| Euclides - Euclid's Elements - 1837 - 112 pages
...base DB 2. that :. AD — DB. 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... | |
| Euclides - 1838 - 264 pages
...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...angle. Let ABCD be a circle, of which the diameter is BC, and centre E : and draw CA, dividing the circle into the segments ABC, ADC, and join BA, AD,... | |
| Robert Simson - Geometry - 1838 - 434 pages
...if the centre falls without the triangle, the angle opposite to the side beyond which it is, being in a segment less than a semicircle, is greater than a right angle : wherefore, if the given triangle be acute angled, the centre of the circle falls within it ; if it... | |
| Euclides - 1840 - 82 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 an obtuse angle. PROP. XXXII. THEOR. If a straight line touches a circle, and from the point of contact... | |
| Euclides - Geometry - 1841 - 378 pages
...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...angle. Let ABCD be a circle, of which the diameter is BC, and centre E; and draw CA, dividing the circle into the segments ABC, ADC, and join BA, AD,... | |
| Euclides - 1842 - 316 pages
...given circumference is 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... | |
| John Playfair - Euclid's Elements - 1842 - 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... | |
| Cambridge univ, exam. papers - 1843 - 50 pages
...bisects them, that is, 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... | |
| Scottish school-book assoc - 1845 - 444 pages
...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 ZCBD = the ZBDC, .-. the whole .ADB is = the two it DAB and DBA, but the ZFDB is also... | |
| Euclid - Geometry - 1845 - 218 pages
...in D. Which was to be 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... | |
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