| 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... | |
| Robert Potts - 1860 - 361 páginas
...arc AD is 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...than a right angle. Let 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.... | |
| 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... | |
| 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... | |
| 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 - 453 páginas
...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... | |
| War office - 1861 - 12 páginas
...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*)*,... | |
| Euclides - 1861
...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 right...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... | |
| 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... | |
| Henry William Watson - 1871 - 285 páginas
...two right angles (Bk. I. Prop. 23). PROPOSITION 13. 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** ABDC be a circle and BC its diameter, and therefore BAC a semicircle, then shall the angle BAC be a... | |
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