...believes the axioms of Euclid, but simply because of the impossibility of thinking the contrary. That " things which are equal to the same are equal to one another " is a truth clear at once to any mind capable of understanding its terms, without the slightest necessity...

...because the single case is not, and cannot be, adequately presented to it. For the universal truth, that things which are equal to the same are equal to one another, cannot be seen in any case until the notion of equality has been acquired. But this notion again never...

...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...

...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...

...than are producible from the deai Now let us turn to the logical and physical side of the question. Things which are equal to the same are equal to one another, and if equals be added to equals the whole are equal. Anatomy teaches us that there is no difference...

...Here again the word is psyche, but containing all the attributes of kardia. The inference is obvious : things which are equal to the same are equal to one another. While we may freely admit that, in the terms of a language, this principle will not rigidly apply,...

...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...

...laws, which they have been taught to believe sacred, and which alone they can possibly comprehend."1 ' Things which are equal to the same are equal to one another,' says Euclid. What applies to the part, will apply to the whole. A political agent, the only political...

...living subject than are producible from the dead. Let us turn to the logical side of the question. Things which are equal to the same are equal to one another. Anatomy teaches us that there is no difference between the male and female larynx save in size, so...

...the evidence of the conclusion is manifest. — Dr. Whewell. 214. 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. —...