Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one... The First Six Books with Notes - Page 3by Euclid - 1822 - 179 pagesFull view - About this book
| 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... | |
| John Mason Good - 1813 - 714 pages
...any centre, at any distance irom that centre. jtiiams.—l. Things which are equal to the same ore **equal to one another. 2. If equals be added to equals, the** whiles ari equal. 3. \f equals be taken from equals, «le remainders aro equal. 4. If equals be added... | |
| 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... | |
| John Greig - 1816 - 224 pages
...circles, 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.... | |
| 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 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.... | |
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