 | John Playfair - Mathematics - 1806 - 320 pages
...Therefore the given arch ADB e Cor. 1. 5. is bisected in D. Which was to be done. Book in PROP. XXXI. THEOR. IN a circle the angle in a semicircle is a...the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment Jess than a semicircle is greater than a right... | |
 | Robert Simson - Trigonometry - 1806 - 548 pages
...circumference DB: therefore the given circumference is bisected in D. Which was to be clone. C PROP. XXXI. THEOR. 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 right angle ; and the angle... | |
 | Sir John Leslie - Geometry, Plane - 1809 - 522 pages
...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,... | |
 | John Mason Good - 1813 - 714 pages
...XXX. Prob. To bisect a given circumference, that is, to divide it into two equal parts. Prop. XXXI. Theor. 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 right angle; and the angle... | |
 | Euclides - 1816 - 592 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 angle; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle... | |
 | Sir John Leslie - Geometry - 1817 - 456 pages
...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,... | |
 | John Playfair - 1819 - 354 pages
...the 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 angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the 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 angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle... | |
 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...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 - Geometry - 1829 - 210 pages
...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... | |
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