 | 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... | |
 | 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... | |
 | 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;... | |
 | 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;... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...circumference DB. Therefore the given circumference is bisected in D. Which was to be done. PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right...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 the segments ABC, ADC, and... | |
 | 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... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...the given arch ADB is bisected in D. Which was to be done. PROP. XXXI. THEOR. In a circle,the angle in a semicircle is a right angle; but the angle in...than a right angle. Let ABCD be a circle, of which the diameter is BC, and centre E; draw CA dividing the circle into the segments ABC, ADC, and join... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...arch DB ; and therefore the given arch ADB is bisected in D. Which was to be done. PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right...than a right angle. Let ABCD be a circle, of which the diameter is BC, and fcentre E ; draw CA dividing the circle into the segments ABC, ADC, and join... | |
 | Euclides - 1833 - 304 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 obtuse. PART 1. The angle in a semicircle is a right angle. Draw a diameter connecting the extremities... | |
 | Euclides - 1834 - 518 pages
...Ihe angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle, ii less than a right angle ; and the angle in a segment less litan a semicircle, is greater than a right angle. Let ABCD be a circle, of which the diameter is BC,... | |
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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. 
