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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 94
by Euclides - 1841
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 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 hi the segment ADC, which is less than a semicircle, is greatef than a right angle. Join AE, and produce...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...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 semicircle is greater than a right angle. Steps of the Demonstration to Part 1st, That the Z in ^ 0 is a right Z1. Prove that Z EAB = Z ABE ;...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 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 Bf angle. the two angles...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 332 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: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 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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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...Z. ABD is less than a right angle a Prop. 32). But L ABD=Z. AFD (m. Prop. 2i) ; therefore Z. AFD or the angle in a segment greater than a semicircle is...less than a right angle. And the angle in a segment AGD less than a semicircle, is greater than a right angle. For take any point G in the segment, and...
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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 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 A, E, and produce...
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Cambridge problems proposed by the moderators to the candidates ..., Volume 2

Cambridge univ, exam. papers - 1843 - 50 pages
...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...than a semi-circle is greater than a right angle. 3. What sum must be invested in the 3 per cent, stock at 94J, to yield an annual income of 500 ?...
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