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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: Viz. the First Six Books, Together with the Eleventh ... - Page 79
by Euclides - 1816 - 528 pages
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853
...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 - 192 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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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - Science - 1854
...THEOREM. The angle (ВАС) in a semicircle (BADC) is a right angle : the angle in a segment (ABGC) greater than a semicircle, is less than a right angle : and the angle (D) in a segment (ADC) less than a semicircle, is greater than a right angle. From the centre, E, draw...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855
...and if it cuts it at right angles it shall bisect it. 7. 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. 8. To inscribe a circle in a given square. ALGEBRA. — (SECOND SECTION.) 1. Add together — (a +...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 318 pages
...in a semicircle is a right angle ; but the angle tn a segment greater than a semicircle is less then a right angle ; and the angle in a segment less than a semicircle is greater than a right angle. Let A BCD be a circle, of which the diameter is BC, and centre E ; draw CA dividing the circle into the...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...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 a semicircle is greater than a right angle. Let AB СD be a circle, of...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...angle at the circumference, upon the same base, that is, upon the same part of the circumference. 13. In a circle, the angle in a semicircle is a right...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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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...the point of contact. 10. In a circle, the angle in a semicircle is a right angle; bu.t the angle iii a segment greater than a semicircle is less than a...less than a semicircle is greater than a right angle. 11. From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - Cabinetwork - 1856 - 216 pages
...two right angles. THEOREM 37. 94. An angle ABD, in a semi-circle, is a right angle ; an 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,...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...in ADC and join AB, AE, AD, D C. The angle BAC is a right.angle ; the angle ABC in the segment ABC greater than a semicircle is less than a right angle ; and the angle ADC in the segment ADC less than a semicircle is greater than a right angle. Because EB is equal to...
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