 | John Playfair - Euclid's Elements - 1842 - 332 pages
...(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... | |
 | Euclides - 1842 - 316 pages
...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... | |
 | 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,... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | Euclid - Geometry - 1845 - 218 pages
...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... | |
 | Euclides - 1845 - 546 pages
...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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...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;... | |
 | 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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AB; but things which are equal to the same are equal to one another... 
