| Francis Bacon - 1850
...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. Lastly:... | |
| William Whewell - 1850
...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... | |
| H. H. Munro - 1850 - 237 sider
...the basis on which the syllogism is founded. 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.... | |
| Henry Aldrich - 1850 - 390 sider
...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 - 1850 - 382 sider
...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 - 1851 - 254 sider
...authority, if not, possibly by the Egyptian documents yet deciphered) — 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... | |
| Maria Georgina Shirreff Grey, Emily Anne Eliza Shirreff - 1851 - 464 sider
...other," it is evidently only another mode of expressing the axiom in geometry, referred to above, " **Things which are equal to the same, are equal to one another."** These are not peculiar principles of particular sciences, but formulae of the essential laws of thought... | |
| John Campbell - 1851 - 549 sider
...Asiatics, the utter destruction of all biblical chronology by this process would be another. " Now, ' **things which are equal to the same are equal to one another.'** If they are anterior to Shoopho's pyramid in Egypt, then Meroe must have been occupied in the earliest... | |
| Euclides - 1852
...compasses. Having these, the reader will be able to draw any of the figures in this book.] AXIOMS. I. **THINGS which are equal to the same are equal to one another.** II. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders... | |
| 1858
...have a gayer or gladder aspect. Mr. Smith's only justification here is a mathematical one : that as **things which are equal to the same are equal to one another,** and both blossoms and tears have been likened to a shower of rain, therefore blossoms may always be... | |
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