The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth of EuclidCassell, Petter, and Galpin, 1859 - 212 σελίδες |
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Σελίδα 200
... cone . Therefore the pyramid upon the base A EBF C G D H is greater than the cone upon the circle A B C D ; but it is also less , for the pyramid is contained within the cone , which is impossible . There- fore the cylinder is not ...
... cone . Therefore the pyramid upon the base A EBF C G D H is greater than the cone upon the circle A B C D ; but it is also less , for the pyramid is contained within the cone , which is impossible . There- fore the cylinder is not ...
Σελίδα 201
... cone , and so on , there will at length remain some segments of the cone , which together are less ( XII . Lem . 1 ) than the excess of the cone above the third part of the cylinder . Let these be the segments upon A E , E B , BF , FC ...
... cone , and so on , there will at length remain some segments of the cone , which together are less ( XII . Lem . 1 ) than the excess of the cone above the third part of the cylinder . Let these be the segments upon A E , E B , BF , FC ...
Σελίδα 203
... cone whose base is the circle A B CD and vertex the point L , has to the cone whose base is the circle E F G H and vertex N , the triplicate ratio of that which AC has to E G. A T N R K E G M B Ꮓ F K For if the cone A B CDL has not to ...
... cone whose base is the circle A B CD and vertex the point L , has to the cone whose base is the circle E F G H and vertex N , the triplicate ratio of that which AC has to E G. A T N R K E G M B Ꮓ F K For if the cone A B CDL has not to ...
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A B and CD A B C D A B is equal adjacent angles altitude angle ABC base B C bisected Cassell's centre circle A B C circle ABCD circumference cone cylinder D E F described diagonal diameter draw equal angles equal Ax equal Const equiangular equimultiples Euclid exterior angle given rectilineal given straight line gnomon greater homologous Illustrated inscribed join less Let A B C multiple opposite angles parallelopiped pentagon perpendicular polygon prism proposition pyramid Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid A B solid angle sphere squares of AC straight line drawn straight lines A B THEOREM three plane angles touches the circle triangle A B C triplicate ratio twice the rectangle vertex Wherefore