 | John Playfair - 1829 - 210 σελίδες
...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 - 1830 - 584 σελίδες
...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 - 1830 - 274 σελίδες
...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 - 1831 - 282 σελίδες
...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 σελίδες
...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 - 1834 - 212 σελίδες
...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... | |
 | 1835 - 684 σελίδες
...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 - 1836 - 524 σελίδες
...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. This is nearly self-evident : let A be the angle, and B the point in the line. On A describe an arc... | |
 | John Playfair - 1836 - 148 σελίδες
...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... | |
 | Euclides - 1837 - 112 σελίδες
...BCD == 2 right Z s, 6. that ZS DBF + DBE = ZS BAD + BCD, 7- that Z DBE = Z BCD. PROPOSITION XXXIII. Problem. Upon a given straight line to describe a segment of a circle containing an angle equal to a given -^ * K rectilineal angle. The proof of case 1st, in which Z c... | |
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Upon a given straight line to describe a segment of a circle, which shall contain aa angle equal to a given rectilineal angle. 
