 | University of Oxford - 1879 - 584 σελίδες
...circumference 011 the same base, that is, on the same arc. 7. Inscribe a circle in a given square. 8. In a circle the angle in a semicircle is a right angle...less than a semicircle is greater than a right angle. 9. Draw a straight line from a given point, either without or in the circumference, which shall touch... | |
 | Edward Harri Mathews - 1879 - 94 σελίδες
...the inscribed quadrilateral and the opposite extenor angle meet in the circumference. Section III. 1. In a circle, the angle in a semi-circle is a right...than a semi-circle is greater than a right angle. The greatest rectangle that can be inscribed in a circle is a square. , 2. From a given circle to cut... | |
 | Isaac Sharpless - 1879 - 282 σελίδες
...therefore BC is equal (I. 7) to EF. Proposition 21. Theorem.—The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle,...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... | |
 | Euclides, James Hamblin Smith - 1879 - 376 σελίδες
...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 σελίδες
...The angle at the centre of a circle is double the angle at the circumference upon the same base. 4. In a circle the angle in a semicircle is a right angle...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... | |
 | 1880 - 880 σελίδες
...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 - 1880 - 426 σελίδες
...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 - 1881 - 236 σελίδες
...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... | |
 | 1882 - 486 σελίδες
...to twice the rectanglecontained by the whole part, together with the squares on the other part. 3. In a circle, the angle in a semicircle is a right...less than a semicircle is greater than a right angle. 4. Inscribe a regular equilateral and equiangular pentagon in a given circle. 5. Similar triangles... | |
 | Mary W I. Shilleto - 1882 - 418 σελίδες
...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... | |
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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. 
