 | 1814 - 1032 páginas
...the 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... | |
 | George Peacock - 1830 - 732 páginas
...are represented, or in terms of which they are expressed: without such a definition, the proposition that " things which are equal to the same are equal to one another," could no longer be considered as axiomatic, inasmuch as we should be at a loss for the principle or... | |
 | Francis Bacon, Basil Montagu - 1831 - 478 páginas
...is 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, Basil Montagu - 1831 - 486 páginas
...is 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.... | |
 | 1834 - 410 páginas
...to Proclus, had preceded him in this attempt : we give the demonstration by Apollonius of the axiom, that things which are equal to the same are equal to one another. He argues, that if A is equal to B, it occupies (may be made to occupy) the same place as B. And if... | |
 | William Josiah Irons - 1837 - 160 páginas
...admits of 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, James Thomson - 1837 - 410 páginas
...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 - 156 páginas
...every 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 - 156 páginas
...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 - 616 páginas
...is similar to that of music termed the declining of a cadence. Again ; the mathematical postulate, , because my thanks cannot any ways be sufficient to attain, I have is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.... | |
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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. 
