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" AB; but things which are equal to the same are equal to one another... "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Side 7
av Euclides - 1853
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...(11. Definition) to AB ; and because the point B is the centre of the circle ACE, BC is equal to AB : 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...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...circle ACE, вc is equal to BA: but it 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 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...
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Ancient Egypt: Her Monuments, Hieroglyphics, History and Archæology, and ...

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...
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Novum Organum: Or, True Suggestions for the Interpretation of Nature

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

Euclid - 1845 - 199 sider
...circle BCD, AC is equal \ to AB ; and because the point B is the centre t is nefim of the circle ACE, BC is equal to BA : But it has been proved that CA...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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...therefore AC is equal to AB; (def. 15.) and because the point B is the centre of the angle ACE, therefore BC is equal to BA ; but it has been proved that CA...equal to AB; but things which are equal to the same thing arc equal to one another ; (ax. 1.) therefore CA is equal to CB ; wherefore CA, AB, BC are equal...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...definition 30) to AB; and because the point B is the centre of the circle ACE, BC is equal (I. def. 30) to BA. But it has been proved that CA is equal to...: but things which are equal to the same are equal (I. axiom 1) to one another; therefore CA is equal to CB; wherefore CA, AB, BC are equal to one another;...
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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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The English Journal of Education, Volum 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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