 | Sir John Leslie - 1809 - 522 σελίδες
...the other, the equal arcs BE and FG, and there results the arc FAE triple of AB. PROP. XXVI. THEOR. The angle in a semicircle is a right angle, the angle in a greater segment is acute, and the angle in a smaller segment is obtuse. Let ABD be an angle in a semicircle,... | |
 | Sir John Leslie - 1817 - 456 σελίδες
...another mode of drawing a parallel through a given point to a given straight line. PROP. XIX. THEOR. The angle in a semicircle is a right angle, the angle in a greater segment is acute, and the angle in a smalkr segment is obtuse. Let ABD be an angle in a semi-circle,... | |
 | Euclides - 1821 - 294 σελίδες
...extremities of the bisected line. , 138 PROP. 31, THEOR. tn a circle, the angle in a semicircle in a right angle , the angle in a segment greater than a semicircle it an acute angle, and the angle in a segment lest than a semicircle is obtuse. PART 1. The angle in... | |
 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...are equal (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 - 1829 - 210 σελίδες
...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... | |
 | Euclides - 1833 - 304 σελίδες
...the connecting lines, are = ; .-. the arcs, which they subtend, are = ; .-., &c. PROP. 31. THEOR. In a circle, the 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... | |
 | 1835 - 684 σελίδες
...they stand -wi cor. 86 (y) Angles in the same segment of a circle are equal to one another 8(i (A) The angle in a semicircle is a right angle ; the angle in a segment, which is greater than a semicircle, is less than a right angle ; and the angle in a segment, which... | |
 | Euclides - 1840 - 82 σελίδες
...equal arches are equal. PROP. XXX. PROB. To bisect a given arch of a circle. A 3 PROP. XXXI. THEOR. The 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 an obtuse angle. PROP. XXXII.... | |
 | Euclides - 1845 - 546 σελίδες
...bisected in DQEF PROPOSITION XXXI. THEOREM. 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 rig/it angle; and \he angle in a segment less than a semicircle is greater than a right angle. Let... | |
 | Euclides - 1853 - 334 σελίδες
...the point D. Which was to be done. PEOP. XXXI. THEOE. In a circle, the angle in a semicircle shall be a right angle ; the angle in a segment greater than a semicircle shall be less than a right angle ; and the angle in a segment less than a semicircle shall be greater... | |
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Angles in the same segment of a circle are equal ; and, if the line joining two points subtends equal angles at two other points on the same side of it, the four points lie on a circle. 
