 | War office - 1861 - 714 pages
...nearer to the centre than the less. 2. 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. 10 DIRECT COMMISSIONS. VOLUNTAKY PORTION. 1. Similar triangles are to one another in the duplicate... | |
 | 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... | |
 | 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... | |
 | War office - 1861 - 260 pages
...up of the half and the part produced. 3. 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 right angle. 4. To describe an equilateral and equiangular hexagon in a given circle. 5. If two triangles have one... | |
 | Euclides - 1862 - 140 pages
...in D. QEF PROPOSITION 31.— THEOREM. 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. (References— Prop. I. 5, 17, 32; III. 22.) Hypothesis. — Let ABC be a circle, of which BC is a... | |
 | Robert Potts - 1863 - 482 pages
...are parallel to two sides of AB CD. 4. 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. The circumferences of three unequal circles, whose centres are A, B, C, pass through a common point... | |
 | Euclides - 1863 - 122 pages
...(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... | |
 | Euclides - 1864 - 448 pages
...bisected in DQEF PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircte is a right angle ; but the angle in a segment greater than a semicircle is...than a semicircle is greater than a right angle. Let ABCD be a circle, of which the diameter is BC, and eenter E. and let CA be drawn, dividing the circle... | |
 | Euclides - 1864 - 262 pages
...bisected in DQEF 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...than a semicircle is greater 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... | |
 | Henry Raper - 1870 - 968 pages
...IK is a diameter, the angle at M, • point on the circumference, is the angle in a semicircle. 142. The angle in a segment greater than a semicircle is less than a right angle. The segment BAG of the circle being greater than a semicircle, the other segment BDCmust be less than... | |
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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. 
