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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: Viz. the First Six Books, Together with the Eleventh ... - Side 11
av Euclid, Robert Simson - 1821 - 516 sider
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The Works of Francis Bacon, Lord Chancellor of England, Volum 3

Francis Bacon - 1850
...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....
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A Manual of Logic: Deductive and Inductive

H. H. Munro - 1850 - 237 sider
...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....
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Of a Liberal Education in General

William Whewell - 1850 - 382 sider
...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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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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Artis logicae rudimenta: with illustrative observations on each section by ...

Henry Aldrich - 1850 - 390 sider
...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....
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Papers for the schoolmaster, Volumer 1-6

...magnitudes are those which may bo so applied to one another as to coincide" the three others. Magnitudes whic'h are equal to the same are equal to one another. If equals arc added 'to equals, the sums are equal. If equals are taken from equals, the remainders are equal,...
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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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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 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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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...POSTULATES. L LET .it be granted that a straight line may be drawn from any one point to any other point. n. That a terminated straight line may be produced to...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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