Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 205
... altitude with AF , viz . GQ or AE . Now the solid AF is to the solid GO in a ratio compounded of the ratios of the ... altitude AE to the altitude GM ( F. 5. ) . But the ratio of the solid AF to the solid GO , is that which is compounded ...
... altitude with AF , viz . GQ or AE . Now the solid AF is to the solid GO in a ratio compounded of the ratios of the ... altitude AE to the altitude GM ( F. 5. ) . But the ratio of the solid AF to the solid GO , is that which is compounded ...
Σελίδα 206
... altitude AE to the altitude GM . Case 2. When the insisting lines are not perpendicular to the bases . Let the parallelograms AC and GK be the bases as before , and let AE and GM be the altitudes of two parallelepipeds Y and Z on these ...
... altitude AE to the altitude GM . Case 2. When the insisting lines are not perpendicular to the bases . Let the parallelograms AC and GK be the bases as before , and let AE and GM be the altitudes of two parallelepipeds Y and Z on these ...
Σελίδα 207
... altitudes reciprocally proportional , are equal ; and parallelepipeds which are equal , have their bases and altitudes ... altitude AE . Take S , so that AC may be to KM as KO to S , and it will be shewn , as was done above , that the ...
... altitudes reciprocally proportional , are equal ; and parallelepipeds which are equal , have their bases and altitudes ... altitude AE . Take S , so that AC may be to KM as KO to S , and it will be shewn , as was done above , that the ...
Σελίδα 208
... altitudes , be cut by planes that are parallel to the bases , and at equal distances from them , the sections are equal to one another . Let ABCD and EFGH be two pyramids , having equal bases BDC and FGH , and equal altitudes , viz ...
... altitudes , be cut by planes that are parallel to the bases , and at equal distances from them , the sections are equal to one another . Let ABCD and EFGH be two pyramids , having equal bases BDC and FGH , and equal altitudes , viz ...
Σελίδα 209
... altitudes QR and ST above those planes , and let the sections be the triangles KLM , NOP ; KLM and NOP are equal to one another . Because the plane ABD cuts the parallel planes BDC , KLM , the common sections BD and KM are parallel ( 14 ...
... altitudes QR and ST above those planes , and let the sections be the triangles KLM , NOP ; KLM and NOP are equal to one another . Because the plane ABD cuts the parallel planes BDC , KLM , the common sections BD and KM are parallel ( 14 ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore