 | Thomas Stantial - Examinations - 1859 - 352 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
...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 - 154 pages
...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 - 366 pages
...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 - 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 - 470 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... | |
 | War office - 1861 - 714 pages
...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 - 464 pages
...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 - 572 pages
...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 - Geometry - 1871 - 320 pages
...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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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. 
