| Euclid, Thomas Tate - 1849 - 120 pages
...is the centre of the circle ACE, BC is equal to BA: But it has been proved that CA is equal to AB; therefore CA, CB are each of them equal to AB; but...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... | |
| Richard Dawes - Teaching - 1849 - 228 pages
...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,... | |
| Secularism - 1849 - 424 pages
...be paid as well as yours, and I should have dĀ£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 ā '"Genins" consists in a special capacity for some particular... | |
| H. H. Munro - Logic - 1850 - 272 pages
...the basis on which the syllogism is founded. They bear some analogy to the mathematical axioms : ā 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.... | |
| Francis Bacon - 1850 - 620 pages
...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.... | |
| Henry Aldrich - Logic - 1850 - 406 pages
...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.... | |
| William Whewell - Education, Higher - 1850 - 416 pages
...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... | |
| William Whewell - Education, Higher - 1850 - 432 pages
...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... | |
| Ephraim George Squier - History - 1851 - 294 pages
...authority, if not, possibly by the Egyptian documents yet deciphered) ā which hypothesis is Euclidean. " Things which are equal to the same are equal to one another." Now, if the " Mundane Egg" be, in the papyric Rituals, the equivalent to Sun, and that, by other hieroglyphical... | |
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