The Elements of Euclid |
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Page 197
... prism is a solid figure contained by plane figures , of which two that are opposite are equal , símilar , and parallel to one another ; and the others parallelograms . XIV . A sphere is a solid figure described by the revolution of a ...
... prism is a solid figure contained by plane figures , of which two that are opposite are equal , símilar , and parallel to one another ; and the others parallelograms . XIV . A sphere is a solid figure described by the revolution of a ...
Page 229
... prism contained by the two triangles D C B b 16. 11 . F c 34. 1 . H d 24.11 . E CGF , DAE , and the three parallelograms CA , GE , EC , is equal to the prism contained by the two triangles CBF , DHE , e C. 11 . and the three ...
... prism contained by the two triangles D C B b 16. 11 . F c 34. 1 . H d 24.11 . E CGF , DAE , and the three parallelograms CA , GE , EC , is equal to the prism contained by the two triangles CBF , DHE , e C. 11 . and the three ...
Page 230
... prism which is C contained betwixt the triangles ALG , CBH . Therefore the so- lid AH is equal to the solid AK . b ... prism which is contained by the two triangles AFG , CDE , and the three parallelograms AD , DG , GC is equal to the ...
... prism which is C contained betwixt the triangles ALG , CBH . Therefore the so- lid AH is equal to the solid AK . b ... prism which is contained by the two triangles AFG , CDE , and the three parallelograms AD , DG , GC is equal to the ...
Page 231
... prism AFGCDE ; the remaining solid , viz . the parallelopiped AH , is equal to the remaining pa- ralleopipe AK . Therefore solid parallelopipeds , & c . Q. E. D. PROP . XXX . THEOR . SOLID parallelopipeds upon the same base , and See ...
... prism AFGCDE ; the remaining solid , viz . the parallelopiped AH , is equal to the remaining pa- ralleopipe AK . Therefore solid parallelopipeds , & c . Q. E. D. PROP . XXX . THEOR . SOLID parallelopipeds upon the same base , and See ...
Page 235
... prisms upon triangular bases , of the same altitude , are to one another as their bases , Let the prisms , the bases of which are the triangles AEM , CFG , and NBO , PDQ the triangles opposite to them , have the same altitude ; and ...
... prisms upon triangular bases , of the same altitude , are to one another as their bases , Let the prisms , the bases of which are the triangles AEM , CFG , and NBO , PDQ the triangles opposite to them , have the same altitude ; and ...
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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