 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.  The Elements of Euclid - Side 63av Euclid - 1838 - 416 siderUten tilgangsbegrensning - Om denne boken
 | Cambridge univ, exam. papers - 1843 - 50 sider
...equal to one another, and the diameter bisects them, that is, divides them into two equal parts. 2. In a circle the angle in a semi-circle is a right...than a semi-circle is greater than a right angle. 3. What sum must be invested in the 3 per cent, stock at 94J, to yield an annual income of £500 ?... | |
 | Euclides - 1845 - 546 sider
...circumference DB. Therefore the given circumference is bisected in DQEF PROPOSITION XXXI. THEOREM. In a circle, the angle in a semicircle is a right...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... | |
 | Scottish school-book assoc - 1845 - 444 sider
...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... | |
 | Euclid - 1845 - 218 sider
...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... | |
 | London univ - 1846 - 326 sider
...(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... | |
 | Nathaniel Bowditch - 1846 - 854 sider
...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... | |
 | Euclid, John Playfair - 1846 - 334 sider
...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... | |
 | Euclides - 1846 - 272 sider
...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... | |
 | Euclides - 1846 - 292 sider
...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 ;... | |
 | John Playfair - 1847 - 340 sider
...by successive 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...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... | |
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