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. The Elements of Euclid - Pagina 246door Euclid - 1838 - 416 pagina’sVolledige weergave - Over dit boek
| 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... | |
| Royal Society (Great Britain), Charles Hutton, Richard Pearson - 1809
...conclude the same tiling, tart are quite contrary to your conclusion, and depend on that common axiom, **that those things which are equal to the same are equal to** each other; which however holds only in homogeneous quantities, as here in comparing a virtual action... | |
| 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 pagina’s
...III. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. I. **THINGS which are equal to the same are equal to one another.** II. . If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the... | |
| 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.... | |
| George Townsend - 1819 - 147 pagina’s
...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 - 317 pagina’s
...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
...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 - 179 pagina’s
...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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