The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth of EuclidCassell, Petter, and Galpin, 1859 - 212 Seiten |
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Seite 205
... cylinder has to the cylinder , the triplicate ratio of that which AC has to E G. Wherefore , similar cones , & c . Q E. D. PROP . XIII . THEOREM . R If a cylinder be cut by a plane parallel to its opposite planes , or bases , it divides ...
... cylinder has to the cylinder , the triplicate ratio of that which AC has to E G. Wherefore , similar cones , & c . Q E. D. PROP . XIII . THEOREM . R If a cylinder be cut by a plane parallel to its opposite planes , or bases , it divides ...
Seite 206
... cylinder P G is greater than the cylinder G Q ; if equal , equal ; and if less , less . Therefore ( V. Def . 5 ) , the axis E K is to the axis K F , as the cylinder B G is to the cylinder G D. Wherefore , if a cylinder , & c . Q.E. D. ...
... cylinder P G is greater than the cylinder G Q ; if equal , equal ; and if less , less . Therefore ( V. Def . 5 ) , the axis E K is to the axis K F , as the cylinder B G is to the cylinder G D. Wherefore , if a cylinder , & c . Q.E. D. ...
Seite 207
... cylinder E O is a circle ( XII . 13 , Cor . ) ES is a cylinder , of which the base is the circle E F G H , and altitude MP . Because the cylinder A X is equal to the cylinder EO . The cylinder A X is to the cylinder ES as ( V. 7 ) the ...
... cylinder E O is a circle ( XII . 13 , Cor . ) ES is a cylinder , of which the base is the circle E F G H , and altitude MP . Because the cylinder A X is equal to the cylinder EO . The cylinder A X is to the cylinder ES as ( V. 7 ) the ...
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Häufige Begriffe und Wortgruppen
A B and CD A B C D A B is equal adjacent angles altitude angle ABC angle B A C 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 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