 | Euclid - Geometry - 1845 - 218 pages
...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 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... | |
 | Euclides - 1845 - 546 pages
...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 is equal to AB ; therefore CA, CB are each of them equal to AB; but things which are equal to the same thing arc equal to one another ; (ax. 1.) therefore CA is equal... | |
 | 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... | |
 | 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... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...circle BCD, AC is equal (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...; now things which are equal to the same are equal f* one another, (1. Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, CB are equal to one another... | |
 | Euclides - 1846 - 292 pages
...equal to AB (Def. 15) ; and because the point B is the centre of the circle ACE, BC is equal to BA : 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 (Ax. 1) ; therefore CA is equal to... | |
 | 1847 - 602 pages
...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,... | |
 | Euclides - 1846 - 272 pages
...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... | |
 | John Daniel Morell - Philosophy, Modern - 1846 - 524 pages
...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,... | |
 | J. D. Morell - Philosophy, Modern - 1847 - 632 pages
...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... | |
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AB; but things which are equal to the same are equal to one another... 
