| Sandhurst roy. military coll - 1859 - 1869 pages
...the two parts, together with twice the rectangle contained by the parts. 4. The opposite angles of a **quadrilateral figure inscribed in a circle, are together equal to two right angles.** 5. In a circle, the angle in a semicircle is a right angle, the angle in a segment greater than a semicircle... | |
| Robert Potts - Geometry, Plane - 1860 - 361 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...two right angles, Let ABCD be a quadrilateral figure** in the circle AB CD. Then any two of its opposite angles shall together be equal to two right angles.... | |
| War office - 1861 - 12 pages
...parallelogram equal to a given rectilineal figure and having an angle equal to a given rectilineal angle. 2. **The opposite angles of any quadrilateral figure inscribed...in a circle are together equal to two right angles.** VOLUNTARY PORTION. 1. If two parallel planes be cut by another plane, their common sections with it... | |
| Alexander Hadden Hutchinson - 1861
...of balls in an incomplete pile of 20 courses, with 44 balls in each side of the base. 5. Prove that **the opposite angles of any quadrilateral figure inscribed...a circle, are together equal to two right angles.** If AB, CD be the opposite sides of a quadrilateral circumscribing a circle whose centre is E, prove... | |
| War office - 1861
...from the opposite angle. Prove this only when the triangle has an obtuse angle. 3. The opposite angle **of any quadrilateral figure inscribed in a circle, are together equal to two right angles.** 4. Triangles and parallelograms of the same altitude are to one another as their bases. 5. If two parallel... | |
| Euclides - 1862
...to the whole angle BED. (ax. 2.) Conclusion. — Therefore, the angles in the same segment, &c. QED **PROPOSITION 22.— THEOREM. The opposite angles of...a circle, are together equal to two right angles.** (References— Prop. 1. 32; III. 21.) Hypothesis. — Let ABCD be a quadrilateral figure inscribed... | |
| Robert Potts - 1864
...the whole angle BET), (ax. 2.) Wherefore the angles in the same segment, &c. QED PROPOSITION XXII. **THEOREM. The opposite angles of any quadrilateral...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.... | |
| Alexander Kennedy Isbister - 1865
...to the whole angle BED. (ax. 2.) Wherefore, the angles in the same segment, &c. QED PROP. XXII.— **THEOREM. The opposite angles of any quadrilateral...a circle, are together equal to two right angles.** (References — Prop. I. 32; in. 21.) Let ABCD be a quadrilateral figure in the circle ABCD. Then any... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...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 of any...angles shall be together equal to two right angles.** Join AC, BD. Then, because the three angles of every triangle are together equal to two right angles,... | |
| Robert Potts - 1868 - 410 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... | |
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