 | Euclides - 1845 - 546 pagina’s
...circumference AD is equal to the circumference DB. Therefore the given circumference is bisected in DQEF PROPOSITION XXXI. THEOREM. In a circle, the angle...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... | |
 | Euclid - 1845 - 218 pagina’s
...DC : the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC, which is greater than a semicircle, is less than a right angle ; and the angle in the segment ADC, which is less than a semicircle, is greater than a right angle. Join AE, and produce... | |
 | Scottish school-book assoc - 1845 - 444 pagina’s
...to AB. PROPOSITION LII. — THEOREM. An angle ADB in a semicircle is a right angle, 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... | |
 | London univ - 1846 - 326 pagina’s
...(2.) &— xy=48y\ xy— y*=3x J ' (3.) *+— a«=0. 9. 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. 10. Inscribe in a given circle an equilateral and equiangular hexagon. 1 1 . Define the sector of a... | |
 | Euclid, John Playfair - 1846 - 334 pagina’s
...DC ; the angle in the semicircle BAC is a right angle ; and the angle in the segment ABC, which is greater than a semicircle, is less than a right angle ; and the angle in the segment ADC, which is less than a semicircle, is greater than a right angle. Join AE, and produce... | |
 | Nathaniel Bowditch - 1846 - 854 pagina’s
...are ernial to each other ; for they are all measured by the same arc, viz. half the arc AB. XLII. 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 1еяч... | |
 | Euclides - 1846 - 292 pagina’s
...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 pagina’s
...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... | |
 | John Playfair - 1847 - 340 pagina’s
...subdivisions, a given arc may be divided into four, eight, sixteen, &c. equal parts. PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right...a semicircle is greater than a right angle. ' Let A BCD be a circle, of which the diameter is BC, and centre E ; draw CA dividing the circle into the... | |
 | Euclides - 1848 - 52 pagina’s
...PROP. XXX. PROBLEM. To bisect a given circumference, that is, to divide it into two equal parts. PROP. XXXI. THEOREM. In a circle, the angle in a semicircle...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. 
