| Charles Bray - Cooperation - 1841 - 694 pages
...no magnitude." " A line is length without breadth."* " Let it be granted," says the mathematician, " that a straight line may be drawn from any one point to any other point," that is, from that which has no parts and no magnitude, to that which has no parts and no magnitude;... | |
| Euclides - 1842 - 316 pages
...trapezium having two, only, of its sides parallel to one another is now called a trapezoid. 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. That a circle... | |
| William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...be done, or to be imagined to be done. The postulates given by Euclid are the following : — 1 . Л line may be drawn from any one point to any other point. 2. A line may be produced (that is, continued or lengthened) at pleasure to any length. 3. A circle may... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...lines are such as 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 drawA from any one point to any other point. 2. That a terminated straight line may be produced to... | |
| James Bates Thomson - Geometry - 1844 - 268 pages
...problems, while axioms are self-evident theorems. Geometers usually enumerate three postulates. 1. 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 any circle may be... | |
| Euclid, James Thomson - Geometry - 1845 - 382 pages
...ways; but it is only the parts into which it is divided by a diameter, that are called semicircles. POSTULATES* 1. Let it be granted, that a straight...may be drawn from any one point, to any other point : f 2. That a terminated straight line may be produced to any length in a straight line : , 3. That... | |
| Euclides - 1845 - 546 pages
...the diameter or the diagonal is the straight line joining two of its opposite angles. 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... | |
| Euclid - Geometry - 1845 - 218 pages
...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... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...lines are such as 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...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. And that a circle may... | |
| Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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. AXIOMS.... | |
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