 | Robert Johnston (F.R.G.S.) - 1869 - Liczba stron: 196
...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 a semicircle is greater than a right angle. ALGEBRA. I. Specimen... | |
 | Henry Raper - 1870 - Liczba stron: 968
...a diameter, the angle at M, • point on the circumference, is the angle in a semicircle. 142. The angle in a segment greater than a semicircle is less than a right angle. The segment BAG of the circle being greater than a semicircle, the other segment BDCmust be less than... | |
 | Richard Wormell - 1870 - Liczba stron: 304
...centre in the arc AC ; consequently they are equal. The angle in a semicircle is a right-angle ; 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. Let... | |
 | Henry William Watson - 1871 - Liczba stron: 320
...right angles (Bk. I. Prop. 23). PROPOSITION 13. The angle in a semicircle is a right angle, and 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. Let ABDC be a circle... | |
 | Euclides, James Hamblin Smith - 1872 - Liczba stron: 376
...ij. ED PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right angle; and 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. Let ABC be a ©,... | |
 | Euclides - 1872 - Liczba stron: 102
...B. QB p. PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right angle; and 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. Let ABC be a 0, 0... | |
 | Henry Major - 1873 - Liczba stron: 588
...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 a semicircle is greater than a right angle. Let BC be a diameter,... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - Liczba stron: 236
...semicircle is a right angle, an angle in a segment less than a semicircle is greater than a right angle, and an angle in a segment greater than a semicircle is less than a right angle. For the angle AOB at the centre may be increased till it becomes two right angles (I. Def. 9), then... | |
 | Francis Cuthbertson - 1874 - Liczba stron: 400
...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 a semicircle is greater than a right angle. Let A PB be a © of... | |
 | Euclides - 1874 - Liczba stron: 342
...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 a semicircle, is greater than a right angle. Let A BCD be a... | |
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The angle in a semicircle is a right angle ; 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. 
