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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 ... - Strona 80
autor: John Playfair - 1855 - Liczba stron: 318
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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 - 1860 - Liczba stron: 453
...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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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - Liczba stron: 12
...contained by the whole and each of the parts are together equal to the square on the whole line. 4. In a circle the angle in a semi-circle is a right...than a semi-circle is greater than a right angle. ALGEBRA. 1 . Multiply a3 — a V + az6 - a;9 by a + x3. 2. Add together (ax*-by*f and (ay* + bx*)*,...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861
...fourth converging fraction to VJI . • 7. 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 semicircle is greater than a right angle. If two chords AB, CD in a circle cut each other at right angles, the sum of the opposite arcs AC and...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861
...is equal to the square on the straight line which is made up of the half and the part produced. 3. In a circle the angle in a semicircle is a right angle,...greater than a semicircle is less than a right angle. 4. To describe an equilateral and equiangular hexagon in a given circle. 5. If two triangles have one...
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...arc DB. Conclusion. — Therefore, the given arc is bisected in D. QEF PROPOSITION 31.— THEOREM. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. (References— Prop. I. 5, 17, 32; III. 22.) Hypothesis. — Let ABC be a circle, of which BC is a...
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Liber Cantabrigiensis: An Account of the Aids Afforded to Poor ..., Tom 2

Robert Potts - 1863
...in c, d. Shew that abed is a parallelogram of which two sides are parallel to two sides of AB CD. 4. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. The circumferences of three unequal circles, whose centres are A, B, C, pass through a common point...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...(THEouEM.)—In a circle (ABCD), the angle in a semicircle (BAC) is a right angle; theannlein a segment (ABC) greater than a semicircle is less than a right angle; and the angle (ADC) in a segment less than a semicircle is greater than a right emgle. Take any point Din the arc...
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