The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 304
... cone , & c . Q. E. D. PROP . XI . THEOR . Cones and cylinders of the same altitude , are to one another as their ... cone AL be to the cone EN . If it be not so , the circle ABCD must be to the circle EFGH , as the cone AL to some solid ...
... cone , & c . Q. E. D. PROP . XI . THEOR . Cones and cylinders of the same altitude , are to one another as their ... cone AL be to the cone EN . If it be not so , the circle ABCD must be to the circle EFGH , as the cone AL to some solid ...
Page 305
... cone , and so on , there must at length remain some segments of the cone which are together less than the solid Z : let these be the segments " Lem- upon EO , OF , FP , PG , GR , RH , HS , SE : ma . therefore the remainder of the cone ...
... cone , and so on , there must at length remain some segments of the cone which are together less than the solid Z : let these be the segments " Lem- upon EO , OF , FP , PG , GR , RH , HS , SE : ma . therefore the remainder of the cone ...
Page 306
... cone AL to the solid X , so is the pyramid of which the base is the polygon ATBYCVDQ , and vertex L , to the pyramid the base of which is the polygon EOFPGRHS , and vertex N : but the cone AL is greater than the pyramid * 14 . 5 ...
... cone AL to the solid X , so is the pyramid of which the base is the polygon ATBYCVDQ , and vertex L , to the pyramid the base of which is the polygon EOFPGRHS , and vertex N : but the cone AL is greater than the pyramid * 14 . 5 ...
Page 307
... cone EN . For , if it be possible , let it be so to the solid I , which is greater than the cone EN : therefore , by inver- sion , as the circle EFGH to the circle ABCD , so is the solid I to the cone AL : but as the solid I to the cone ...
... cone EN . For , if it be possible , let it be so to the solid I , which is greater than the cone EN : therefore , by inver- sion , as the circle EFGH to the circle ABCD , so is the solid I to the cone AL : but as the solid I to the cone ...
Page 308
... cone ABCDL has not to the cone EFGHN the triplicate ratio of that which AC has to EG , the cone ABCDL must have the triplicate of that ratio to some solid which is less or greater than the cone EFGHN . First , let it have it to a less ...
... cone ABCDL has not to the cone EFGHN the triplicate ratio of that which AC has to EG , the cone ABCDL must have the triplicate of that ratio to some solid which is less or greater than the cone EFGHN . First , let it have it to a less ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole