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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. "
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... - Page 144
by Robert Potts - 1876 - 403 pages
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...base DB 2. that :. AD — DB. PROPOSITION XXXI. Theorem. In a circle, the angle 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...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...the angle in a semicircle is a right angle; tut the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment...angle. Let ABCD be a circle, of which the diameter is BC, and centre E : and draw CA, dividing the circle into the segments ABC, ADC, and join BA, AD,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 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 figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...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, is an obtuse angle. PROP. XXXII. THEOR. If a straight line touches a circle, and from the point of contact...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...circle, the angle in a semicircle is a rig hi angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment...angle. Let ABCD be a circle, of which the diameter is BC, and centre E; and draw CA, dividing the circle into the segments ABC, ADC, and join BA, AD,...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...given circumference is bisected in D. QEF PROP. XXXI. THEOR. IN a circle, the angle 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...four, eight, sixteen, &c. equal parts. , PROP. XXXI. THEOR. In a circle, the angle 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...
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Cambridge problems proposed by the moderators to the candidates ..., Volume 2

Cambridge univ, exam. papers - 1843 - 50 pages
...bisects them, that is, divides them into two equal parts. 2. In a circle the angle in a semi-circle is a right angle ; but the angle in a segment greater than a semi-circle is less than a right angle ; and the angle in a segment less than a semi-circle is greater than a right...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...and an angle DBA in a segment greater than a semicircle is less than a right angle, and an angle AED in a segment less than a semicircle is greater than a right angle. and v DC=CB, the ZCBD = the ZBDC, .-. the whole .ADB is = the two it DAB and DBA, but the ZFDB is also...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...in D. Which was to be done. PROPOSITION XXXI. THEOR. — In a circle, the angle 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...
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