| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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.... | |
| 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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