| Euclides - 1848 - 52 páginas
...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 at...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... | |
| 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... | |
| Euclid, Thomas Tate - 1849 - 120 páginas
...BA: 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** (Axiom 1.) ; therefore CA is equal to cu; wherefore CA. AB, BC are equal to one another; and the triangle... | |
| 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... | |
| Richard Dawes - 1849 - 228 páginas
...which many of them would turn to a good purpose. Even a knowledge of the axioms of Euclid, such as " **things which are equal to the same are equal to one another."** If equals be added to equals the wholes are equal. If equals be added to unequals, the wholes are unequal,... | |
| 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... | |
| Francis Bacon - 1850 - 620 páginas
...similar to that of music termed the declining of a cadence. Again; the mathematical postulate, that **"things which are equal to the same are equal to one another,"** is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.... | |
| William Whewell - 1850 - 432 páginas
...It may be said, indeed, that every step in analysis is a syllogism, in which the major is the Axiom, **Things which are equal to the same are equal to one another;** and the minor is a proposition that two certain forms of symbols have been proved to be equal to the... | |
| Henry Aldrich - 1850 - 406 páginas
...to be reared, and the final appeal in argument. They bear some analogy to the mathematical axioms, **Things which are equal to the same are equal to one another;** and, Things of which one is equal and the other not equal to the same, are not equal to one another.... | |
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