| 1841
...arrangement, how can the celebrated demand in the theory of parallels rank under the same head as that " **things which are equal to the same are equal to one another."** The misplacement of this axiom about parallels has cost many a trial at this old difficulty, and procured... | |
| John Playfair - 1842 - 317 sider
...But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; now **things which are equal to the same are equal to one another,** (1. Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, CB are equal to one another ; and the... | |
| 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 - 1843 - 147 sider
...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 properly... | |
| Francis Bacon - 1844 - 336 sider
...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. Lastly... | |
| George Robins Gliddon - 1844 - 66 sider
...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) - 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 - 1845 - 199 sider
...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,... | |
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