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 55
... segment is that which is contained by the straight line and the circumference . ] This definition appears to be an interpolation . It is not used and need not be remembered . VIII . An angle in a segment is the angle contained by two ...
... segment is that which is contained by the straight line and the circumference . ] This definition appears to be an interpolation . It is not used and need not be remembered . VIII . An angle in a segment is the angle contained by two ...
Σελίδα 71
... segments of circles which do not coincide . Q. E. D. Corollary . If there be two segments of circles on the same base or chord , the larger segment contains the smaller angle . PROP . XXIV . THEOREM , Similar segments of circles upon ...
... segments of circles which do not coincide . Q. E. D. Corollary . If there be two segments of circles on the same base or chord , the larger segment contains the smaller angle . PROP . XXIV . THEOREM , Similar segments of circles upon ...
Σελίδα 78
... segment A HB . But the angle DAB is equal ( Const . ) to the angle C. Therefore the angle C is equal ( I. Ax . 1 ) to the angle in the segment A H B. Wherefore , upon the given straight line A B , the segment of a circle A H B is ...
... segment A HB . But the angle DAB is equal ( Const . ) to the angle C. Therefore the angle C is equal ( I. Ax . 1 ) to the angle in the segment A H B. Wherefore , upon the given straight line A B , the segment of a circle A H B is ...
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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