| 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... | |
| Horatio Nelson Robinson - 1860 - Liczba stron: 453
...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
...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,... | |
| Euclides - 1861
...Rhumbs ; 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...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... | |
| War office - 1861 - Liczba stron: 12
...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*)*,... | |
| Woolwich roy. military acad - 1861
...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... | |
| War office - 1861
...is equal to the square on the straight line which is made up of the half and the part produced. 3. **In a circle the angle in a semicircle is a right angle,...greater than a semicircle is less than a right angle.** 4. To describe an equilateral and equiangular hexagon in a given circle. 5. If two triangles have one... | |
| Euclides - 1862
...arc DB. Conclusion. — Therefore, the given arc is bisected in D. QEF PROPOSITION 31.— 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; III. 22.) Hypothesis. — Let ABC be a circle, of which BC is a... | |
| Robert Potts - 1863
...in c, d. Shew that abed is a parallelogram of which two sides are parallel to two sides of AB CD. 4. **In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle.** The circumferences of three unequal circles, whose centres are A, B, C, pass through a common point... | |
| Euclides - 1863
...(THEouEM.)—In a circle (ABCD), the angle in a semicircle (BAC) is a right angle; theannlein a segment (ABC) **greater than a semicircle is less than a right angle; and the angle** (ADC) in a segment less than a semicircle is greater than a right emgle. Take any point Din the arc... | |
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