| Mathematics - 1835 - 684 pages
...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... | |
| Alexander Smith - Ethics - 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... | |
| Reginald Rabett - Bible - 1835 - 408 pages
...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 - 750 pages
...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... | |
| Edward Tagart - Logic - 1837 - 156 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... | |
| Euclid - Geometry - 1837 - 410 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.... | |
| William Josiah Irons - 1837 - 160 pages
...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 - Geometry - 1837 - 332 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... | |
| Robert Simson - Geometry - 1838 - 434 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 - 156 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... | |
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