 | Euclid, John Playfair - 1853 - 336 sider
...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 CA ii equal to AB ; therefore CA, CB are each of them equal to AB ; nowfthings which are equal to the... | |
 | sir George Ramsay (9th bart.) - 1853 - 282 sider
...intervention of any general axiom, that the side AB is equal to the side A C. The general axiom, that things which are equal to the same are equal to one another, cannot make the conclusion one whit more evident than it was before. We see at once from the particular... | |
 | J. Stevenson Bushnan - 1854 - 268 sider
...truths — also such propositions as that, when equals are taken from equals, equals remain ; that things which are equal to the same are equal to one another ; that things which are doubles or halves of the same, are equal to one another; that twice four are... | |
 | William Somerville Orr - 1854 - 422 sider
...truths — also such propositions as that, when equals are taken from equals, equals remain ; that things which are equal to the same are equal to one another ; that things which are doubles or halves of the same, are equal to one another ; that twice four arc... | |
 | John Playfair - 1855 - 340 sider
...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...them equal to AB ; now things which are equal to the eame are equal to one another, (1. Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, CB are... | |
 | Robert Potts - 1855 - 588 sider
...that the evidence of the conclusion is manifest.—Dr Whewell. 199. The mathematical postulate, that " things which are equal to the same are equal to one another, 1 ' is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.—Bacon.... | |
 | Edward Tagart - 1855 - 524 sider
...of nature and fact. In mathematical reasoning, no axiom is more constantly employed than this — ' things which are equal to the same are equal to one another.' Are the ideas of equality and inequality in the mind of a child before things have been observed, measured,... | |
 | Euclides - 1863 - 122 sider
...equal (Def. 15) to AB. 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 the two straight lines CA, CB, are each of them equal to AB. But things which are equal to the same... | |
 | Edward Wilton - 1863 - 306 sider
...etymologically, and with the latter, territorially ; and not forgetting the timehonoured axiom of Euclid, that " things which are equal to the same are equal to one another :" the conclusion seems irresistible, that lim and Azem are but component parts of a single proper... | |
 | Oxford Architectural & Historical Society - 1864 - 808 sider
...assailants should find such difficulty in grasping so palpahle a truism as the first axiom of Euclid, that " things which are equal to the same are equal to one another," or should refuse to apply it to lines and curves and geometrical figures. They even reverse it when... | |
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AB; but things which are equal to the same are equal to one another... 
