| Euclides - 1845 - 546 páginas
...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 - 1845 - 382 páginas
...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 páginas
...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) - 1845 - 632 páginas
...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 - 1846 - 334 páginas
...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 páginas
...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 - 1846 - 524 páginas
...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 páginas
...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 páginas
...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 - 1847 - 632 páginas
...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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