| Euclides - 1845 - 546 pages
...point. II. That a terminated straight line may be produced to any length in a straight line. III. And that a circle may be described from any centre at...centre. AXIOMS. I. THINGS which are equal to the same thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals... | |
| Euclid, James Thomson - Geometry - 1845 - 382 pages
...point : f 2. That a terminated straight line may be produced to any length in a straight line : , 3. That a circle may be described from any centre, at any distance from that centre. J AXIOMS. 1. Things which are equal to the same, or to equals, are equal to one another. 2. If equals... | |
| 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... | |
| 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... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. 1 . THINGS which are equal to the same thing are equal to one another. 2. If equals be added to equals,... | |
| 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,... | |
| 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 - 1847 - 128 pages
...point : 2. That a terminated straight line may be produced to any length in a straight line : and 3. That a circle may be described from any centre, at any distance from that centre. A postulate (from postulare) is a demand so reasonable that it cannot fail to be granted; or, in other... | |
| 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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