 | Euclides - 1845 - 546 pages
...right angle; but the angle in a segment greater than a semicircle is less than a rig/it angle; and \he angle in a segment less than a semicircle is greater than a right angle. Let ABCD be a circle, of which the diameter is BC, and centre E ; and draw CA, dividing the circle into... | |
 | Euclid - Geometry - 1845 - 218 pages
...if 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 : wherefore, if the given triangle be acuteangled, the centre of the circle falls within it ; if it... | |
 | Scottish school-book assoc - 1845 - 444 pages
...and an angle DBA in a segment greater than a semicircle is less than a right angle, and an angle AED in a segment less than a semicircle is greater than a right angle. and v DC=CB, the ZCBD = the ZBDC, .-. the whole .ADB is = the two it DAB and DBA, but the ZFDB is also... | |
 | London univ - 1846 - 326 pages
...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. 10. Inscribe in a given circle an equilateral and equiangular hexagon. 1 1 . Define the sector of a... | |
 | Nathaniel Bowditch - 1846 - 854 pages
...arc DKF, that is, by half a semicircle or by a quadrant ; therefore the angle DEF is a right one. An angle in a segment less than a semicircle is greater than a right angle. Thus, if GUI be a segment less than a semi-circle, the arc GKI on which it stands must be greater than... | |
 | Euclides - 1846 - 292 pages
...if the centre fall without the triangle, the angle opposite to the side beyond which it falls, being in a segment less than a semicircle, is greater than a right angle : Wherefore, if the given triangle be acute-angled, the centre of the circle will fall within it ;... | |
 | Euclides - 1846 - 272 pages
...21. B. 3.), and therefore the angle ABC is also less than a right angle. PART 3. — The angle ABC in a segment less than a semicircle is greater than a right angle. For assume in the opposite circumference any point D, and draw DA and DC. Therefore since in the quadrilateral... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...20. n 0—1) (n—2) 6X5X4 angle, but 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." See Euclid iii. 31. 2. " Describe a circle in a given triangle." See Euclid iv. 4. Tate's Geometry... | |
 | Great Britain. Council on Education - Education - 1848 - 532 pages
...in a semicircle is a right angle, but 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. 3. Similar triangles are to each other in the duplicate ratio of their homologous (or corresponding)... | |
 | Euclides - 1848 - 52 pages
...in a semicircle is a right angle ; but 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. PROP. XXXII. THEOREM. If a straight line touch a circle, and from the point of contact a straight line... | |
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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. 
