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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. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Page 78
by Euclid, John Playfair - 1846 - 317 pages
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...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 in a segment less than a semicircle is greater than a right angle. Let ABCD be a circle, of which the diameter is BC, and centre E ; and draw CA dividing the circle into...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...if the centre falls without the triangle, the angle opposite to the side beyond which it is, being in a segment less than a semicircle, is greater than a right angle : wherefore, if the given triangle be acute-angled, the centre of the circle falls within it ; if it...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...if the centre falls without the triangle, the angle opposite to the side beyond which it is, being in a segment less than a semicircle, is greater than a right angle : wherefore, if the given triangle be acute-angled, the centre of the circle falls within it ; if it...
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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
...semicircle shall be a right angle ; the angle in a segment greater than a semicircle shall be less than a right angle ; and the angle in a segment less than a semicircle shall be greater than a right angle. Let ABC be a circle, and from one of the extremities c of any...
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Elements of geometry and mensuration

Thomas Lund - Geometry - 1854 - 522 pages
...right angle; / BAD 'in a segment' greater than a semi-circle is less than a right angle, and / BCD ' in a segment' less than a semi-circle is greater than a right angle. Join 0D; then since OA = OD, / OAD= L ODA (26) ; and since OB=OD, / OBD = t ODB, .-. / ADB= t OAD +...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 334 pages
...parts. PROP. XXXI. THEOR. O * In a circle, the angle in a semicircle is a right angle ; but the angle tn a segment greater than a semicircle is less then a...CA dividing the circle into the segments ABC, ADC, an<J join BA, AD, DC ; the angle in the semicircle BAC is a right angle ; and the angle in the segment...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...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. 8. To inscribe a circle in a given square. ALGEBRA. — (SECOND SECTION.) 1. Add together — (a +...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...if the centre falls without the triangle, the angle opposite to the side beyond which it is, being in a segment less than a semicircle, is greater than a right angle (III. 31). Conversely, if the given triangle be acute-angled, the centre of the circle falls within...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 pages
...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 in a segment less than a semicircle is greater than a right angle. EUCLID (B). 1. DEFINE a line, a superficies, and the centre of a circle. 2. Upon the same base, and...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - Cabinetwork - 1856 - 482 pages
...angle BAD, in a segment greater than a semi-circle, is less than a right angle ; and an angle, BED, in a segment less than a semi-circle, is greater than a right angle. Produce AB to F, draw В C to the centre, and, because CA is equal to CB, the angle CBA is equal to...
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