| William Thomas Brande, George William Cox - Science - 1867 - 1088 pages
...assumed, or taken for granted. Euclid has constructed his Elements on the three following 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 a circle... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...certainly be convenient if this restriction were universally adopted.] POSTULATES. Let it be granted, 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. And that... | |
| William Thomas Brande - Encyclopedias and dictionaries - 1867 - 1092 pages
...assumed, or taken for granted. Euclid lias constructed his Elements on the three following postulates: 1. **That a straight line may be drawn from any one point to any other point.** 2. That a terminated straight lino may be produced to any length in a straight line. 3. That a circle... | |
| Robert Potts - 1868 - 410 pages
...parallel: and the diameter, or the diagonal is the straight liue 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.** IL That a terminated straight line may be produced to any length in a straight line. m. AXIOMS. I.... | |
| James Smith - 1870 - 634 pages
...that his first problem (Prop. I, Book 1) should be based upon the simplest of the postulates, viz. : " **Let it be granted, that a straight line may be drawn from any one point to any other point"** Thus, Euclid begins by showing us how to construct an equilateral triangle. There can be no doubt that... | |
| Euclides - 1871
...construction of figures and the properties of geometrical mag--tudes. POSTULATES. Let it be granted I. **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... | |
| Elias Loomis - Geometry - 1871 - 302 pages
...which is contained an exact number of times in each of them. BOOK V PROBLEMS Postulates. 1 A a'.raight **line may be drawn from any one point to any other point.** 2. A terminated straight line may be produced to any length in a straight line. 3. From the greater... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...construction of figures and the prqperties pf geometrical magnitudes. POSTULATES. Let it be granted I. **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... | |
| Henry Major - Student teachers - 1873
...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. That a circle... | |
| William Alexander Myers - Circle-squaring - 1873 - 238 pages
...sin. A = ± VR 2 — cos. 2 A, And cos. A — ± VR 2 — sin. 2 A. POSTULATES. Let it be granted : 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. And that a... | |
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