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" Let it be granted that a straight line may be drawn from any one point to any other point. "
Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ... - Page 220
by James Bates Thomson - 1844 - 237 pages
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A treatise on navigation, and nautical astronomy

Edward Riddle - Nautical astronomy - 1824 - 572 pages
...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 described...
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Elements of Geometry, Containing the First Six Books of Euclid

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

Robert Simson - Trigonometry - 1827 - 546 pages
...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 - 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....
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 pages
...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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The United Service Journal and Naval and Military Magazine, Part 3

Military art and science - 1831 - 618 pages
...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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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
...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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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...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 First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...also are two angles which are together equal to two right angles. POSTULATES.* 1. Let it be granted, that a straight line may be drawn from any one point, to any other point :.). writers rather improperly use urcb) and chord receive their names from the bow (in Latin arcvs),...
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