 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 right angle ; and the angle in a segment less than a semicircle is greater than a right angle.  General Announcement - McGill University - Page 30by McGill University - 1910Full view - About this book
 | Euclides - 1833 - 304 pages
...angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is an acute angle ; and the angle in a segment less than a semicircle is obtuse. PART 1. The angle in a semicircle is a right angle. Draw a diameter connecting the extremities... | |
 | Euclid - 1835 - 540 pages
...Book III. PROP. XXXI. THEOR. ^ /— ' 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. Let ABCD be a circle, of which the diameter is BC, and centre E ; and draw CA, dividing the circle... | |
 | John Playfair - Geometry - 1836 - 148 pages
...Which was to be done. PROP. XXII. THEOR. In a circle, the angles 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. Let ABCD be a circle, of which the diameter is BC, and centre E ; and draw CA, dividing the circle... | |
 | Mathematics - 1836 - 366 pages
...right angles to the same plane. 3. In a circle the angle in a semicircle is a right angle, but 1829 the angle in a segment greater than a semicircle is...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
...ART. 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... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...sixteen, &c. equal parts. PROP. XXXI. THEOR. 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. Let A BCD be a circle, of which the, diameter is BC, and centre E ; draw CA dividing the circle into... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...bisected in D. PROPOSITION 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. Let ABCD be a circle, of which the diameter is BC, and centre E ; and draw CA dividing the circle into... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...AD — DB. PROPOSITION 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. Steps of the Demonstration to Part 1st, That the Z in ^ 0 is a right Z1. Prove that Z EAB = Z ABE ;... | |
 | Euclides - 1838 - 264 pages
...Which was to be done.PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right angle; tut the angle in a segment greater than a semicircle is...less than a semicircle is greater than a right angle. Let ABCD be a circle, of which the diameter is BC, and centre E : and draw CA, dividing the circle... | |
 | Robert Simson - Geometry - 1838 - 434 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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