 | John Playfair - Geometry - 1829 - 210 pages
...segment greater than a semicircle is acute; and the angle in a segment less than a semicircle is obtuse. Let ABCD be a circle, of which the diameter is BC, and the centre E; draw C\ dividing the circle into the two segments ABC, ADC; draw BA, AD, DC; the angle... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...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...ABCD be a circle, of which the diameter is BC, and fcentre E ; draw CA dividing the circle into the segments ABC, ADC, and join BA, AD, DC ; the angle... | |
 | Euclides - 1834 - 518 pages
...segment greater than a semicircle, ii less than a right angle ; and the angle in a segment less litan a semicircle, is greater than a right angle. Let ABCD be a circle, of which the diameter is BC, and the centre E ; and draw CA, dividing the circle into the segments ABC, ADC, and join BA, AD, DC : the... | |
 | Euclid - 1835 - 540 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 acute-angled, the centre of the circle falls within it; if it... | |
 | John Playfair - Geometry - 1836 - 148 pages
...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...circle into the segments ABC, ADC, and join BA, AD, DC ; the angle in, the semicircle BAG is a right angle ; and the angle in the segment ABC, which is greater... | |
 | Mathematics - 1836 - 366 pages
...angle, but 1829 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. 4. If two triangles have the sides about equal angles reciprocally proportional, they are equal. 5.... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...73. The angle in a segment greater than the semicircle is less than a right angle, ibid. ART. 74. The angle in a segment less than a semicircle is greater than a right angle,ibid. ART. 75. If a tangent and a chord of a circle be drawn from the same point, ths angle between... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...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. Steps of the Demonstration to Part 1st, That the Z in ^ 0 is a right Z1. Prove that Z EAB = Z ABE ;... | |
 | John Playfair - Euclid's Elements - 1837 - 332 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 acute angled, the centre of the circle falls within it ; if it... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 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 acute-angled, the centre of the circle falls within it ; if it... | |
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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. 
