| 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... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...triangles formed by joining their extremities are equiangular to each other. PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral figure, inscribed...a circle, are together 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... | |
| Euclides - 1872 - 102 pages
...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 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... | |
| Henry Major - Student teachers - 1873 - 580 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...in a circle are together equal to two right angles. Let ABCD be a quadrilateral figure inscribed in ABCD , any two of its opposite angles shall be together... | |
| University of Madras - 1874 - 502 pages
...line AB in C so that the rectangle contained by AC, CB may be twice the square on AC. II. Provp that the opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. Also state and prove the converse of this proposition. III. Inscribe a circle in a given triangle.... | |
| Braithwaite Arnett - 1874 - 130 pages
...the centre, it shall cut it at right angles ; and if it cut it at right angles it shall bisect it. 6. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. From the point A in the circumference of the circle APQB three chords AP, AQ, and AB are drawn so that... | |
| Euclides - 1874 - 342 pages
...angle BED (Ax. 2). Wherefore, the angles in the same segment, &c. Q ED PROPOSITION 22. — Theorem. The opposite angles of any quadrilateral figure inscribed,...a circle, are together equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD. Then any two of its opposite angles shall together... | |
| Edward Atkins - 1874 - 428 pages
...segment, &c. QED and also = 2 {. BED. .". i BAD = t BED. BAC = BEC, and Proposition 22.— Theorem. The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. Let ABCD be a quadrilateral figure inscribed in the circle ABCD. Any two of its opposite angles shall... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...of the ©: and join QH. Then segment APQBH is > a semicircle; . ..-. LAPH= L PROPOSITION XV. 77/i? opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles. Let ABFG be a quadrilateral figure inscribed in the circle ABF. Then shall the L s ABF, AGF be together... | |
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