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 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 ...
Seite 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 ...
Seite 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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Häufige Begriffe und Wortgruppen
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