| John Playfair - Geometry - 1829 - 210 pages
...B4C is equal to the angle ADC in the alternate segment ADC. ED. B « PROPOSITION XXXIII. PROBLEM. On **a given straight line to describe a segment of a circle, which shall contain an angle equal to a given** rectilineal angle ; that is, to describe a segment such that all the angles described in it shall be... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...ingenuity, in problems of contact. PBOP. 60. Prob. 7. (Eue. iii. 33.) Upon a given straight line AB **to describe a segment of a circle which shall contain an angle equal to a given angle** ABC. Let AQ В be the segment required, and P its centre. Then, because the angle А В С is equal... | |
| Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...tangent, touching the circles on opposite sides. The demonstration is the same as the last. PROBLEM XVI. **Upon a given straight line to describe a segment of a circle, which shall contain** a given angle ; that is, a segment, such that the inscribed angles, having their vertices in the arc... | |
| John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...integrals of x*dm, y-dm, and xydm for the whole spheroid being given. TRINITY COLLEGE, MAY 1830. 1. **UPON a given straight line to describe a segment of a circle** containing an angle equal to a given rectilineal angle. 3x~ — 2xy — if1 2. Reduce the fraction... | |
| Euclides - 1834 - 518 pages
...segment of the circle. Wherefore, if a straight line, &c. QBD /> PROPOSITION XXXIII. See N. PROR. — **Upon a given straight line to describe a segment of a circle, which shall contain** aa angle equal to a given rectilineal angle. Let AB be the given straight line, and the angle at C... | |
| Francis Joseph Grund - Geometry, Plane - 1834 - 212 pages
...tangent, touching the circles on opposite sides. The demonstration is the same as the last. PROBLEM XVII. **Upon a given straight line to describe a segment of a circle, which shall contain** a given angle ; that is, a segment, such that the inscribed angles, having their vertices in the arc... | |
| Mathematics - 1835 - 684 pages
...ingenuity, in problems of contact. PROP. 60. Prob. 7. (Eue. iii. 33.) Upon a given straight line AB **to describe a segment of a circle which shall contain an angle equal to a given angle** ABC. Let AQ В be the segment required, and P its centre. Then, because the angle А В С is equal... | |
| Robert Mudie - Mathematics - 1836 - 542 pages
...right angle ; and an angle in a segment greater than a semicircle is always less than a right angle. **The difference of the angle from a right angle is...in a given line, an angle equal to a given angle.** CONSTRUCTING AN ANGLE. 397 This is nearly self-evident : let A be the angle, and 11 the point in the... | |
| John Playfair - Geometry - 1836 - 148 pages
...AE, EC is equal to the rectangle BE, ED. Wherefore, if two straight lines, &c. QED PROP. XXV. PROB. **Upon a given straight line to describe a segment of a circle,** containing an angle equal to a given angle. Let AB be the given straight line, and the angle at C the... | |
| Andrew Bell, Robert Simson - Euclid's Elements - 1837 - 290 pages
...remaining angle DBE is equal to the angle BCD in the alternate segment of the circle. PROPOSITION XXXIU/ **PROBLEM. - Upon a given straight line to describe a segment of a circle,** containing an angle equal to a given rectilineal angle. Let AB be the given straight line, and the... | |
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