 | Euclid, Robert Simson - 1829 - 548 sider
...Euclid had given, has been deceived in applying what is manifest, when understood of magnitudes, unto ratios, viz. that a magnitude cannot be both greater...evident axiom when understood of magnitudes ; yet Kuclid does not make use of it to infer that those ratios which are the same to the same ratio, are... | |
 | Timothy Walker - 1829 - 138 sider
...and are to geometry, what the foundations are to a building. Euclid's axioms are the following : I. Things which are equal to the same are equal to one another. 2k If equals be added to equals the wholes are equal. 3. If equals be taken from equals, the remainders... | |
 | William Sewell - 1830 - 390 sider
...experiment. A child never doubts that the fire which burnt him yesterday, will burn him to-day, or that two things which are equal to the same, are equal to one another, where he .has once seen the axiom illustrated by a single example—and hence one great advantage in... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Robert Simson - 1835 - 544 sider
...therefore A is not less than B," &c. Here it is said, that " A would have a less ratio to C than B has to C," or, which is the same thing, that B would have...which are the same to the same ratio, are the same to one another; but explicitly demonstrates this in Prop. 1 1. of Book 5. The demonstration we have... | |
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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. 
