| Robert Simson - Trigonometry - 1806 - 546 pages
...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 pages
...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... | |
| Charles Butler - 1814 - 582 pages
...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... | |
| English literature - 1814 - 1032 pages
...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 pages
...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 pages
...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 - 354 pages
...But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; now **things which are equal to the same are equal to one another** .I. Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, B are equal to one another ; and the triangle... | |
| George Townsend - 1819 - 156 pages
...circumstance indeed so very surprising, that if I had time to prosecute the inquiry, I might prove, that as **things which are equal to the same, are equal to one another,** the Patriarchs are the Caesars, and the Caesars the sons of Jacob, because they are both synonymous... | |
| Henry Aldrich - 1821 - 300 pages
...reared, and as the final appeal in argument. They benr some slight analogy to the mathematical axioms, **Things which are equal to the same are equal to one another** ; and, Things of which one is equal and the other not equal to the same, are not equal to one another.... | |
| Euclid - 1822 - 222 pages
...a circle may be described from any centre, /&, ff, at any distance from that centre. M o Axioms. 1. **Things which are equal to the same are equal to one another.** 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders... | |
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