| George Lees - 1826
...diameter AC, is a tangent to the circle ; and no straight line can be drawn between the tangent and **circumference, from the extremity of the diameter, so as not to cut the circle. Let** B be any point in the straight line AB, join this point and the centre D. Then, because DAB is a right... | |
| Robert Simson - 1827 - 513 sider
...D. PROP. XVI. THEOR. The straight line drawn at right angles to the diameter of See N. a circle,from **the extremity of it, falls without the circle ; and no straight line can be drawn** from the extremity, between that straight line and the circumference, so as not to cut the circle -,... | |
| Euclid, Robert Simson - 1829 - 516 sider
...square of EK, and the straight line EH less than EK. .Wherefore the diameter, &c. QED PROP. XVI. THEOR. **THE straight line drawn at right angles to the diameter...between that straight line and the circumference from** ther extremity, so as not to cut the circle ; or which is the same thing, no straight line can make... | |
| Euclides - 1834
...nearer t to the centre than FG. Wherefore, the diameter, &c. y. ED PROPOSITION XVI. See N. THEOR. — **The straight line drawn at right angles to the diameter of a circle, from the extremity of it,** Jails without the circle ; and no straight line can be drawn from the extremity, between that straight... | |
| Robert Simson - 1835 - 513 sider
...diameter," &c. QED PROP. XVI. THEOR. The straight line drawn at right angles to the dia- See N. meter **of a circle, from the extremity of it, falls without...extremity of the diameter, so as not to cut the circle;** or, which is the same thing, no straight line can make so great an acute angle with the diameter at... | |
| Euclid - 1835 - 513 sider
...less than " any rectilineal angle." COR. From this it is manifest, that the straight line whick is **drawn at right angles to the diameter of a circle from the extremity of it,** touches the circle ; and that it touches it only in one point, because, if it did meet the circle in... | |
| 1836 - 472 sider
...is always greater than the more remote; and the greater is nearer to the centre than the less. XVI. **The straight line drawn at right angles to the diameter of a circle, from the extremity of it,** fulls without the circle ; and no straight line can be drawn between that straight line and the circumference,... | |
| John Playfair - 1837 - 318 sider
...centre ; and, conversely, the farther the chord is from the centre, the shorter it is. PROP. XVI. THEOR. **The straight line drawn at right angles to the diameter...extremity of the diameter, so as not to cut the circle.** In AE take any point F, join DF and let DF meet the circle in C. Because DAF is a right angle, it is... | |
| Euclides - 1837 - 88 sider
...that BH > FK, 2. that EH" < EK" and .'. EH < EK. PROPOSITION XVI. (Argument ad absurdum). Theorem. **The straight line drawn at right angles to the diameter...straight line and the circumference from the extremity,** so as not to cut the circle. Steps of the Demonstration. Part 1st. That the right line from the extremity... | |
| Euclid, Robert Simson - 1838 - 416 sider
...of EK, and the straight line EH less than EK. Wherefore the diameter, &c. Q,. ED , PROP. XVI. THEOR. **THE straight line drawn at right angles to the diameter of a circle, from the extremity of** if, falls without the circle ; and no straight line can be drawn between that straight line and the... | |
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