The Elements of Euclid |
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Page 261
... pyramid ABCG to the two prisms in the pyra- mid DEFH : and likewise if the pyramids now made , for ex- ample , the two OMNG , STYH , be divided in the same man- ner ; as the base OMN is to the base STY , so shall the two prisms in the ...
... pyramid ABCG to the two prisms in the pyra- mid DEFH : and likewise if the pyramids now made , for ex- ample , the two OMNG , STYH , be divided in the same man- ner ; as the base OMN is to the base STY , so shall the two prisms in the ...
Page 262
... pyramid OMNG to the two prisms in the pyramid STYH ; and so are all four to all four : and the same thing may be shown of the prisms made by divid- ing the pyramids AKLO and DPRS , and of all made by the same number of divisions ...
... pyramid OMNG to the two prisms in the pyramid STYH ; and so are all four to all four : and the same thing may be shown of the prisms made by divid- ing the pyramids AKLO and DPRS , and of all made by the same number of divisions ...
Page 263
... pyramid DEFH . In the same manner it may be de- monstrated , that the base DEF is not to the ABC , as the pyramid DEFH to any solid which is less than the pyramid ABCG . Nor can the base ABC be to the base DEF , as the py- ramid ABCG to ...
... pyramid DEFH . In the same manner it may be de- monstrated , that the base DEF is not to the ABC , as the pyramid DEFH to any solid which is less than the pyramid ABCG . Nor can the base ABC be to the base DEF , as the py- ramid ABCG to ...
Page 264
... pyramid FGHKLN . Divide the base ABCDE into the triangles ABC , ACD , ADE ; and the base FGHKL into the triangles ... pyramid ABCM to the pyramid FGHN ; and the triangle ACD to the triangle FGH , as the pyramid ACDM to the pyramid FGHN ...
... pyramid FGHKLN . Divide the base ABCDE into the triangles ABC , ACD , ADE ; and the base FGHKL into the triangles ... pyramid ABCM to the pyramid FGHN ; and the triangle ACD to the triangle FGH , as the pyramid ACDM to the pyramid FGHN ...
Page 265
... pyramid ABCDEM to the pyramid FGHKLN . There fore pyramids , & c . Q. E. D. c 22. 5 . PROP . VII . THEOR . EVERY prism having a triangular base may be divided into three pyramids that have triangular bases , and are equal to one another ...
... pyramid ABCDEM to the pyramid FGHKLN . There fore pyramids , & c . Q. E. D. c 22. 5 . PROP . VII . THEOR . EVERY prism having a triangular base may be divided into three pyramids that have triangular bases , and are equal to one another ...
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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