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" ... a circle. 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. The opposite angles of any quadrilateral... "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 135
by Euclides - 1833
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 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...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - Geometry, Plane - 1809 - 493 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,...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 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...
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Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ...

Sir John Leslie - Geometry - 1817 - 432 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,...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 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...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 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...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 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...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 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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