 | John Playfair - 1806 - 320 Seiten
...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... | |
 | Robert Simson - 1806 - 546 Seiten
...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... | |
 | David Phineas Adams, William Emerson, Samuel Cooper Thacher - 1808 - 708 Seiten
...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... | |
 | John Mason Good - 1813 - 714 Seiten
...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... | |
 | Euclides - 1814 - 560 Seiten
...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... | |
 | Charles Butler - 1814 - 582 Seiten
...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... | |
 | 1814 - 1032 Seiten
...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... | |
 | Euclides - 1816 - 588 Seiten
...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,... | |
 | John Greig - 1816 - 224 Seiten
...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.... | |
 | John Playfair - 1819 - 350 Seiten
...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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Let it be granted that a straight line may be drawn from any one point to any other point. 
