Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one... The First Six Books with Notes - Página 3por Euclid - 1822 - 179 páginasVista completa - Acerca de este libro
| Euclid - 1845 - 218 páginas
...But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; But things which are equal to the same are equal to one another || ; therefore CA is equal to CB ; wherefore CA, « i Axiom. AB, BC are equal to one another ; and... | |
| Euclides - 1846 - 272 páginas
...any distance. 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...another. 2. If equals be added to equals, the wholes will be equal. 3. If from equals, equals be taken, the remainders are equal. 4. If to unequals, equals... | |
| 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 - 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... | |
| 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 (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... | |
| 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... | |
| 1849 - 424 páginas
...be paid as well as yours, and I should have d£20,000 a-year instead of 4s. a-day; becanse you see things which are equal to the same are equal to one another.' The Spectator, of April 28, 1849, says — '"Genins" consists in a special capacity for some particular... | |
| Oliver Lorenzo Barbour, New York (State). Supreme Court - 1849 - 706 páginas
...uninfluenced by the demonstration of the simplest problem in Euclid, and to which the axiom, " that things which are equal to the same are equal to one another," would be too abstruse for comprehension. The judgment and the note were familiar. and their relation... | |
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