 | Euclides - 1838 - 264 pages
...was to be done.PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right angle; tut 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,... | |
 | Robert Gibson, James Ryan - Surveying - 1839 - 452 pages
...each other, for they are all measured by half the arc they stand on, viz. by half the arc AB Fig. 36. Cor. 3. Hence an angle in a segment greater than a...the arc AB is less than a semicircle, therefore half the arc AB, or the angle ADB, is less than half a semicircle, and consequently less than a right angle.... | |
 | Euclides - 1840 - 192 pages
...ABD is less than a right angle a Prop. 32). But L ABD=Z. AFD (m. Prop. 2i) ; therefore Z. AFD or the angle in a segment greater than a semicircle is less than a right angle. And the angle in a segment AGD less than a semicircle, is greater than a right angle. For take any... | |
 | Euclides - Geometry - 1841 - 378 pages
...Which was to be done. PROP. XXXI. THEOR. In, a circle, the angle in a semicircle is a rig hi 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 ABCD be a circle,... | |
 | Euclides - 1842 - 316 pages
...bisected in D. QEF 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 angle. Let ABC D be a circle,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...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 angle. Let A BCD be a circle,... | |
 | Cambridge univ, exam. papers - 1843 - 50 pages
...divides them into two equal parts. 2. In a circle the angle in a semi-circle is a right angle ; but the angle in a segment greater than a semi-circle is less than a right angle ; and the angle in a segment less than a semi-circle is greater than a right angle. 3. What sum must... | |
 | Euclid - Geometry - 1845 - 218 pages
...done. PROPOSITION 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 angle. Let ABCD be a circle,... | |
 | Scottish school-book assoc - 1845 - 444 pages
...to AB. PROPOSITION LII. — THEOREM. An angle ADB in a semicircle is a right angle, and an angle DBA in a segment greater than a semicircle is less than a right angle, and an angle AED in a segment less than a semicircle is greater than a right angle. and v DC=CB, the... | |
 | Euclides - 1845 - 546 pages
...in DQEF 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 rig/it angle; and \he angle in a segment less than a semicircle is greater than a right angle. Let... | |
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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. 
