 | Euclid - 1835 - 540 σελίδες
...AD, DC; the angle in the semicircle BAG 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... | |
 | John Playfair - 1836 - 114 σελίδες
...given circumference is bisected in D. Which was to be done. PROP. XXII. THEOR. In a circle, the angles in a semicircle is a right angle ; but the angle in...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... | |
 | University of Cambridge - 1836 - 366 σελίδες
...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.... | |
 | 1836 - 472 σελίδες
...circle, the angle in a simicircle is a right angle ; but the angle in a segment greater than a simicircle is less than a right angle; and the angle in a segment less than a simicircle is greater than a right angle. Cor. From this it is manifest, that if one angle of a triangle... | |
 | George Darley - 1836 - 172 σελίδες
...two right angles, (ART. 37,) ADC must be equal to one right angle. This, &c. [See NOTE Z.] ART. 73. The angle in a segment greater than a semicircle is less than a right angle. Let ABC be a segment greater than a semicircle. Then ADC is less than a right angle. DEM. Draw the... | |
 | John Playfair - 1836 - 488 σελίδες
...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 hi the segment ADC, which is less than a semicircle, is greatef than a right angle. Join AE, and produce... | |
 | Euclides - 1837 - 112 σελίδες
...Demonstration. 1. Prove that (in AS ACD, BCD,) base AD = base DB 2. that :. AD — DB. PROPOSITION XXXI. Theorem. In a circle, the angle in 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 ;... | |
 | Andrew Bell - 1837 - 240 σελίδες
...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 Bf angle. the two angles... | |
 | John Playfair - 1837 - 332 σελίδες
...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... | |
 | Euclid - 1838 - 478 σελίδες
...DB : therefore the given circumference is bisected in D. Which was to be done. PROP. XXXI. THEOR. ln a circle, the angle in a semicircle is a right angle...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... | |
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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. 
