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 159
... proved equal to the base F C. Therefore the angle FAD is equal ( I. 8 ) to the angle FBC . But it has been proved that GA is equal to B H , and also A F to FB . Therefore FA and A G are equal to FB and B H , each to each , and the angle ...
... proved equal to the base F C. Therefore the angle FAD is equal ( I. 8 ) to the angle FBC . But it has been proved that GA is equal to B H , and also A F to FB . Therefore FA and A G are equal to FB and B H , each to each , and the angle ...
Σελίδα 166
... proved to be perpen- dicular to the other plane CK . Therefore the plane DE is at right angles to the plane CK . In like manner , it may be proved that all planes which pass through AB are at right angles to the plane CK . Therefore ...
... proved to be perpen- dicular to the other plane CK . Therefore the plane DE is at right angles to the plane CK . In like manner , it may be proved that all planes which pass through AB are at right angles to the plane CK . Therefore ...
Σελίδα 173
... proved to be equal and similar to one another . Q. E. D. This proposition is not sufficiently general , as it refers only to rectangular parallelo- pipeds , which are equal by coincidence . To extend it to those solids which are equal ...
... proved to be equal and similar to one another . Q. E. D. This proposition is not sufficiently general , as it refers only to rectangular parallelo- pipeds , which are equal by coincidence . To extend it to those solids which are equal ...
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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