| 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 - 1046 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 - 234 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 - 546 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 - 542 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 - 210 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 - 156 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.... | |
| Timothy Walker - Geometry - 1829 - 138 pages
...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. i « f 3. Let it be granted that a circle may be described from any centre, at any distance from that... | |
| English literature - 1829 - 430 pages
...convenient to substitute for it. How do you reconcile the admission of Euclid's postulate, " that a straight line may be produced to any length in a straight line, 1 ' with the neces-, I. «*_ xy — x + y, II. 3x* — 2xy + y 3 — 4>x — 4y + 3 = 0. III. x>=xy... | |
| |