 | Robert Potts - 1868 - 434 pages
...the whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QEI». PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral...circle, are together equal to two right angles. Let AB CD be a quadrilateral figure in the circle A BCD. Then any two of its opposite angles shall together... | |
 | James Maurice Wilson - Geometry - 1868 - 150 pages
.... 13 COR. 3. The angle in a semicircle is a right angle . . 13 COR. 4. The opposite angles of every quadrilateral figure inscribed in a circle are together equal to two right angles . 14 COR. 5. The locus of a point at which a given straight line subtends a constant angle is an arc... | |
 | E. M. Reynolds - Geometry - 1868 - 172 pages
...= £ 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 pages
...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... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...the triangles formed by joining their extremities are equiangular to each other. PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral...equal to two right angles. Let ABCD be a quadrilateral fig. inscribed in a 0 . Then must each pair of its opposite is lie together equal to two rt. L s. Draw... | |
 | Euclides - 1872 - 102 pages
...proofs, based on the same conceptions, of the important propositions xxn. and xxxi. PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral...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... | |
 | Royal United Services Institute for Defence Studies - Military art and science - 1872 - 742 pages
...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... | |
 | Henry Major - Student teachers - 1873 - 588 pages
...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...angles. Let ABCD be a quadrilateral figure inscribed in ABCD , any two of its opposite angles shall be together equal to two right angles. Join AC, BD. The... | |
 | University of Madras - 1873 - 436 pages
...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... | |
 | Euclides - 1874 - 342 pages
...angle BAD is equal to the whole angle BED (Ax. 2). Wherefore, the angles in the same segment, &c. Q ED PROPOSITION 22. — Theorem. The opposite angles of...two right angles. Let ABCD be a quadrilateral figure in the circle ABCD. Then any two of its opposite angles shall together be equal to two right angles.... | |
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The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. 
