 | John Playfair - 1806 - 320 sider
...AD, DC ; the angle in the semicircle BAG is a right angle ; 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 semiciriite is greater than a right angle. Join £iE, and produce... | |
 | Robert Gibson - 1806 - 486 sider
...measured by half the arc they stand on. viz. bv half the arc AB. ftg. 26. . Plate I. Cor. 3. Hence an angle in a segment greater than a semicircle is less than a right angle ; thus ADB is measured by half the arc AB, but as the arc AB is less than a semicircle, therefore half... | |
 | Robert Simson - 1806 - 546 sider
...AD, DC; the angle in the semicircle BAC la a right angle ; and the angle in the segment ABO, 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 an^le. Join AE, and produce... | |
 | Robert Gibson - 1808 - 482 sider
...measured by half the arc they stand on* viz. by half the arc AB. fig. 26. Plate I. Cor. 3. Hence an angle in a segment greater than a semicircle is less than a right angle ; thus ADB is measured by half the arc AB, but as the arc AB is less than a semicircle, therefore half... | |
 | Robert Gibson - 1811 - 582 sider
...are all measured by half the arc they stand on, viz. by hall the arc AB. fig. 26. Cor. 3. Hence an angle in a segment greater than a semicircle is less than a right angle ; thus ADB is measured by half the arc AB, but as the arc AB is less than a semicircle, therefore half... | |
 | John Mason Good - 1813 - 722 sider
...lines. Prop. XXX. Prob. To bisect a given circumference, that is, to divide it into two equal parts. Prop. XXXI. Theor. In a circle, the angle in a semicircle...less than a semicircle is greater than a right angle. Prop. XXXII. Theor. If a straight line touches я circle, an J from the point of contact a straight... | |
 | Euclides - 1814 - 560 sider
...draw CD at right angles to AB, and join AD, DB : The circumference ADB is bisected in the point D. PROP. XXXI. THEOR. IN a circle, the angle in a semicircle...angle. Let ABCD be a circle, of which the diameter is EC, and centre E; and draw CA, dividing the circle into the segments ABC, ADC, and join BA, AD, DC;... | |
 | Robert Gibson - 1814 - 558 sider
...are all measured by balf the arc they stand on, viz. by half the arc AB. l Fig. 26. Cor. 3. Hence an angle in a segment greater than a semicircle is less than a right angle ; thus ADB is measured by half the arc AB, but as the arc AB is less thai* a semicircle, therefore... | |
 | Robert Gibson - 1818 - 502 sider
...are all measured by half the arc they stand on, viz. by half the arc AB. fig. 26. Cor. 3. Hence an angle in a segment greater than a semicircle is less than a right angle ; thus ADB is measured by half the arc AB, but as the arc AB is less than a semicircle, therefore half... | |
 | John Playfair - 1819 - 354 sider
...centre (Cor. 1. 3.) : Wherefore the arch AD is equal to the arch DB : and therefore the given arch ADB is bisected in D. Which was to be done. PROP. XXXI....semicircle is greater than a right angle. Let ABCD be a cir.de, of which the diameter is BC, and centre E ; draw CA dividing the circle into the segments ABC,... | |
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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. 
