 | Sandhurst roy. military coll - 1859 - 672 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 - 380 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.... | |
 | Alexander Hadden Hutchinson - 1861 - 128 pages
...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 - 714 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... | |
 | War office - 1861 - 260 pages
...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 - 140 pages
...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... | |
 | Euclides - 1864 - 262 pages
...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.... | |
 | Robert Potts - 1865 - 528 pages
...to the whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QED PROPOSITION XXn. 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 bfe equal to two right angles.... | |
 | Euclides - 1865 - 402 pages
...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 - 426 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,... | |
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The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles. 
