 | 1835 - Liczba stron: 684
...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... | |
 | Edward Tagart - 1837 - Liczba stron: 156
...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... | |
 | John Playfair - 1837 - Liczba stron: 332
...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 - Liczba stron: 410
...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 - Liczba stron: 160
...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... | |
 | Robert Simson - 1838 - Liczba stron: 434
...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 - Liczba stron: 156
...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... | |
 | Nicholas Patrick Wiseman - 1841 - Liczba stron: 618
...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... | |
 | Francis Bacon - 1841 - Liczba stron: 616
...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 - Liczba stron: 616
...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.... | |
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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. 
