Elements of Geometry and Trigonometry |
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Page 56
... half the arc FDB ( Prop . XVIII . ) ; therefore , DEB A E D B is measured by half of FDB ; that is , by half of DB + DF , or half of DB + AC . In the same manner it might be proved that the angle AED is measured by half of AFD + BC ...
... half the arc FDB ( Prop . XVIII . ) ; therefore , DEB A E D B is measured by half of FDB ; that is , by half of DB + DF , or half of DB + AC . In the same manner it might be proved that the angle AED is measured by half of AFD + BC ...
Page 57
... half the semicircumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC , is measured by the half of AMD plus the half of DC , or by half the whole arc AMDC . It might be shown , by taking the ...
... half the semicircumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC , is measured by the half of AMD plus the half of DC , or by half the whole arc AMDC . It might be shown , by taking the ...
Page 65
... half the arc AKB ( Prop , XXI . ) . Also , the angle AMB , being an inscribed angle , is measured by half the arc AKB : hence we have AMB = ABF = EBD - C : hence all the angles in- scribed in the segment AMB are equal to the given angle ...
... half the arc AKB ( Prop , XXI . ) . Also , the angle AMB , being an inscribed angle , is measured by half the arc AKB : hence we have AMB = ABF = EBD - C : hence all the angles in- scribed in the segment AMB are equal to the given angle ...
Page 70
... half the parallelogram FC , and the triangle FAE half the parallelogram FD ( Book I. Prop , XXVII . Cor . ) . Now , if from the parallelogram FC , there be taken the par- allelogram FD , there will remain the parallelogram AC : and if ...
... half the parallelogram FC , and the triangle FAE half the parallelogram FD ( Book I. Prop , XXVII . Cor . ) . Now , if from the parallelogram FC , there be taken the par- allelogram FD , there will remain the parallelogram AC : and if ...
Page 74
... half its aliirde . For , the triangle ABC is half of the par- allelogram ABCE , which has the same base BC , and the same altitude AD ( Prop . II . ) ; but the area of the parallelogram is equal to BC AD ( Prop . V. ) ; hence that of ...
... half its aliirde . For , the triangle ABC is half of the par- allelogram ABCE , which has the same base BC , and the same altitude AD ( Prop . II . ) ; but the area of the parallelogram is equal to BC AD ( Prop . V. ) ; hence that of ...
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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