 | Euclides - 1845 - 546 pages
...circumference is bisected 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... | |
 | London univ - 1846 - 326 pages
...9. 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. 10. Inscribe in a given circle an equilateral and equiangular hexagon. 1 1 . Define the sector of a... | |
 | Nathaniel Bowditch - 1846 - 854 pages
...arc DKF, that is, by half a semicircle or by a quadrant ; therefore the angle DEF is a right one. An angle in a segment less than a semicircle is greater than a right angle. Thus, if GUI be a segment less than a semi-circle, the arc GKI on which it stands must be greater than... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 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 then a right angle ; and the angle in a segment less than a semicircle is greater than a right... | |
 | Euclides - 1846 - 292 pages
...if the centre fall without the triangle, the angle opposite to the side beyond which it falls, 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 will fall within it ;... | |
 | Euclides - 1846 - 272 pages
...21. B. 3.), and therefore the angle ABC is also less than a right angle. PART 3. — The angle ABC in a segment less than a semicircle is greater than a right angle. For assume in the opposite circumference any point D, and draw DA and DC. Therefore since in the quadrilateral... | |
 | John Playfair - Euclid's Elements - 1847 - 340 pages
...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...a semicircle is greater than a right angle. ' Let A BCD be a circle, of which the diameter is BC, and centre E ; draw CA dividing the circle into the... | |
 | Great Britain. Council on Education - Education - 1848 - 532 pages
...different things, taking r of them together. Section 3. 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... | |
 | Bengal (India) - 1848 - 520 pages
...of a triangle are together greater than the third side. 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... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...different things, taking r of them together. SECTION III. 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... | |
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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. 
