 | Rev. John Allen - Astronomy - 1822 - 508 pages
...(as ABC), in a segment greater than a semicircle, is less than a right angle; and an angle (as ADC), in a segment less than a semicircle, is greater than a right angle. Let E be the centre of the circle, join AE, and produce BA, as to F; and because, in the triangle EAB,... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...two right angles. THEOREM 37. 94. An angle ABD, in a semi-circle, is a right angle ; an angle BAD, in a segment greater than a semi-circle, is less than a right angle ; and an angle, BED, in a segment less than a semi-circle, is greater than a right angle. Produce AB to F,... | |
 | James Mitchell - Mathematics - 1823 - 666 pages
...semi-circle, or standing upon a semi-circle or diameter. An ancle in a semi-circle, is a right-angle. An angle in a segment, greater than a semi-circle, is less than a right-angle. An angle in a segment, less than a semi-circle, is greater than a right-angle. ANGULAR,... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...; the angle in the semicircle ВАС is a right angle ; and the angle in the segment ABC, which is greater than a semicircle, is less than a right angle; and the angle in the segment ADC, which is less than a semicircle, is greater than a right angle. Join AE, and produce... | |
 | 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 - 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... | |
 | 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;... | |
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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. 
