| 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... | |
| Euclid, John Playfair - 1846 - 334 páginas
...(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 is equal to AB ; therefore CA, CB are each of them equal to AB** ; now things which are equal to the same are equal f* one another, (1. Axiom) ; therefore CA is equal... | |
| Euclides - 1846 - 292 páginas
...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 - 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 - 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... | |
| 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... | |
| Bengal council of educ - 1848 - 394 páginas
...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 (India) - 1848 - 520 páginas
...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... | |
| Euclid, Thomas Tate - 1849 - 120 páginas
...circle BCD, AC is equal (Definition 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...which are equal to the same are equal to one another** (Axiom 1.) ; therefore CA is equal to cu; wherefore CA. AB, BC are equal to one another; and the triangle... | |
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