| 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 - 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
...2.) Conclusion. — Therefore, the angles in the same segment, &c. QED PROPOSITION 22.— THEOREM. The opposite angles of any quadrilateral figure inscribed...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 - 1865 - 528 pages
...whole angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QED PROPOSITION XXn. 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 AB CD. Then any two of its opposite angles shall together... | |
| Euclides - 1865 - 402 pages
...III. 20. 2. The angles in the same segment of a circle are equal to one another. ........ m. 21. 3. The opposite angles of any quadrilateral figure inscribed...in a circle, are together equal to two right angles . . . HI. 22. 4. In equal circles, equal angles stand upon equal arcs, whether the angles be at the... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...whole angle BED. [Axiom 2. Wherefore, the angles in the same segment &c. QED 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... | |
| Robert Potts - 1868 - 434 pages
...angle BED. (ax. 2.) Wherefore the angles in the same segment, &c. QEI». PROPOSITION XXII. THEOREM. The opposite angles of any quadrilateral figure inscribed...a 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... | |
| James Maurice Wilson - Geometry - 1868 - 150 pages
.... 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 - 172 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.... | |
| General Medical Council (Great Britain) - 1869 - 402 pages
...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... | |
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