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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 Euclid - Side 8
av Euclid - 1838 - 416 sider
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 sider
...II. That a terminated straight line may be produced to any length in a straight line. HI. And thai a circle may be described from any centre, at any...centre. AXIOMS. , I. THINGS which are equal to the same thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 sider
...magnitudes, unto ratios, viz. that a magnitude cannot be both greater and less than another. That those things which are equal to the same are equal to one another, is a most evident axiom when understood of magnitudes ; yet Euclid does not make use of it to infer...
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The Monthly Anthology, and Boston Review, Volum 5

David Phineas Adams, Samuel Cooper Thacher - 1808
...confound our two articles. " In the Celtic" says he, " the article an signifies the and that." But as things, which are equal to the same, are equal to one another, it is easy to prove, since an means that, and //•.- means that, that an and the are in the English...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 5

John Mason Good - 1813
...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 irom that centre. jtiiams.—l. Things which are equal to the same ore equal to one another. 2. If...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...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. AX IOM S. I. THINGS which are equal to the same are equal to one another. II. If equals be added to...
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Easy Introduction to Mathematics, Volum 2

Charles Butler - 1814
...ACE, BC is equal to BA, by the \5th definition; therefore CA,.CB are each of them equal to AB ; but things which are equal to the same are equal to one another, by the 1st' axiom; wherefore CA and CB are equal to one another, being each equal to AB ; consequently...
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The Scots Magazine and Edinburgh Literary Miscellany, Volum 76

1814
...contrary, they are such 35, considered separately, do not afford room for a single inference. — That things which are equal to the same, are equal to one another, and that the whole is greater than its part, considered in themselves, are mere barren truisms. The...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...magnitudes, unto ratios, viz. that a magnitude cannot be both greater and less than another. That those things which are equal to the same are equal to one another, is a most.evident axiom when understood of magnitudes ; yet Euclid does not make use of it to infer,...
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An Introduction to the Use of the Globes ... 3. Ed. Corr. and Enl

John Greig - 1816
...because they divide the globe into unequal parts, called segments, as o C b and A ob B D. 2. Axioms.* 1. Things which are equal to the same, are equal to one another. * Axiom, implies a plain, self-evident troth or proposition, which is no sooner proposed but understood....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 sider
...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...centre. AXIOMS. I. THINGS which are equal to the same thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equate...
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