| Alexander Smith (M.A.) - 1835
...of mathematical axioms. Take such instances as these, " all the parts are equal to the whole," — " **things which are equal to the same are equal to one another."** Why must we at once affirm that these propositions are true, and that the contrary of them cannot be... | |
| John Playfair - 1837 - 318 sider
...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, James Thomson - 1837 - 390 sider
...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 - 1837 - 135 sider
...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, Robert Simson - 1838 - 416 sider
...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 - 1839 - 148 sider
...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. Lastly... | |
| 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. Lastly... | |
| 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... | |
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