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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 Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...right angle ; and an angle in a segment greater than the semicircle is less than a right angle ; and an angle in a segment less than a semicircle is greater than a right angle. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 pages
...are together equal to two right angles. 5. 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 angle in a segment Jess than a semicircle is greater than a right angle. 6. If from any point without a circle two straight...
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A test-book for students; comprising sets of examination papers upon ...

Thomas Stantial - 1859
...is a right angle ; the angle in a segment less than a semicircle is greater than a right angle ; and the angle in a segment greater than a semicircle is less than a right angle. C. For the proof of this proposition what ascertained facts of circles are needed ? State also a corollary...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...equal to the arc DB. Therefore the given arc ADB is bisected in D. Q EF PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right...ABCD be a circle, of which the diameter is BC, and center E. and let CA be drawn, dividing the circle into the segments ABC, ADC. Join BA,AD,DC. Then...
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Government examinations, a companion to 'Under government' and a key to the ...

Joseph Charles Parkinson - 1860
...circumference upon the same base, that is, upon the same part of the circumference. 12. PROP. XXXI. — In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. 13. ABC is a triangle of which the angle A is acute; show that the square of BC is less than the squares...
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A complete practical guide to her majesty's Civil service, by a certificated ...

Civil service
...circumference upon the same base, that is, upon the same part of the circumference. PHOP. XXI. — In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. ABC is a triangle of which the angle A is acute ; show that the square of BC is less than the squares...
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Guide to the three services: civil, naval, and military

John Paxton Hall - 1860
...circumference. PEOP. XXXI. — In a circle, the angle in a semicircle is a right angle ; but the angle is a segment greater than a semicircle is less than a...less than a semicircle is greater than a right angle. ABC is a triangle of which the angle A is acute ; show that the square of BC is less than the squares...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...half of the same arc Hence the theorem. THEOREM IX. An angle in a semicircle is a right angle ; an angle in a segment greater than a semicircle is less than a right angle; and an angle in a segment less than a semicircle is greater than a right angle. (Th. 8) ; that is, one...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...that 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. (Const.) Join AE,...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...Rhumbs ; but the division into single degrees cannot be performed by Euclid's Geometry. РROP. 31. — THEOR. In a circle, the angle in a semicircle is a...less than a semicircle is greater than a right angle. COTS. 10, I. Psts. 1 & 2. DEM. Def. 15, I. 5,1. Axs. 1, 2. Def. 10, 1. 22, Ш. 32, I. If a side of...
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