number which signifies nothing while thus isolated ; but if there is a second rectangle B , the base of which contains twelve units , and the altitude ...
Page 74
... altitudes ; and parallelograms of the same altitude are to each other as their bases : for , let B be the common base , and C and D the altitudes of two parallelograms :. then , B × C : B × D :: C : D , ( Book II . Prop . VII . ) And if ...
... altitudes ; and parallelograms of the same altitude are to each other as their bases : for , let B be the common base , and C and D the altitudes of two parallelograms :. then , B × C : B × D :: C : D , ( Book II . Prop . VII . ) And if ...
Page 75
... altitude multiplied by the half sum of its parallél bases . Let ABCD be a trapezoid , EF its alti- D 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 ...
... altitude multiplied by the half sum of its parallél bases . Let ABCD be a trapezoid , EF its alti- D 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 ...
Page 77
... altitude AE is the difference of the same lines ; therefore the rectangle AKLE is equal to ( AB + BC ) x ( AB— E F GI H D C B K BC ) . But this rectangle is composed of the two parts ABHE + BHLK ; and the part BHLK is equal to the ...
... altitude AE is the difference of the same lines ; therefore the rectangle AKLE is equal to ( AB + BC ) x ( AB— E F GI H D C B K BC ) . But this rectangle is composed of the two parts ABHE + BHLK ; and the part BHLK is equal to the ...
Page 78
... altitude BD ( Prop . II . Cor . 1. ) . The triangle HBC is in like manner half of the square AH : for the angles BAC , BAL , being both right angles , AC and AL form one and the same straight line parallel to HB ( Book I. Prop . III ...
... altitude BD ( Prop . II . Cor . 1. ) . The triangle HBC is in like manner half of the square AH : for the angles BAC , BAL , being both right angles , AC and AL form one and the same straight line parallel to HB ( Book I. Prop . III ...
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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 consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides 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 solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex