 | Ephraim George Squier - 1851 - 294 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...the circle ACE, BC is equal to BA. But it has been proved that AC is equal to AB ; therefore AC, BC are each of them equal to AB ; but things which are equal to the same are equal to one 4 I Axiom. another d therefore AC is equal to BC ; wherefore AC, AB, BC are equal to one another; and... | |
 | 1852 - 588 Seiten
..."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... | |
 | 1858 - 422 Seiten
...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... | |
 | Euclides - 1852 - 48 Seiten
...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... | |
 | 1867 - 524 Seiten
...science. The man who tells me that he cannot believe that " the whole is greater than the part," or " that things which are equal to the same are equal to one another," cannot step over the very threshold of geometry. Nor are these axioms confined to self-evident truths.... | |
 | Francis Garden - 1867 - 228 Seiten
...affections of the thing thought about, not of our thought about it. PART III. ON SYLLOGISM. § 1. AXIOMS. I. THINGS which are equal to the same are equal to one another. II. A part of a part is a part of the whole. III. A predicate of a predicate is a predicate of the... | |
 | Robert Potts - 1868 - 434 Seiten
...CE, therefore .BCis equal to AB; but it has been proved that AC is equal to AB ; therefore AC, .BC are each of them equal to AB ; but things "which are equal to the same thing are equal to one another ; therefore .4 C is equal to BC; (ax. 1.) wherefore AB, BC, CA are equal... | |
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AB; but things which are equal to the same are equal to one another... 
