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. The London Magazine - Page 4511827Full view - About this book
| 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... | |
| Francis Bacon, Basil Montagu - Law - 1831
...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.... | |
| 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
...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.... | |
| Education - 1834
...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
...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 - 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... | |
| Euclid - 1835 - 513 pages
...magnitudes, to ratios, viz. that a magnitude cannot be both greater and less than another. That those **things which are equal to the same are equal to one another,** is a most evident axiom when understood of magnitudes; yet Euclid does not make use of it to infer,... | |
| Mathematics - 1835
...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 (M.A.) - 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... | |
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