| Henry Latham - 1857 - 390 pages
...pass through one point within the triangle the arcs will together form a complete circumference. 2. **The straight line drawn at right angles to the diameter...from the extremity of it falls without the circle.** If AB be a fixed chord of a circle, AC and AD any two other chords making equal angles with AB; prove... | |
| Sandhurst roy. military coll - 1859 - 672 pages
...contained by the whole and each of the parts are together equal to the square on the whole line. 3. **The straight line drawn at right angles to the diameter...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. VOLUNTARY... | |
| Euclides - 1860 - 288 pages
...square on EH is less than the square on EK, EH is less than EK. henee the straight line PROPOSITION XVI. **THEOREM. The straight line drawn at right angles to...from the extremity of it, falls without the circle** ; (2) and a straight line making an acute angle with the diameter at its extremity cuts the circle.... | |
| John Playfair - Geometry - 1860 - 334 pages
...conversely, the farther the chord is from the centre, the shorter it is. PROP. XVI. THEOR. The straight Ime **drawn at right angles to the diameter of a circle,...of it, falls without the circle ; and no straight** Une . can be drawn between that straight line and the circumference, from the extremity of the. diameter,... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...straight line and the perpendicular AE. QED COB. From this it is manifest, that the straight line which is **drawn at right angles to the diameter of a circle from the extremity of it** touches the circle ; (In. def. 2.) and that it touches it only in one point, because, if it did meet... | |
| Euclides - 1861 - 464 pages
...The best position therefore for the oars is in the Une of the Neatest width, AB. PROP. 16.— THEOn. **The straight line drawn at right angles to the diameter...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 ;... | |
| Euclides - 1862 - 172 pages
...FG. (in. def. 5.) Wherefore, the diameter, &c. QED PROP. XVI.— THEOREM. The straight line which is **drawn at right angles to the diameter of a circle,...without the circle ; and no straight line can be drawn** from the extremity between that straight line and the circumference, which does not cut the circle,... | |
| Euclides - 1862 - 140 pages
...equal to DA; therefore DH is less than DK. 4. Therefore the point H is within the circle. which is **drawn at right angles to the diameter of a circle, from the extremity of it,** touches the circle (III. def. 2); and that it touches it only in one point, because if it did meet... | |
| Euclides - 1864 - 262 pages
...BCis nearer to the center than FG. (iil. def. 5.) Wherefore the diameter, &c. Q.KD. PROPOSITION XVI. **THEOREM. The straight line drawn at right angles to...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 :... | |
| Euclides - 1864 - 448 pages
...straight line and the perpendicular AE. QED COR. From this it is manifest, that the straight line which is **drawn at right angles to the diameter of a circle from the extremity of it** touches the circle ; (ln. def. 2.) and that it touches it only in one point, because, if it did meet... | |
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