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 - Seite 4511827Vollansicht - Über dieses Buch
| 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... | |
| 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... | |
| 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... | |
| 1883
...straight and crooked would have no more meaning to him than red and blue to the Wind. The axiom, that **things which are equal to the same are equal to one another,** is only a particular case of the predication of similarity ; if there were no impressions, it is obvious... | |
| Stewart W. and co - 1884
...but it has been proved that CA is equal to AB ; therefore CA, CB, are each of them equal to AB ; but **things which are equal to the same are equal to one another** ; therefore CA is equal to CB ; wherefore CA, AB, BC, are equal to one another ; and the triangle ABC... | |
| Euclides - 1884
...angles CBE, EBA, ABD. But the angles CBE, EBD have been proved equal to the same three angles ; and **things which are equal to the same are equal to one another** ; therefore the angles CBA, ABD are equal to the angles CBE, EBD. ' (Ax. 1) But CBE, EBD are two right... | |
| Euclid, John Casey - 1885 - 312 Seiten
...is the centre of the circle ACE, BC is equal to BA. Hence we have proved. AC = AB, and BC = AB. But **things which are equal to the same are equal to one another** (Axiom i.) ; therefore AC is equal to BC ; therefore the three lines AB, BC, CA are equal to one another.... | |
| Euclides - 1885
...AB . BE is equal to the figure AE. Hence the rectangle AB . CB is equal to the figure AE. And since **things which are equal to the same are equal to one another,** the rectangle AC . CB, together with the square, on CB, is equal to the rectangle AB . CB. , Or thus... | |
| Henry James Clarke - 1885 - 265 Seiten
...the unreasonableness of such a desire. What then am I to do ? I need not ask how I am to prove that **things which are equal to the same are equal to one another** : this truth is one of which I have a clear perception ; I feel sure that I know it by immediate intuition,... | |
| 1886
...same time be and not be ; (2) that if equals be added to equals the wholes are equal ; and (3) that **things which are equal to the same are equal to one another.** It so happens that each of these propositions which he has assumed to be true is, if true, much more... | |
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