| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| Euclides - 1861 - 464 pages
...Euclid's Geometry. РROP. 31. — THEOR. 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.** 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... | |
| Robert Johnston (F.R.G.S.) - Civil service - 1872 - 212 pages
...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... | |
| |