 | H. H. Munro - 1850 - 272 σελίδες
...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 σελίδες
...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... | |
 | John Campbell - 1851 - 566 σελίδες
...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... | |
 | Ephraim George Squier - 1851 - 294 σελίδες
...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 - 496 σελίδες
...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 - 152 σελίδες
...other point. n. That a terminated straight line may be produced to any length in a straight line. III. And that a circle may be described 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.... | |
 | Euclides - 1852 - 48 σελίδες
...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... | |
 | 1858 - 422 σελίδες
...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... | |
 | 1852 - 588 σελίδες
..."Yes." " And the three baskets three days too?" "Yes." Well, thought I, if it be a true axiom that things which are equal to the same are equal to one another, then a grape vine and a basket are identical ! So, finding the rabbinical logic of this poor deluded... | |
 | Euclides - 1853 - 146 σελίδες
...other point. n. That a terminated straight line may be produced to any length in a straight line. in. And that a circle may be described from any centre,...which are equal to the same are equal to one another. H. If equals be added to equals, the wholes are equal. m. If equals be taken from equals, the remainders... | |
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Let it be granted that a straight line may be drawn from any one point to any other point. 
