| Robert Simson - Trigonometry - 1806 - 546 pages
...sides of the triangle, the angle opposite to this side, being in a semicircle, is a right angle ; and, **if the centre falls without the triangle, the angle...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... | |
| Robert Gibson - Surveying - 1806 - 486 pages
...is less than half a semicircle, and consequently less than a right angle, fig. 26. Cor. 4. An angle **in a segment less than a semicircle, is greater than a right angle,** for since the arc AEC is greater than a semicircle, its half, which is the measure of the angle ABC,... | |
| John Playfair - Mathematics - 1806 - 320 pages
...proved, and is not self-evident. angle. When the centre falls without the triangle, the angle Book IV. **opposite to the side beyond which it is, being in a segment** s^~*"^ less than a semicircle, is greater than a right angle. Wherefore if the given triangle be acute... | |
| Robert Gibson - 1808 - 482 pages
...is less than half a semicircle, and consequently less than a right angle, fig. 26. Cor. 4. An angle **in a segment less than a semicircle, is greater than a right angle,** for since the arc AEC is greater than a semicircle, 'its half, which is the measure of the angle ABC,... | |
| Robert Gibson - Surveying - 1811 - 580 pages
...is less than half a semicircle, and consequently less than a right angle. Fig. sr. Cor. 4 An angle **in a segment less than a semicircle, is greater than a right angle,** for since the arc AEC is greater than a semicircle, its half, which is the measure of the angle ABC,... | |
| John Mason Good - 1813 - 714 pages
...angle; but 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.** Prop. XXXII. Theor. If a straight line touches я circle, an J from the point of contact a straight... | |
| Robert Gibson - Surveying - 1814 - 558 pages
...ADBis less than half a semicircle, and consequently less than a right angle. Fig. У!. Cor. 4. An angle **in a segment less than a semicircle, is greater than a right angle,** for since the arc AEC is greater than a semicircle, its half, which is the measure of the angle ABC,... | |
| Euclides - 1816 - 588 pages
...sides of the triangle, the angle opposite to this side, being in a semicircle, is a right angle; and, **if the centre falls without the triangle, the angle...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... | |
| Robert Gibson - Surveying - 1818 - 502 pages
...is less than half a semicircle, and consequently less than a right angle. fig. 26. Cor. 4. An angle **in a segment less than a semicircle, is greater than a right angle,** for since the arc AEC is greater than a semicircle, its half which is the measure of the angle ABC,... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...sides of the triangle, the angle opposite to this side, being in a semicircle, is a right angle : and **if the centre falls without the triangle, the angle...less than a semicircle, is greater than a right angle** Wherefore, if the given triangle be acute angled, the ceatre of Ihe circle falls within it : if it... | |
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