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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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## Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...is equal to the arc DB. Therefore the given arc ADB is bisected in DQEF 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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## The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...given arc ADB is bisected in DQEF PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircte is a right angle ; but the angle in a segment greater...ABCD be a circle, of which the diameter is BC, and eenter E. and let CA be drawn, dividing the circle into the segments ABC, ADC. Join BA, AD, DC. Then...
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## Guide to the Civil service

Henry White - 1864
...line from a given point, either without or in the circumference, which shall touch a given circle. 7. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. • ALGEBRA. Set to candidates for the Admiralty who selected Algebra as a subject of Examination....
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## First Practical Lines of Geometrical Drawing ...

J F H. De Rheims - 1865
...cut it at right angles, and if it cuts it at right angles it shall bisect it. Prop. 31. — Theorem. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. EUCLID, BOOK VI. Prop. 2. — Theorem. If a straight line be drawn parallel to one of the sides of...
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## The college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...circumference DB ; •wherefore the circumference ADB is bisected in D. QEF 117 PROP. XXXI.— 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 ; in. 22.) Let ABCD be a circle, of which the diameter is BC, and...
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## Report of the Secretary for Public Instruction ...

...touches it on the inside or outside. 9. Prove that the angle in a semicircle is a right angle ; but that the angle in a segment greater than a semicircle is...less than a semicircle is greater than a right angle. ., 40 PROBLEMS. 10. Pivide a right angle into three equal angles. 11. In the base of a triangle, find...
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## A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - 1866 - Liczba stron: 404
...from a given point in one of its sides. 2. 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. 3. Triangles, and also parallelograms, having the same altitude, are to one another, &c. 4. If a straight...
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## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - Liczba stron: 400
...arc AD is equal to the arc DB. Wherefore the given arc is bisected at DQEF PROPOSITION 31. THEOREM. In a circle the angle in a semicircle is a right angle;...than a right angle. Let ABCD be a circle, of which BC is .a diameter and E the centre ; and draw CA, dividing the circle into the segments ABC, ADC, and...
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## Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - Liczba stron: 349
...the radius. PROPOSITION XXXI. THEOREM. In a circle, 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 ABC be a © , O its centre, and BC a diameter. Draw AC, dividing the © into the segments ABC, ADC....
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## Civil service guide

Robert Johnston (F.R.G.S.) - 1872 - Liczba stron: 178
...in a semicircle is a right angle; but the an?le in a segment greater than a semicircle is less tban a right angle ; and the angle in a segment less than a semicircle is greater than a right angle. ALGEBRA. I. Specimen Paper. (Time, 3 hours.) 1. Find (1) the sum, (2) the difference, of the two expressions...
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