...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...

...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...

...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...

...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,...

...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...

...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...

...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...

...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...

...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...

...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...