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" 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 Elements of Euclid for the Use of Schools and Colleges: Comprising the ... - Page 102
by Euclid, Isaac Todhunter - 1867 - 400 pages
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 196 pages
...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 semicircle is greater than a right angle. The greatest rectangle that can be inscribed in a circle is a square. 4. Cut off a segment from a given...
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Papers for the schoolmaster, Volumes 1-6

582 pages
...omitted it ? 2. A segment of a circle being given, describe the circle of which it is the segment. 3. In a circle, the angle in a semicircle is a right...than a semicircle is less than a right angle ; and t'ne right angle in a segment less than a semicircle is greater than a right angle. State the converse...
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A Manual of Surveying for India, Detailing the Mode of Operations on the ...

Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...each other or they are all measured by hp1P the arc they stand on, viz. by half the arc AB. Cor. 3. An angle in a segment greater than a semicircle is less than a right angle; thus ADB is measured by half the arc AB, but as the arc AB is less than a semi-circle, the arc AB or...
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Five Years in an English University, Volume 2

Charles Astor Bristed - 1852 - 470 pages
...angle at the circumference, upon the same base, that is, upon the same part of the circumference. 5. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. 6. If a straight line be drawn parallel to one of the sides of a triangle, it will cut the other sides,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Geometry - 1853 - 336 pages
...sixteen, &c. equal parts. N PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right angle i but the angle in a segment greater than a semicircle...than a right angle. Let ABCD be a circle, of which the diameter is BC, and centre E ; draw CA dividing the circle into the segments ABC, ADC, and join...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...ad, dc; the angle in the semicircle bac is a right angle ; and the angle in the segment abc, which is greater than a semicircle, is less than a right angle ; and the angle in the segment adc, which is less than a semicircle, is greater than a right angle. Join ae, and produce...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...DC : the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC, which is greater than a semicircle, is less than a right angle ; and the angle in the segment ADC, which is less than a semicircle, is greater than a right angle. Join AE, and produce...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...AD, DC: the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC, which is greater than a semicircle, is less than a right angle ; and the angle in the segment ADC, which is less than a semicircle, is greater than a right angle. 3omAE, and produce...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...right angle. Hence the angle in the semicircle BAC is a right angle ; the angle in the segment ABC greater than a semicircle is less than a right angle ; and the angle ADC in the segment less than a semicircle is greater than a right angle. Which was to be proved. COB....
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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 522 pages
...them must be a right angle. 54. PROP. VI. The 'angle in a segment' equal to a semi-circle is a right angle ; in a segment greater than a semi-circle is less than a right angle ; and in a segment less than a semi-circle is greater than a right angle. Let ABCD be a circle of which AB...
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