 | Pierce Morton - 1830 - 584 sider
...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 arc equal. 3. If equals be taken from equals, the remainders... | |
 | George Peacock - 1830 - 732 sider
...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 sider
...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;... | |
 | Thomas Perronet Thompson - 1833 - 168 sider
...But it has been shown that BC is equal to BG ; wherefore AL and BC are each of them equal to BG. And things which are equal to the same, are* equal to one another ; therefore AL is equal to BC. Wherefore from the point A a straight line AL has been drawn, equal... | |
 | Francis Bacon, Basil Montagu - 1831 - 486 sider
...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... | |
 | 1834 - 416 sider
...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... | |
 | Reginald Rabett - 1835 - 408 sider
...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... | |
 | Euclid - 1835 - 540 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 equal. III. If equals be taken from equals, the remainders... | |
 | Alexander Smith - 1835 - 350 sider
...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... | |
 | Alexander Smith (M.A.) - 1835 - 750 sider
...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... | |
| |
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. 
