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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 94
by Euclides - 1841 - 351 pages

A test-book for students; comprising sets of examination papers upon ...

Thomas Stantial - Examinations - 1859 - 356 pages
...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 - 380 pages
...in D. Q EF PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is...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 - 154 pages
...the circumference. 12. PROP. XXXI. — In a circle, the angle in a semicircle is a right angle; but the angle in a segment greater than a semicircle is...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 pages
...of the circumference. PHOP. XXI. — In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is...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 pages
...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 - 472 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...

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

Euclides - 1860 - 288 pages
...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,...

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

Woolwich roy. military acad - 1861 - 572 pages
...method the 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...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...