...science. The man who tells me that he cannot believe that " the whole is greater than the part," or " that things which are equal to the same are equal to one another," cannot step over the very threshold of geometry. Nor are these axioms confined to self-evident truths....

...affections of the thing thought about, not of our thought about it. PART III. ON SYLLOGISM. § 1. AXIOMS. I. THINGS which are equal to the same are equal to one another. II. A part of a part is a part of the whole. III. A predicate of a predicate is a predicate of the...

...: it must always have been true that " truth is a virtue," as it must always have been true that " things which are equal to the same are equal to one another." And if moral or mathematical truth is thus co-eternal with God, it cannot be something independent...

...another. I would remind you of an expression which I made use of in prayer on this platform this week — "Things which are equal to the same are equal to one another." If then we are equally like Jesus, we shall be like one another. Thus shall we learn to love one another,...

...must owe something to each of these. Let it be granted for instance that the universal judgment, " things which are equal to the same are equal to one another," is not merely suggested but learned by experience. Still, the fact that experience takes this form is...

...must owe something to each of these. Let it be granted for instance that the universal judgment, " things which are equal to the same are equal to one another," is not merely suggested but learned by experience. Still, the fact that experience takes this form is...

...properties as emotion we shall not only have established points of resemblance between the two (for things which are equal to the same are equal to one another), but we shall have actually reached the common ground, or kind of border-land, upon which internal emotion...

...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...

...3. That a circle can be described from any centre, with any radius. COMMON NOTIONS, OR AXIOMS. 1 . Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes will be equal. 4. If to unequals, equals be added, the...

...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,...