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
| Peter Nicholson - Mathematics - 1825 - 372 pages
...But it has been proved dial CA is equal to AB ; therefore CA, CB, are each of diem equal to AB ; but **things which are equal to the same are equal to one another** (1st Axiom.) tiierefore CA is equal to CB ; wherefore CA, AB, BC, are equal to one another j and the... | |
| Euclid - 1826 - 180 pages
...but it has been shown that CA is equal to AB : therefore CA, св, are each of them equal to AB. And **things which are equal to the same are equal to one another.** Whence CA is equal to св ; wherefore the three, CA, AB, вс, are equal to one another ; and, consequently,... | |
| Euclides - 1826
...continually produced shall meet on that side where the angles are less than two right angles. 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... | |
| John Martin Frederick Wright - 1827
...understood and admitted." " Very good, Sir, though not precisely in the language of Euclid. But what is **the first axiom of Euclid, or of Geometry, as I may...equals be taken from equals the remainders are equal."** " Very good ?" Mr. B. next interrogated one and then another, until having got through the twelve axioms,... | |
| John Martin F. Wright - 1827
...understood and admitted." " Very good, Sir, though not precisely in the language of Euclid. But what is **the first axiom of Euclid, or of Geometry, as I may...equals be taken from equals the remainders are equal."** " Very good ?" Mr. B. next interrogated one and then another, until having got through the twelve axioms,... | |
| George Bentham - 1827 - 298 pages
...which a syllogistic conclusion can be founded ? Such may, perhaps, be found the four following : 1. **Things which are equal to the same, are equal to one another.** 2. When of two things, one only is equal to a third, and the other is not equal to that third, these... | |
| Leeds grammar sch - 1828
...: but Patience is equal to Poverty ; therefore Patience and Economy are each equal to Poverty ; but **things which are equal to the same are equal to one another;** therefore Patience and Economy are equal to one another ; wherefore the three, Patience, Economy, and... | |
| 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... | |
| George Peacock - Algebra - 1830 - 685 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 - 272 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... | |
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