| 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... | |
| 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... | |
| 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... | |
| Euclides - 1852
...one point to any 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.... | |
| 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... | |
| 1852
..."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 - 1852
...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 - 1853
...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... | |
| Euclides - 1853 - 147 sider
...one point to any other point. II. That a terminated straight line may be produced to any length in a **straight line. III. And that a circle may be described...centre. AXIOMS. I. Things which are equal to the same** thing are equal to one another. II. If equals be added to equals, the wholes are equal. III. If equals... | |
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