| Rev. James Mcosh - 1860
...as the " Common Notions," so far as they relate to quantity, prefixed by Euclid to his Elements. " **Things which are equal to the same are equal to one another."** " If equals be added to equals, the wholes are equal." " If equals be taken from equals, the remainders... | |
| 1862
...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... | |
| 1862
...insisted on by Mr. Lewes and others : namely, that alcohol replaced a certain amount of food ; and " as **things which are equal to the same are equal to one another,"** he inferred that if a glass of ale was equal to a slice of mutton, in its satisfying effect, and that... | |
| George Ramsay - 1862 - 136 sider
...in the first place, what are called the Axioms of Mathematics or the Science of Quantity, such as " **Things which are equal to the same, are equal to one another."** " If equals be added to equals, or subtracted from equals, the wholes, or the remainders, will be equal."... | |
| Edward Wilton - 1863
...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... | |
| Oxford Architectural & Historical Society - 1864
...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... | |
| Evan Lewis - 1865 - 93 sider
...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... | |
| James McCosh - 1866 - 406 sider
...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... | |
| Charles Knight - 1866
...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... | |
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