 | 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... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...(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 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 - 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 - 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... | |
 | 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 council of educ - 1848 - 394 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 (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... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...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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AB; but things which are equal to the same are equal to one another... 
