| Edward Riddle - Nautical astronomy - 1824 - 572 pages
...lines intersect each other, they cannot both be parallel to the same straight line. POSTULATES. 1. **Let it be granted that a straight line may be drawn from any one point to any other point.** 2. That a straight line may be produced to any length in the same direction. 3. That a circle may be... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...are in the same plane, and which, being produced ever so far both ways, do not meet. POSTULATES. 1. **Let it be granted that a straight line may be drawn from any one point to any other point.** 2. That a terminated straight line may be produced to any length in a straight line. 3. That a circle... | |
| Euclid - 1826 - 236 pages
...being infinitely produced either way, do not meet one another.* POSTULATES. 1. Grant, that a right **line may be drawn from any one point to any other point.** 2. That a finite right line may be produced directly forwards. 3. That a circle may be described with... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...in the same plane, and which being produced ever so far both ways, do not meet. POSTULATES. I. L.et **it be granted that a straight line may be drawn from any one point to any other point.** If. That a terminated straight line may be produced to any length in a straight line. III. And that... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 pages
...to attend to the latter criterion of parallelism. POSTULATES. (39) I. Let it be granted that a right **line may be drawn from any one point to any other point.** (40) II. Let it be granted that a finite right line may be produced to any length in a right line.... | |
| John Playfair - Geometry - 1829 - 186 pages
...plane figures, of straight lines, and of rectilineal angles, is called Plane Geometry. POSTULATES. 1. **LET it be !granted that a straight line may be drawn from any one point to any other point.** 2. That a terminated straight line may be produced to any length in a straight line. 3. That a circle... | |
| Military art and science - 1831 - 618 pages
...recourse to some mechanical method for drawing a curve through them. One of Euclid's postulates is, " **Let it be granted that a straight line may be drawn from any one point to any other point;"** but I know of no one which snys that a curve line may be drawn through a number of points. The practical... | |
| Timothy Walker - Geometry - 1829 - 158 pages
...demonstrated, because it is self-evident. These cases are called postulates, and are the following : 1. **Let it be granted that a straight line may be drawn from any one point to any other point.** 2. Let it be granted that a terminated straight line may be produced to any length in a straight line.... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...piece of paper for a plane, with a pen,* a ruler, and a pair of compasses, it is evident, that, first, **a straight line may be drawn from any one point to any other point** ; 2ndly, a terminated straight line may be produced to any length in a straight line ; 3dly, from the... | |
| Euclid - 1835 - 540 pages
...lines are such as are in the same plane, and which being produced ever so far both ways, do not meet. **POSTULATES. I. LET it be granted that a straight line...may be drawn from any one point to any other point.** II. That a terminated straight line may be produced to any length in a straight line. III. And that... | |
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