| Euclides - 1837 - Liczba stron: 88
...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 - 1837 - Liczba stron: 240
...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 - Liczba stron: 318
...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 - 1838 - Liczba stron: 416
...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... | |
| Euclides - 1842
...AD, 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 A, E, and produce... | |
| John Playfair - 1842 - Liczba stron: 317
...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... | |
| Cambridge univ, exam. papers - 1843 - Liczba stron: 30
...equal to one another, and the diameter bisects them, that is, divides them into two equal parts. 2. **In a circle the angle in a semi-circle is a right...than a semi-circle is greater than a right angle.** 3. What sum must be invested in the 3 per cent, stock at 94J, to yield an annual income of £500 ?... | |
| Euclides - 1845
...circumference DB. Therefore the given circumference is bisected in DQEF PROPOSITION XXXI. THEOREM. **In a circle, the angle in a semicircle is a right...a segment greater than a semicircle is less than a** rig/it angle; and \he angle in a segment less than a semicircle is greater than a right angle. Let... | |
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