...dilutions, and the pure ideal. The result would determine whether the dictum of opponents be just, that things which are equal to the same are equal to one another. So much by way of exordium. I now proceed to the subject in hand. The propriety of alternating medicines...

...dilutions, and the pure ideal. The result would determine whether the dictum of opponents be just, that things which are equal to the same are equal to one another. So much by way of exordium. I now proceed to the subject in hand. The propriety of alternating medicines...

...etymologically, and with the latter, territorially ; and not forgetting the timehonoured axiom of Euclid, that " things which are equal to the same are equal to one another :" the conclusion seems irresistible, that lim and Azem are but component parts of a single proper...

...assailants should find such difficulty in grasping so palpahle a truism as the first axiom of Euclid, that " things which are equal to the same are equal to one another," or should refuse to apply it to lines and curves and geometrical figures. They even reverse it when...

...Euclid are felt to be true in every age, and among every people : "The whole is greater than its part." "Things which are equal to the same, are equal to one another." There may be truths which reason can neither discover nor comprehend; but nothing can be true which...

...principle in all such cases is either, ' Things are the same which are the same with a third,' or ' things which are equal to the same are equal to one another.' Much confusion is avoided by allotting reasoning of this description to a separate head. As there is...

...mentions that Apollonius attempted to prove the axioms, and cites his investigation of the theorem, that things which are equal to the same are equal to one another, in which, as may be supposed, propositions are assumed not more obvious than the theorem itself. Vitruvius...

...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...

...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....

...: 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...