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" Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one... "
The Elements of Euclid [book 1] for beginners, by J. Lowres - Page 10
by Euclides - 1852
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The Works of Francis Bacon, Lord Chancellor of England, Volume 3

Francis Bacon - 1841 - 616 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....
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The Dublin Review, Volume 11

Nicholas Patrick Wiseman - 1841 - 618 pages
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...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...
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Nuces Philosophical

Sir Edward Johnson - Language and languages - 1842 - 622 pages
...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,...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...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...
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Lectures on the Principles of Demonstrative Mathematics

Philip Kelland - Algebra - 1843 - 168 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...
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Ancient Egypt: Her Monuments, Hieroglyphics, History and Archæology, and ...

George Robins Gliddon - Egypt - 1844 - 92 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...
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Novum Organum: Or, True Suggestions for the Interpretation of Nature

Francis Bacon - Induction (Logic) - 1844 - 348 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....
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The English Journal of Education, Volume 3

1845 - 404 pages
...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...
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The Quarterly Review, Volume 76

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 - 632 pages
...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...
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