 | George Darley - 1836 - 172 páginas
...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... | |
 | Euclides - 1837 - 112 páginas
...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 - 290 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 Bf angle. the two angles... | |
 | John Playfair - 1837 - 332 páginas
...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 - 470 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 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 - 1838 - 264 páginas
...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 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... | |
 | Robert Simson - 1838 - 434 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 - 192 páginas
...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 - 82 páginas
...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 - 378 páginas
...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 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. 
