The Elements of Euclid |
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Page 236
Euclid Robert Simson. Book XI . CF ; wherefore the prisms , which are their halves " , aré to one- another as the base AE to the base CF ; that is , as the triangle AEM to the triangle CFG . d 28. 11 . PROP . XXXIII . THEOR . a 24.11 . b ...
Euclid Robert Simson. Book XI . CF ; wherefore the prisms , which are their halves " , aré to one- another as the base AE to the base CF ; that is , as the triangle AEM to the triangle CFG . d 28. 11 . PROP . XXXIII . THEOR . a 24.11 . b ...
Page 251
... prisms shall be equal to one another . Let the prisms ABCDEF , GHKLMN be of the same alti- tude , the first wherefore is contained by the two triangles ABE , CDF , and the three parallelograms AD , DE , EC ; and the other by the two ...
... prisms shall be equal to one another . Let the prisms ABCDEF , GHKLMN be of the same alti- tude , the first wherefore is contained by the two triangles ABE , CDF , and the three parallelograms AD , DE , EC ; and the other by the two ...
Page 257
... prisms which together are greater than half of the whole pyramid . Ꭰ Let there be a pyramid of which the base is the triangle ABC and its vertex the point D : the pyramid ABCD may be divided into two equal and similar pyra mids having ...
... prisms which together are greater than half of the whole pyramid . Ꭰ Let there be a pyramid of which the base is the triangle ABC and its vertex the point D : the pyramid ABCD may be divided into two equal and similar pyra mids having ...
Page 258
... prisms of the same al- ' titude , of which one has a parallelogram for its base , and the other a triangle that is half of the parallelogram , these prisms are equal to one another ; therefore the prism having the parallelo- gram EBFG ...
... prisms of the same al- ' titude , of which one has a parallelogram for its base , and the other a triangle that is half of the parallelogram , these prisms are equal to one another ; therefore the prism having the parallelo- gram EBFG ...
Page 259
... prisms is greater than either of the pyramids of which the triangles AEG , HKL b 15. 11 . are the bases , and the vertices the points H , D ; because if EF be joined , the prism having the parallelogram EBFG for its base , and KH the ...
... prisms is greater than either of the pyramids of which the triangles AEG , HKL b 15. 11 . are the bases , and the vertices the points H , D ; because if EF be joined , the prism having the parallelogram EBFG for its base , and KH the ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore