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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, containing the first six books, with a selection of ... - Σελίδα 112
των Euclides - 1874
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 σελίδες
...arc AD is 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...than a semicircle is greater than a right angle. Let ABCD be a circle, of which the diameter is BC, and center E. and let CA be drawn, dividing the circle...

Government examinations, a companion to 'Under government' and a key to the ...

Joseph Charles Parkinson - 1860 - 154 σελίδες
...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...

A complete practical guide to her majesty's Civil service, by a certificated ...

Civil service - 366 σελίδες
...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...

Guide to the Three Services: Civil, Naval, and Military

John Paxton Hall - 1860 - 186 σελίδες
...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...

Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - 1860 - 470 σελίδες
...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...

Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 σελίδες
...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,...

Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 σελίδες
...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*)*,...

Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 σελίδες
...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 right...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...

Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1861 - 572 σελίδες
...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...

The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 320 σελίδες
...two right angles (Bk. I. Prop. 23). PROPOSITION 13. The angle in a semicircle is a right angle, and the angle in a segment greater than a semicircle is...than a semicircle is greater than a right angle. Let ABDC be a circle and BC its diameter, and therefore BAC a semicircle, then shall the angle BAC be a...




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