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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... "
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... - Side 88
av Sir John Leslie - 1820 - 465 sider
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 sider
...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 right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment Jess than...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 522 sider
...away from 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,...is obtuse. Let ABD be an angle in a semicircle, or that stands on the semicircumference AED; it is a right angle.For ABD, being an angle at the circumference,...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 542 sider
...away from 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,...smaller segment is obtuse. Let ABD be an angle in a semicirclej or that stands on the semicircumference AED; it is a right angle. For ABD, being an angle...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 542 sider
...(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....
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833 - 304 sider
...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...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

1835 - 684 sider
...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,...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 sider
...subtending 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,...
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The London University Calendar

London univ - 1846 - 326 sider
...equations : Sx+4 30-2*7*— 14 ' 5 ~ x-6 ~ 10 ' (2.) &— xy=48y\ xy— y*=3x J ' (3.) *+— a«=0. 9. 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...
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 196 sider
...square and one side of a rectangle which is equal to the square, find the other side. 3. In 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...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 sider
...elementary principles, is as impossible as the trisection of an angle. PROP. XXXI. THEOREM. In 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 anyle in a segment less than...
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