 | 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... | |
 | Euclid - Geometry - 1810 - 554 pages
...been shown, that BC is equal to BG; wherefore AL and BC are each of them equal to BG; and thinge that are equal to the same are equal to one another; therefore the straight lme AL is equal to BC . Wherefore from the given point A a straight line AL • has been drawn... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | 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 - Circle-squaring - 1819 - 350 pages
...been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC. Wherefore, from the given point A, a straight line AL has been drawn... | |
 | 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... | |
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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. 
