| James Maurice Wilson - Geometry - 1868
.... 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 - 112 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.... | |
| Dr. Francis Hawkins - 1869
...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 - 349 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
...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
...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
...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... | |
| c. foster and co - 1873
...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... | |
| James Martin (of the Wedgwood inst, Burslem) - 1874
...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.... | |
| 1874
...of the ©: and join QH. Then segment APQBH is > a semicircle; . ..-. LAPH= L PROPOSITION XV. 77/i? **opposite angles of any quadrilateral figure inscribed...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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