 | Euclid, Isaac Todhunter - 1867 - 424 pagina’s
...angles BAC, BEC in it, are equal, by the first case. For the same reason, because the segment CAED is greater than a semicircle, the angles CAD, CED...the whole angle BAD is equal to the whole angle BED. [Axiom 2. Wherefore, the angles in tJie same segment &c. QED PROPOSITION 22. THEOREM. Tin opposite... | |
 | Euclid, Isaac Todhunter - 1867 - 426 pagina’s
...angles BAC, BEC in it, are equal, by the first case. For the same reason, because the segment CAED is greater than a semicircle, the angles CAD, CED...the whole angle BAD is equal to the whole angle BED. [Axiom 2. Wherefore, the angles in the same segment &c. QED PROPOSITION 22. THEOREM. The opposite angles... | |
 | Robert Potts - 1868 - 434 pagina’s
...circle, therefore the segment B 'ADC is greater than a semicircle ; for the same reason, because CBED is greater than a semicircle, the angles CAD, CED,...the whole angle BAD is equal to the whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QEI». PROPOSITION XXII. THEOREM. The opposite... | |
 | E. M. Reynolds - 1868 - 172 pagina’s
...= £ the convex angle A OS. Therefore ADS + ACS = ^{AOS + AOB], Therefore ADB + ACS = 2fi. COR. 1. The opposite angles of any quadrilateral figure inscribed in a circle are equal to 2R. COB. 2. The angle on a semicircumference or in a semicircle is a right angle. COR. 3.... | |
 | General Medical Council (Great Britain) - 1869 - 402 pagina’s
...drawn from the centre to the point of contact is perpendicular to the line touching the circle. 8. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. 9. From a given circle to cut off a segment which shall contain an angle equal to a given rectilineal... | |
 | Royal United Services Institute for Defence Studies - 1872 - 742 pagina’s
...proves that the angles in the same segment of a circle are equal to one another. The 22nd proves that the opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles, and The 5th of the IV shows how to describe a circle about a given triangle. Sailing along a coast... | |
 | Euclides - 1872 - 102 pagina’s
...based on the same conceptions, of the important propositions xxn. and xxxi. PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral figure, inscribed in a circle, are together equal to two right angle*. Let ABCD be a quadrilateral fig. inscribed in a ©. Then must each pair of its opposite nbe... | |
 | University of Madras - 1873 - 436 pagina’s
...together with three times the square on BD is equal to four times the square on AB. VIII. Prove that the opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. (a.) ABCD is a quadrilateral figure inscribed in a circle ; the opposite sides AB and DC are produced... | |
 | Henry Major - 1873 - 588 pagina’s
...the angles BAC, BEC in it, are equal. For the same reason, because CAED is greater than a semicircle, CAD, CED are equal. Therefore, the whole angle BAD is equal to the whole BED. XXII. — The opposite angles of any quadrilateral figure inscribed in a circle are together equal... | |
 | Edward Atkins - 1874 - 426 pagina’s
...the angles BAG, BEC in it are equal by the first case. For the same reason, because the segment CBED is greater than a semicircle, the angles CAD, CED...the whole angle BAD is equal to the whole angle BED (Ax. 2). Therefore, the angles in the same segment, &e. QED and also = 2 i BED. .-. ^ BAD = ^ BED.... | |
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CBED is greater than a semicircle, the angles CAD, CED are equal : therefore the whole angle BAD is, equal to the whole angle BED. 
