 | Euclides - 1842 - Liczba stron: 316
...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... | |
 | Sir Edward Johnson - 1842 - Liczba stron: 622
...word which is equivalent to any one of them, must, therefore, also be equivalent to the others, since things which are equal to the same, are equal to one another. I have said that when we wish to convert a noun into a verb, we do so by prefixing the word to. Thus,... | |
 | John Playfair - 1842 - Liczba stron: 332
...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... | |
 | Philip Kelland - 1843 - Liczba stron: 168
...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 - Liczba stron: 348
...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 - Liczba stron: 92
...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 - Liczba stron: 632
...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... | |
 | 1845 - Liczba stron: 404
...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... | |
 | Euclid - 1845 - Liczba stron: 218
...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... | |
 | 1847 - Liczba stron: 602
...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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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. 
