| Euclid - 1845 - 199 páginas
...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... | |
| 1845
...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... | |
| the london university calendar - 1846
...(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 - 451 páginas
...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... | |
| John Playfair - 1846 - 317 páginas
...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
...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
...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 - 317 páginas
...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
...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 is...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... | |
| Great Britain. Council on Education - 1848
...different combinations that may be made of n different things, taking r of them together. Section 3. 1. **In a circle the angle in a semicircle is a right angle,...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)... | |
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