The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 230
... pyramid ABCG to the two prisms in the pyramid DEFH : and likewise if the pyramids now made , for example , the two OMNG , STYH , be divided in the same manner ; as the base OMN is to the base STY , so are the two prisms in the pyramid ...
... pyramid ABCG to the two prisms in the pyramid DEFH : and likewise if the pyramids now made , for example , the two OMNG , STYH , be divided in the same manner ; as the base OMN is to the base STY , so are the two prisms in the pyramid ...
Page 231
... pyramid ABCG be to the pyramid DEFH . For , if it be not so , the base ABC must be to the -base DEF , as the pyramid ABCG to a solid either less than the pyramid DEFH , or greater than it ‡ . First , let it be to a solid less than it ...
... pyramid ABCG be to the pyramid DEFH . For , if it be not so , the base ABC must be to the -base DEF , as the pyramid ABCG to a solid either less than the pyramid DEFH , or greater than it ‡ . First , let it be to a solid less than it ...
Page 232
... pyramid ABCG to any solid which is greater than the pyramid DEFH . For , if it be possible , let it be so to a greater , viz . the solid Z. And because the base ABC is to the base DEF as the pyramid ABCG to the solid Z ; by inversion ...
... pyramid ABCG to any solid which is greater than the pyramid DEFH . For , if it be possible , let it be so to a greater , viz . the solid Z. And because the base ABC is to the base DEF as the pyramid ABCG to the solid Z ; by inversion ...
Page 233
... pyramid ABCM * 5 . 12 . to the pyramid FGHN ; and the triangle ACD to the triangle FGH , as the pyramid ACDM to the pyramid FGHN ; and also the triangle ADE , to the triangle FGH , as the pyramid ADEM to the pyramid FGHN ; as all the ...
... pyramid ABCM * 5 . 12 . to the pyramid FGHN ; and the triangle ACD to the triangle FGH , as the pyramid ACDM to the pyramid FGHN ; and also the triangle ADE , to the triangle FGH , as the pyramid ADEM to the pyramid FGHN ; as all the ...
Page 234
... pyramid of which the base is the triangle ABD , and ver- tex the point C , is equal to the pyramid , the base of which is the triangle EBC , and vertex the point D. Again , be- cause FCBE is a parallelogram of which the diameter is CE ...
... pyramid of which the base is the triangle ABD , and ver- tex the point C , is equal to the pyramid , the base of which is the triangle EBC , and vertex the point D. Again , be- cause FCBE is a parallelogram of which the diameter is CE ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore