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 London Magazine - Page 455by John Scott, John Taylor - 1827Full view - About this book
| John Playfair - Geometry - 1837 - 318 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.** (1. Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, CB are equal to one another ; trtrmgte... | |
| Euclid - Geometry - 1837 - 390 pages
...referred to (he work itself. It may be farther remarked, that the author adopts only the one axiom, " that **things which are equal to the same, are equal to one another** ;" deriving from this, as corollaries, such of the other axioms, as he requires in his subsequent reasonings.... | |
| Edward Tagart - Logic - 1837 - 135 pages
...individual comprehended in it ; which is analogous to the axiom, or common notion of equality, that **things which are equal to the same are equal to one another,** or that the whole is made up of all the parts. A syllogism, to make a homely simile, is a kind of two-pronged... | |
| William Josiah Irons - 1837
...proof. Our minds perceive all such truths by a direct glance. If any man should require proof that ' **things which are equal to the same are equal to one another,'** he would never get any such proof. If he should find by experience that it had been so, in a million... | |
| Euclid - Geometry - 1838 - 416 pages
...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 equals. m. If equals be taken from enuals, the remainders... | |
| Richard W. Green - Algebra - 1839 - 148 pages
...dividing the 1st, x= — >£ Transposing and dividing the 2d, x= — —Jr. 5 Now, as it is evident that **things which are equal to the same, are equal to one another** ; one value of x is equal to the other value of x ; thus, ^. * 23— 3y _10+2y ~2~ ~~" ~5~ Destroying... | |
| Francis Bacon - 1841
...similar to that of music termed the declining of a cadence. 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.... | |
| Francis Bacon - 1841
...similar to that of music termed the declining of a cadence. 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.... | |
| Nicholas Patrick Wiseman - 1841
...arrangement, how can the celebrated demand in the theory of parallels rank under the same head as that " **things which are equal to the same are equal to one another."** The misplacement of this axiom about parallels has cost many a trial at this old difficulty, and procured... | |
| John Playfair - Euclid's Elements - 1842 - 317 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,** (1. Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, CB are equal to one another ; and the... | |
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