| Euclid, Robert Simson - Geometry - 1829 - 516 pages
...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 - Geometry - 1829 - 129 pages
...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 - Classical education - 1830 - 371 pages
...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 - Algebra - 1830 - 732 pages
...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 - Geometry - 1830 - 584 pages
...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 - Law - 1831 - 478 pages
...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 - Euclid's Elements - 1833 - 150 pages
...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 pages
...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... | |
| Education - 1834 - 416 pages
...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 - Trigonometry - 1835 - 513 pages
...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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