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 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 ...
Σελίδα 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. ...
Σελίδα 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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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