| 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) - English literature - 1845 - 628 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... | |
| 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... | |
| Euclides - 1846 - 292 pages
...But it has been shewn that BC is equal to BG; therefore AL and BC are each of them equal to BG : And **things which are equal to the same are equal to one another** ; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL... | |
| John Daniel Morell - Philosophy, Modern - 1846 - 536 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... | |
| Bengal (India) - 1848 - 520 pages
...but belong to a higher and larger science. As examples of such axioms he gives that of mathematics, " **things which are equal to the same are equal to one another,"** which can equally well be applied to logic, thereby insinuating that the observations of "philosophia... | |
| Bengal council of educ - 1848 - 396 pages
...but belong to a higher and larger science. As examples of such axioms he gives that of mathematics, " **things which are equal to the same are equal to one another,"** which can equally well be applied to logic, thereby insinuating that the observations of " philosophia... | |
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