 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...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 - 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... | |
 | Euclides - 1848 - 52 pages
...two equal parts. PROP. XXXI. THEOREM. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than 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 - Education - 1848 - 532 pages
...parallelogram is double of the triansle. 3. In a circle, the angle in a semicircle is a right anile; but the angle in a segment greater than a semicircle is...less than a semicircle is greater than a right angle. 4. To describe a circle in a given square. 0. Ratios that are equal to the same ratio are equal to... | |
 | Bengal (India) - 1848 - 520 pages
...together greater than the third side. 7. In a circle, the angle in a semicircle is a right angle, but the angle in a segment greater than a semicircle is...less than a semicircle is greater than a right angle. 8. In equal circles, angles, whether at the centres or circumferences, have the same ratio which the... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...six persons. Here re = 6 and r — 3 So that 1.2.3. ~ 1.2.3 = 20. n 0—1) (n—2) 6X5X4 angle, but the angle in a segment greater than a semicircle is...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. Committee on Education - Education - 1848 - 514 pages
...of the sides of the parallelogram. 3. In a circle, the angle in a semicircle is a right anyle ; but the angle in a segment greater than a semicircle is less than a right angle, and llie angle in a segment less than a semicircle is greater than a right angle. 4. To describe a circle... | |
 | Bengal council of educ - 1848 - 394 pages
...are equal to 2 right angles, .'. /_ ABC + /_ ADC = 2 right angles but ABC Z_ a right angle .'. ADC in a segment less than a semicircle is greater than a right angle. 8. \E ABCD and HLM are two equal circles, their centres being 0, G. AOB and HGK are two angles at the... | |
 | John Playfair - Euclid's Elements - 1849 - 332 pages
...in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less then a right angle ; and the 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 ; draw CA dividing the circle into the... | |
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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. 
