| Robert Gibson - Surveying - 1811 - 578 pages
...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 - 714 pages
...into two equal parts. Prop. XXXI. Theor. In a circle, the angle in a semicircle is a right angle; but **the angle in a segment greater than a semicircle is...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 pages
...bisected in the point D. PROP. XXXI. THEOR. IN a circle, the angle in a semicircle is a right angle ; but **the angle in a segment greater than a semicircle is...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 - Surveying - 1814 - 562 pages
...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... | |
| Euclides - 1816 - 592 pages
...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 AE, and produce... | |
| Robert Gibson - Surveying - 1818 - 500 pages
...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 pages
...Which was to be done. PROP. XXXI. THEOR. In a circle, the angle in a semicircle is a right angle ; but **the angle in a segment greater than a semicircle is...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,... | |
| John Playfair - Circle-squaring - 1819 - 348 pages
...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... | |
| Rev. John Allen - Astronomy - 1822 - 518 pages
...in D. PROP. XXXI; THEOR. The angle (BAC) in a semicircle, is a right angle; but an angle (as ABC), **in a segment greater than a semicircle, is less than a right angle ; and** an angle (as ADC), in a segment less them a semicircle, is greater than a right angle. Let E be the... | |
| George Watson - Navigation - 1822 - 72 pages
...a semicircle is greater than a right angle. 197. An angle in a semicircle is a right angle. 199. An **angle in a segment greater than a semicircle is less than a right angle.** 200. An angle at the circumference of a circle is half the angle at the centre, standing on the same... | |
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