 | George Lees - 1826 - 276 pages
...VIII. THEOREM. . . i In a circle, the angle BAC in a semicirle is a right angle ; but, the angle ABC in a segment greater than a semicircle, is less than a right angle ; and the angle ADC, in, a segment, less than a semicirle, is greater than a right angle. Produce BA to F, takeE, the... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...eirele, the angle in a semieirele is a right angle ; but the angle in a segment greater than a semieirele is less than a right angle ; and the angle in a segment less than a semieirele is greater than a. right angle. Let ABCD be a eirele, of whieh the diameter is BC, and eentre... | |
 | Nathaniel Bowditch - Nautical astronomy - 1826 - 732 pages
...arch DKF, that is, by half a semicircle or by rt quadrant ; therefore the angle DEF is a right one. An angle in a segment less than a semicircle is greater than a right angle. ' J* Thus if GHI be a segment less than a semicircle, the arch GLI on which it stands must be greater... | |
 | Nathaniel Bowditch - Nautical astronomy - 1826 - 764 pages
....N equal to each other ; for they are all measured by the same arch, viz. half the arch AB. XLII. An angle in a segment greater than a semicircle is less than a right angle. Thus if ABC be a segment greater than a semicircle, the arch AC on which it stands must be less than... | |
 | Euclides - 1826 - 226 pages
...COROLLARY. Hence it is manifest, when the centre of the circle falls within the triangle, the angle BAC, in a segment greater than a semicircle, is less than a right angle; but when the centre falls on the right line в с, the angle BAC, in a semircircle, is a right angle;... | |
 | Euclid - 1826 - 234 pages
...COROLLARY. Hence it is manifest, when the centre of the circle falls within the triangle, the angle BAC, in a segment greater than a semicircle, is less than a right angle ; but when the centre falls on the right line вс, the angle BAC, in a semrrcircle, is a right angle;... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...Which was to be done. 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 semicircle is greater than a right angle. Let ABCD be a circle, of which the diameter is BC, and centre E; and draw CA, dividing the circle into... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...(XXVIII), and therefore the given arc is bisected in B. PROPOSITION XXXI. THEOREM. (389) In a circle the angle in a semicircle is a right angle, the angle in a segment greater than a semicircle is acute, and the angle in a segment less than a semicircle is obtuse. Part 1°. — The angle ABC in... | |
 | John Playfair - Geometry - 1829 - 210 pages
...is evident from the demonstration. ED. PROPOSITION XXXI. THEOREM. The angle at the circumference of a semicircle is a right angle; the angle in a segment greater than a semicircle is acute; and the angle in a segment less than a semicircle is obtuse. Let ABCD be a circle, of which... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...semi-circumference, that is, by a quadrant. Cor. 2. (Eue. iii. 31 second part of.) The angle, which is in a segment greater than a semicircle, is less than a right angle ; and the angle, which is in a segment less than a semicircle, is greater than a and let the diameters A Qj, QQ, be... | |
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... a circle. 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. 
