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 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