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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

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...

## 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...