| 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... | |
| 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... | |
| Euclides - 1846
...other point : n. That a terminated straight line may be produced to any length in a straight line : in. **That a circle may be described from any centre, at...which are equal to the same are equal to one another.** n. If equals be added to equals, the wholes are equal. in. If equals be taken from equals, the remainders... | |
| John Playfair - 1846 - 317 sider
...other 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,... | |
| J. D. Morell - 1846
...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,... | |
| Euclides - 1846
...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... | |
| 1847
...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
...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
...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... | |
| Euclides - 1848
...other point. II. That a terminated straight line may be produced to any length in a straight line. HI. **And that a circle may be described from any centre...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... | |
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