 | Francis Bacon - 1850 - 620 pagine
...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:... | |
 | Henry Aldrich - 1850 - 406 pagine
...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 - 432 pagine
...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 - 272 pagine
...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 - 416 pagine
...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 - 294 pagine
...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... | |
 | John Campbell - 1851 - 566 pagine
...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 - 496 pagine
...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... | |
 | Euclides - 1852 - 48 pagine
...a circle may be described from any centre, with any distance from that centre as radius. AXIOMS. 1. Things which are equal to the same, are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders... | |
 | Euclides - 1852 - 152 pagine
...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... | |
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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. 
