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" 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, or that stands on the semicircumference AED; it is a right angle. "
Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious ... - Seite 88
von Sir John Leslie - 1817 - 432 Seiten
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 542 Seiten
...away from the other, the equal arcs BE and PG, and there results the arc FAE triple of AB. PROP. XXVI. THEOR. The angle in a semicircle is a right angle,...on the semicircumference AED; it is a right angle. For ABD, being an angle at the circumference, is half of the angle at the centre on the same base AED...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1809 - 522 Seiten
...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,...stands on the semicircumference AED; it is a right angle.For ABD, being an angle at the circumference, is half of the angle at the centre on the same...
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Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ...

Sir John Leslie - 1811 - 524 Seiten
...angles within a circle, the opposite intercepted arcs are equal to the semicircumference *. PROP. XXII. THEOR. The angle in a semicircle is a right angle,...on the semicircumference AED; it is a right angle. For ABD, being an angle at the circumference, is half of the angle at the centre on the same base AED...
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Rudiments of Plane Geometry: Including Geometrical Analysis, and Plane ...

Sir John Leslie - 1828 - 228 Seiten
...a circle, are together equal to the angle contained in the segment opposite to its vertex. PROP. XL THEOR. The angle in a semicircle is a right angle,...is obtuse. Let ABD be an angle in a semicircle, or standing on the circumference AED; it is a right angle. For ABD, being an angle at the circumference,...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 542 Seiten
...(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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Geometry, plane, solid, and spherical. To which is added, in an appendix ...

Pierce Morton - 1830 - 300 Seiten
...conversely ; also, any angles at the circumference are as the arcs upon which they stand cor. 86 (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 Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833 - 304 Seiten
...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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The First Six Books of the Elements of Euclid: With a Commentary and ...

Dionysius Lardner - 1838 - 382 Seiten
...arc is bisected in B. Draw the right lines AB and C 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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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 196 Seiten
...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 Seiten
...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 angle in a segment less than...
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