| Euclid - 1838 - 416 páginas
...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 right angle. Let ABCD be a circle, of which** the diameter is BC, and centre E ; and draw CA, dividing the circle into the segments ABC, ADC, and... | |
| Euclides - 1838
...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...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 the segments ABC, ADC, and... | |
| Euclid - 1838 - 416 páginas
...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 - 1841
...Which was to be done. PROP. XXXI. THEOR. In, a circle, the angle in a semicircle is a rig hi angle; **the angle in a segment greater than a semicircle is...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 the segments ABC, ADC, and... | |
| John Playfair - 1842 - 317 páginas
...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 - 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... | |
| 1843
...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 ?... | |
| Robert Potts - 1845
...equal to the circumference DB. Therefore the given circumference is bisected in DQEF PROPOSITION XXXI. **THEOREM. In a circle, the angle in a semicircle is...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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