 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 4531827Full view - About this book
 | Thomas Harper - Metaphysics - 1881 - 798 pages
...Principle in order of reduction. PROLEGOMENON I. The Law of equality is usually expressed in this wise: Things which are equal to the same are equal to one another. Here, at length, a Principle is set before us, which seems to carry on its front a capacity for becoming... | |
 | 1881 - 516 pages
...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 - 308 pages
...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 - 756 pages
...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 - Psychology - 1882 - 722 pages
...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... | |
 | Biography - 1883 - 836 pages
...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 - 272 pages
...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 - 182 pages
...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 - Euclid's Elements - 1885 - 340 pages
...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 - 340 pages
...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... | |
| |
