| 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.... | |
| 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.... | |
| 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... | |
| 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... | |
| 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.... | |
| ...magnitudes are those which may bo so applied to one another as to coincide" the three others. Magnitudes **whic'h are equal to the same are equal to one another. If equals** arc added 'to equals, the sums are equal. If equals are taken from equals, the remainders are equal,... | |
| 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... | |
| 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... | |
| 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... | |
| Euclides - 1852
...POSTULATES. L LET .it be granted that a straight line may be drawn from any one point to any other point. n. **That a terminated straight line may be produced to...from any centre, at any distance from that centre.** [These three postulates are equivalent in practice to allowing a pen, a ruler, and a pair of compasses.... | |
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