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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. "
The London Magazine - Seite 451
1827
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Elements of geometry: consisting of the first four,and the sixth, books of ...

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...
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Lectures on the Principles of Demonstrative Mathematics

Philip Kelland - 1843 - 147 Seiten
...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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Novum Organum: Or, True Suggestions for the Interpretation of Nature

Francis Bacon - 1844 - 336 Seiten
...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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Ancient Egypt: Her Monuments, Hieroglyphics, History and Archæology, and ...

George Robins Gliddon - 1844 - 66 Seiten
...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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The Quarterly Review

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...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 Seiten
...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...
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The English Journal of Education, Band 3

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...
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The Biblical review, and Congregational magazine [formerly The ..., Band 4

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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An Historical and Critical View of the Speculative Philosophy of ..., Band 1

J. D. Morell - 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,...
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Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

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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