Again ; 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. The London Magazine - Page 4511827Full view - About this book
| Euclides - 1842
...has been proved that C л is equal to A в ; therefore CA, c в are each of them equal to AB : but **things which are equal to the same are equal to one another** (1. Axiom) ; therefore CA is equal to cв ; wherefore c A, AB, вc are equal to one another ; and the... | |
| Philip Kelland - Mathematics - 1843 - 147 pages
...I propose to take up the same subject, and inquire, for the sake of precision, whether the truth, " **things which are equal to the same are equal to one another,"** is demonstrable or not. If it be an immediate consequence of our conception of equality, then is it... | |
| Logic - 1844 - 336 pages
...similar to that of music termed the declining of a cadence. Again ; 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.... | |
| George Robins Gliddon - Egypt - 1844 - 66 pages
...Asiatics, the utter destruction of all biblical chronology by thia process would be another. Now, " **things which are equal to •the same are equal to one another."** If they are anterior to Shoopho's pyramid in Egypt, then Weroe must have been occupied in the earliest... | |
| William Gifford, Sir John Taylor Coleridge, John Gibson Lockhart, Whitwell Elwin, William Macpherson, William Smith, Sir John Murray IV, Rowland Edmund Prothero (Baron Ernle) - English literature - 1845
...discovery, that both languages admit of the same Erse interpretation, upon the geometrical principle that **things which are equal to the same are equal to one another.** This argument however depends for its validity on the accuracy of his remaining assumption, that the... | |
| Euclid - Geometry - 1845 - 199 pages
...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, « i Axiom. AB, BC are equal to one another ; and... | |
| 1845
...By the whole of any quantity we understand the sum of all its parts ; thus, AB = AD + DC + CB. 70. " **Things which are equal to the same are equal to one another** " ; that is, if a = m and b = m, a is equal to b. 71. In any arithmetical operation, " quantities which... | |
| 1847
...proved by the use of axioms in the form of propositions, that is not itself evident. The axiom, that **things which are equal to the same are equal to one another,** is not the proof that A and B, being equal to C, are themselves equal. The latter truth, which is particular,... | |
| J. D. Morell - Philosophy, Modern - 1846
...judgments, as we have seen in our analysis of Locke, are at first particular and concrete. The axiom, " **things which are equal to the same are equal to one another,"** never suggests itself to a child's mind. and yet as soon as reason is developed enough to observe equality,... | |
| Euclides - 1846
...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. 3. If from equals, equals be taken, the... | |
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