 | 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... | |
 | 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... | |
 | 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... | |
 | 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,... | |
 | George Townsend - 1819 - 156 Seiten
...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... | |
 | John Playfair - 1819 - 354 Seiten
...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... | |
 | Henry Aldrich - 1821 - 300 Seiten
...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 Seiten
...line. 3. That 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... | |
 | Peter Nicholson - 1825 - 1046 Seiten
...But it has been proved dial CA is equal to AB ; therefore CA, CB, are each of diem equal to AB ; but things which are equal to the same are equal to one another (1st Axiom.) tiierefore CA is equal to CB ; wherefore CA, AB, BC, are equal to one another j and the... | |
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Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term. 
