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" 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. And that a circle may be described from any centre, at any distance from... "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Page 11
by John Playfair - 1855 - 318 pages
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 158 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. 3. Le.t it be granted that a circle may be described from any centre, at any distance from that centre....
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 129 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...
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The London University Magazine, Volume 1

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

Pierce Morton - Geometry - 1830 - 584 pages
...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 greater of two straight lines, a part may be cut off equal to the less ; and 4thly,...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 183 pages
...be produced to any length in a right line. 3. That a circle may be described from any centre, See N. at any distance from that centre. AXIOMS. 1. Things, which are equal to the same, are equal io one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken...
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Magazine of Natural History: And Journal of Zoology, Botany ..., Volume 7

John Claudius Loudon, Edward Charlesworth, John Denson - Natural history - 1834 - 698 pages
...book marks an epoch in the progress of natural history in Britain. One of Euclid's postulates is, " a circle may be described from any centre, at any distance from that centre:" so, in nature, there is not an object which may not become the centre of a thousand associating circumstances....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...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 a circle may be described from any centre, at any distance from that centre. AXIOMS....
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...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 greater of two straight lines, a part may be cut off equal to the less ; and 4thly,...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 332 pages
...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...centre. AXIOMS. 1 . THINGS which are equal to the same thing are equf.l to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...abbreviated expression, meaning the ^auje as in draw a straight line from one of them to the other. 2. That a terminated straight line may be produced to any length in a straight line : 3. That a circle may be described from any centre, at any distance from that centre.* AXIOMS. 1. Things...
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