| Aristotle, Walter Mooney Hatch - 1879 - 589 sider
...instincts resulting from education. (lJ 'Induction' or 'mental association' applies to such cases as that **'things which are equal to the same are equal to one another'** — a truth which we can prove by bringing forward certain numbers and quantities. Induction being... | |
| Christian evidence society - 1879
...things, this maxim we apply to the actual material of this world. Did we apply, eg, the axiom that **things which are equal to the same are equal to one another** to actual things, we should first have to ascertain the fact that the two things were exactly equal,... | |
| Isaac Todhunter - 1880 - 400 sider
...BC is equal to BA. [Definition 15. But it has been shewn that CA is equal to AB ; therefore CA and **CB are each of them equal to AB. But things which are equal to the same** thing are equal to one another. [Axiom I. Therefore CA is equal to CB. Therefore CA, AB, BC are equal... | |
| Euclides - 1881
...the circle BCD, AC is equal (Def. 15) to AB. And because the point B is the centre of the circle ACE, **BC is equal to BA. But it has been proved that CA is equal to AB. Therefore** the two straight lines CA, CB, are each of them equal to AB. But things which are equal to the same... | |
| Herbert Spencer - 1881
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — **"Things which are equal to the same are equal to one another,"** can, by multiplied application, do more than establish the equality of some series of magnitudes. But... | |
| 1881
...always begin with an invocation to the Pleiades, thus fixing the original November date of the feast. " **Things which are equal to the same are equal to one another."** I have already adduced evidence to show that the Serbian Christmas feast is substantially a more primitive... | |
| 1881
...premises, the science of mathematics is " fundamentally wrong," and that it is an error to believe that **things which are equal to the same, are equal to one another,** or that the whole is greater than its parts. Accordingly, were it true that Freethinkers differed from... | |
| Alexander Kennedy Isbister - 1882
...B ig the centre of the circle ACE, therefore BC is equal to В A. But it has been proved that С A **is equal to AB ; therefore CA, CB are each of them...equal to AB ; but things which are equal to the same** thing are equal to one another ; (ax. 1) therefore CA is equal to CB i wherefore С A, AB, BC, are... | |
| Herbert Spencer - 1882
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — " **Things which are equal to the same are equal to one another,"** can, by multiplied application, do more than establish the equality of some series of magnitudes. But... | |
| Euclid, Isaac Todhunter - 1883 - 400 sider
...ACE, BC is equal to BA. [Definition 15. But it has been shewn that CA is equal to AB; therefore CA and **CB are each of them equal to AB. But things which are equal to the same** thing are equal to one another. [Axiom 1. Therefore CA is equal to CB. Therefore CA, AB, BC are equal... | |
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