 | Henry White - 1864 - 156 pages
...either without or in the circumference, which shall touch a given circle. 7. 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... | |
 | J. F. H. de Rheims - Geometrical drawing - 1865 - 336 pages
...and if it cuts it at right angles it shall bisect it. Prop. 31. — 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... | |
 | Robert Potts - 1865 - 528 pages
...Therefore the given arc ADB is bisected in DQE p. / PROPOS1TION XXX1. THEOREM. In a circle, the angle in a semicircle is a right angle ; but the angle in a legment greater than a semicircle is less than a right angle; and the angle in a segment less than... | |
 | Euclides - 1865 - 402 pages
...a given circumference, that Is, to divide it into two equal parts. Prop. 31. 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...arc DB. Wherefore the given arc is bisected at DQEF PKOPOSITION 31. 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... | |
 | Edinburgh univ - 1868 - 334 pages
...answers, must be exhibited. VIII. HIGHER MATHEMATICS. 22af October 1867. 1. 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... | |
 | Robert Johnston (F.R.G.S.) - Civil service - 1869 - 196 pages
...either without or in the circumference, which shall touch a given circle. 7. 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... | |
 | Henry Major - Student teachers - 1873 - 588 pages
...passes through the centre: therefore the arc AD is equal to the arc DB. XXXI. — 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... | |
 | Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...= two right angles. (i. 24) Similarly it may be proved that PROPOSITION XVI. 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... | |
 | Euclides - 1874 - 342 pages
...Therefore the given arc ADJB is bisected in DQEF PROPOSITION 31. — 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... | |
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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 angle. 
