 | University of Oxford - Greek language - 1879 - 412 pages
...equal to the square on half the line. 7. 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. 8. Describe a square on a given straight line. 9. Divide a given straight line into two parts, so that... | |
 | University of Oxford - Education, Higher - 1879 - 586 pages
...the circle of which it is a segment. 9. 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. If two straight lines cut one another within a circle, the rectangle contained by the segments... | |
 | Euclides, James Hamblin Smith - 1879 - 376 pages
...the radius. PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right angle ; and the angle in a segment greater than a semicircle is...less than a right angle ; and the angle in a segment lest than a is greater than a right angle. Let ABC be a 0, O its centre, and BC a diameter. Draw AC,... | |
 | Sandhurst roy. military coll - 1880 - 68 pages
...the circumference upon the same base. 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. Circles are described on the sides of a triangle as diameters. Show that their points of intersection... | |
 | Nautical astronomy - 1880 - 880 pages
...are ei/ttat to each other ; for they are all measured by the same arc, viz. half the arc AR XLH. An angle in a segment greater than a semicircle is less than a right angle. Thus, if ABC be a segment greater than a semicircle, the arc AC on which it stands must be less than... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...when the centre falls without the triangle, the angle opposite to the side beyond which it is, being in a segment less than a semicircle, is greater than a right angle. [III. 31. Therefore, conversely, if the given triangle be acuteangled, the centre of the circle falls... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...hke manner, by drawing a straight line from the point A, within the angle BAC, it may be shown that the angle in a segment greater than a semicircle is less than a rigbt angle. l,-Itrase. — To draw a perpendicular to a straight line from one of its extremities... | |
 | Mary W I. Shilleto - 1882 - 418 pages
...will be touched by another circle. 3. In a circle, the angle in a semicircle is a right angle, and the angle in a segment greater than a semicircle is...less than a semicircle is greater than a right angle. The greatest rectangle that can be inscribed in a circle is a square. 4. Inscribe a regular quindecagon... | |
 | Isaac Sharpless - Geometry - 1882 - 292 pages
...The angle in a semicircle is aright angle; the angle in a segment greater than a semicircle, is lens than a right angle ; and the angle in a segment less...than a semicircle, is greater than a right angle. ADC, and join BA, AD, DC; the angle in the semicircle BA C is a right angle ; the angle in the segment... | |
 | 1883 - 248 pages
...the centre of a circle is double the angle at the circumference standing on the same arc. Deduce that the angle in a segment greater than a semicircle is less than a right angle, and the angle in a semicircle is a right angle. 8. Prove that, if a straight line touch a circle and from the point of... | |
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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. 
