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 Elements of Euclid - Página 246por Euclid - 1838 - 416 páginasVista completa - Acerca de este libro
| Euclides - 1842 - 320 páginas
...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... | |
| John Playfair - 1842 - 332 páginas
...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... | |
| Sir Edward Johnson - 1842 - 622 páginas
...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,... | |
| Philip Kelland - 1843 - 168 páginas
...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 - 348 páginas
...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 - 88 páginas
...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... | |
| Euclid - 1845 - 218 páginas
...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... | |
| 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 - 628 páginas
...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... | |
| 1847 - 602 páginas
...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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