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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, the parts read in the University of Cambridge [book ... - Page 4
by Euclides - 1846
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 520 pages
...diftance from that centre. AXIOMS. I. THINGS which are equal to the fame are equal to one another. II. If equals be added to equals, the wholes are equal....equals be taken from equals, the remainders are equal. If equals be added to unequals, the wholes are unequal. If equals be taken from unequals, the remainders...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...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...which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...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 Monthly Anthology, and Boston Review, Volume 5

David Phineas Adams, William Emerson, 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) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...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
...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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The Scots Magazine and Edinburgh Literary Miscellany, Volume 76

English literature - 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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Easy Introduction to Mathematics, Volume 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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...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...which are equal to the same are equal to one another. II. . If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the...
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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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