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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The Elements of Euclid - Side 8
av Euclid - 1838 - 416 sider
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Of a Liberal Education in General; and with Especial Reference 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...
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Negro-mania: Being an Examination of the Falsely Assumed Equality of 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...
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The Serpent Symbol, and the Worship of the Reciprocal Principles of Nature ...

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...
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Thoughts on Self-culture, Addressed to Women

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...
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The first two books of the Elements of Euclid, with additional figures ...

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....
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The New quarterly review, and digest of current literature, Volum 7

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...
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The British Millennial Harbinger, Volum 5

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...
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The Elements of Euclid [book 1] for beginners, by J. Lowres

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...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

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...
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The first six books of the Elements of Euclid, with numerous exercises

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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