 | Reginald Rabett - 1835
...equal to 500, so must the former (as the representative of the latter,) be equal to 500 ; because ' things which are equal to the same are equal to one another.' But as the «ir«nj/*or or stenographical character q is a cypher, and no letter, or letters, of the... | |
 | 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... | |
 | 1835
...demonstrating the propositions of the following sections, and are therefore here premised : — 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... | |
 | 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.... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
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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. 
