| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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... | |
| 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... | |
| 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;... | |
| 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... | |
| 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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