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 164
... meet one another when produced . produced and meet ; and let the straight line G H be their common section . In GH , take any point K , and join A K and BK . Let them be G KH F E Because A B is perpendicular to the plane E F it is ...
... meet one another when produced . produced and meet ; and let the straight line G H be their common section . In GH , take any point K , and join A K and BK . Let them be G KH F E Because A B is perpendicular to the plane E F it is ...
Σελίδα 165
... meet one another . But they do not meet , because they are parallel ( Hyp . ) . Therefore the straight lines EF and GH do not meet when produced on the side of FH . In the same manner , it may be proved that EF and GH do not meet when ...
... meet one another . But they do not meet , because they are parallel ( Hyp . ) . Therefore the straight lines EF and GH do not meet when produced on the side of FH . In the same manner , it may be proved that EF and GH do not meet when ...
Σελίδα 211
... meet the less sphere . Also the other planes between the quadrants BX and K X do not meet the less sphere . From the point A draw A I perpendicular to the plane of the quadrilateral S OPT , and join IO . In the same manner , as it was ...
... meet the less sphere . Also the other planes between the quadrants BX and K X do not meet the less sphere . From the point A draw A I perpendicular to the plane of the quadrilateral S OPT , and join IO . In the same manner , as it was ...
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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