| Mathematics - 1836 - 335 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.... | |
| Mathematics - 1836 - 472 pages
...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 - Euclid's Elements - 1836 - 128 pages
...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 - Euclid's Elements - 1836 - 311 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** hi the segment ADC, which is less than a semicircle, is greatef than a right angle. Join AE, and produce... | |
| Euclides - Euclid's Elements - 1837 - 88 pages
...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 a right...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 - Euclid's Elements - 1837 - 240 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 Bf angle. the two angles... | |
| John Playfair - Geometry - 1837 - 318 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... | |
| Euclid, Robert Simson - Geometry - 1838 - 416 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 - 1840
...Z. ABD is less than a right angle a Prop. 32). But L ABD=Z. AFD (m. Prop. 2i) ; therefore Z. AFD or **the angle in a segment greater than a semicircle is...less than a right angle. And the angle in a segment** AGD less than a semicircle, is greater than a right angle. For take any point G in the segment, and... | |
| Euclides - 1840
...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** an obtuse angle. PROP. XXXII. THEOR. If a straight line touches a circle, and from the point of contact... | |
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