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" LET it be granted that a straight line may be drawn from any one point to any other point. "
The Elements of geometry; or, The first six books, with the eleventh and ... - Page 5
by Euclides - 1855
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A treatise on navigation, and nautical astronomy

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...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

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...
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Elements of Geometry, Containing the First Six Books of Euclid

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...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

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...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

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....
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

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...
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The United Service Journal and Naval and Military Magazine, Part 3

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...
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Elements of Geometry: With Practical Applications, for the Use of Schools

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....
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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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