| Robert Simson - Trigonometry - 1827 - 546 pages
...is bisected in D. Which was to be done. PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right... | |
| Euclides - 1833 - 304 pages
...angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is an acute angle ; and the angle in a segment less than a semicircle is obtuse. PART 1. The angle in a semicircle is a right angle. Draw a diameter connecting the extremities... | |
| Euclides - 1834 - 518 pages
...bisected in D. Which was to be done. PROPOSITION XXXI. THEOR — In a circle, Ihe angle in a semicircle is a right angle ; but the angle in a segment greater...than a right angle ; and the angle in a segment less litan a semicircle, is greater than a right angle. Let ABCD be a circle, of which the diameter is BC,... | |
| Euclid - 1835 - 540 pages
...Which was to be done. Book III. PROP. XXXI. THEOR. ^ /— ' In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right... | |
| Mathematics - 1836 - 366 pages
...angle in a semicircle is a right angle, but 1829 the angle in a segment greater than a semicircle is less than a right angle, and the angle in a segment...less than a semicircle is greater than a right angle. 4. If two triangles have the sides about equal angles reciprocally proportional, they are equal. 5.... | |
| George Darley - Euclid's Elements - 1836 - 172 pages
...ART. 73. The angle in a segment greater than the semicircle is less than a right angle, ibid. ART. 74. The angle in a segment less than a semicircle is greater than a right angle,ibid. ART. 75. If a tangent and a chord of a circle be drawn from the same point, ths angle between... | |
| John Playfair - Geometry - 1836 - 148 pages
...bisected in D. Which was to be done. PROP. XXII. THEOR. In a circle, the angles in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right... | |
| Mathematics - 1836 - 488 pages
...equal arches are subtended by equal straight lines. XXXI. In a circle, the angle in a simicircle is a right angle ; but the angle in a segment greater than a simicircle is less than a right angle; and the angle in a segment less than a simicircle is greater... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...the given arc is bisected in D. PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...four, eight, sixteen, &c. equal parts. PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right... | |
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