| 1874
...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... | |
| Madras - 1874
...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.... | |
| James Bryce - 1874
...III. 22).— Hence also if a quadrilateral figure be inscribed in a circle, its two opposite angles **are together equal to two right angles. Let ABCD be a quadrilateral figure inscribed in** a circle, any two of its opposite angles are together equal to two right angles. Join the centre 0... | |
| Education Department,London - 1876
...В are tangents at A, B, and AD is a diameter. Shew that the angle AC В is twice the angle BAD. 3. **The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles.** The lines bisecting any angle of the inscribed quadrilateral and the opposite exterior angle meet in... | |
| Edward Atkins - 1876
...<fee. QED mid also = 2 i BED. .'. ^ BAD = i. BED. i BAC = /: EEC, and i CAD = ^ CED. .-. i BAD = ^ UED. **Proposition 22.— Theorem. The opposite angles of...any quadrilateral figure inscribed in a circle are** togetlier equal to two right angles. Let ABCD be a quadrilateral figure inscribed in the circle ABCD.... | |
| H. Loehnis - 1876
...bo equal to a given rectilineal figure. ADDITIONAI, GEOMETRY. 7. Prove that the opposite angles of a **quadrilateral figure inscribed in a circle are together equal to two right angles.** When can a parallelogram be inscribed in a circle ? 8. Rectangles of the same altitude are one to another... | |
| Robert Potts - Geometry - 1876 - 403 pages
...to the whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QED PROPOSITION XXII. **THEOREM. The opposite angles of any quadrilateral figure inscribed in a circle,** art together equal to twu right angles. Let ABCD be a quadrilateral figure in the circle ABCD. Then... | |
| D. Tierney - 1877
...straight line which joins their centres being produced, shall pass through that point of contact. 7. **The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles.** From the point C, the straight lines CA and CB are drawn touching the circle PAB whose centre is O... | |
| Āryabhaṭa - 1878
...eirck from a point, cither within its circumference or without it. PROP. XLI. TIIEOREM. (E. 3. 22). **The opposite angles of any quadrilateral figure inscribed...in a circle, are together equal to two right angles** and conversely if the opposite angles of a quadrilateral figure are together equal to two right angles,... | |
| Euclides, James Hamblin Smith - Geometry - 1878 - 349 pages
...equiangular to each other. PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral figure, i **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 L s be together equal to two rt. L s. Draw... | |
| |