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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. "
The Theory and Practice of Surveying: Containing All the Instructions ... - Page 38
by Robert Gibson - 1811 - 508 pages
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First Practical Lines of Geometrical Drawing ...

J. F. H. de Rheims - Geometrical drawing - 1865 - 338 pages
...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 a semicircle is greater than a right angle. EUCLID, BOOK VI. Prop....
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...D. QEF 117 PROP. 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 angle. (References— Prop....
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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 a semicircle is greater than a right angle. Let ABCD be a circle,...
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The Edinburgh university calendar

Edinburgh univ - 1868 - 334 pages
...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 a semicircle is greater than a right angle. 2. Of two straight...
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Civil service guide

Robert Johnston (F.R.G.S.) - Civil service - 1869 - 196 pages
...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...
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The practice of navigation and nautical astronomy. [With] Tables ..., Volume 26

Henry Raper - 1870 - 974 pages
...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...
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...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...
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 320 pages
...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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...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 ©,...
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Elements of geometry, containing the first two (third and fourth ..., Part 2

Euclides - 1872 - 102 pages
...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...
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