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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 Nineteenth Century, Volum 30

1891
...must presuppose the admission of certain postulates on the part of both dramatist and audience. If that a circle may be described from any centre, at any distance from that centre, is matter of opinion, we can prove no mathematical proposition ; and, without some appropriate conceded...
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Free Exchange: Papers on Political and Economical Subjects Including ...

Louis Mallet - 1891 - 356 sider
...Mill's " Principles of Pol. Econ.," cap. 21. exports exchange for the same quantity of money. And since things which are equal to the same are equal to one another, the imports and exports which are equal in money price would, if money were not used, precisely exchange...
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Novum Organum: Or, True Suggestions for the Interpretation of Nature

Francis Bacon - 1893 - 245 sider
...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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The Popular Science Monthly, Volum 8

1876
...the same time be and not be ; 2. That if equals be added to equals, the wholes are equal ; 3. That things which are equal to the same are equal, to one another. It so happens that each of these propositions which he lias assumed to be true is, if true, much more...
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Hume, with Helps to the Study of Berkeley: Essays

Thomas Henry Huxley - 1896 - 319 sider
...straight and crooked would have no more meaning to him, than red and blue to the blind. The axiom, that things which are equal to the same are equal to one another, is only a particular case of the predication of similarity; if there were no impressions, it is obvious...
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Sermons Preached on Special Occasions, 1860-1889

Henry Parry Liddon - 1897 - 359 sider
...; it must always have been true that " truth is a virtue," as it must always have been true that " things which are equal to the same are equal to one another." And if moral or mathematical truth is thus co-eternal with God, it cannot be something independent...
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Containing book II. Positive science

Shadworth Hollway Hodgson - 1898
...and also, by means of the plane, of parallel straight lines, in which use is made of the postulate " that a terminated straight line may be produced to any length in a straight line," that is, of the conception of infinity. The idea, that the direction of a straight line is not altered...
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Mind, Volum 7

George Croom Robertson, George Frederick Stout, George Edward Moore - 1898
...circles ' respectively. In the following, eg : — ' Two straight lines cannot enclose a space ' ; ' A circle may be described from any centre at any distance from that centre ' ; ' Hull lies due north of London,' the matter becomes more doubtful. Is our assertion, eg, about...
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A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV., Bok 1

Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 sider
...that is to say a terminated, straight line may be produced to any length in that straight line. 3. That a circle may be described from any centre, at any distance from that centre, that is, with a radius equal to any finite straight line drawn from the centre. NOTES ON THE POSTULATES....
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Advancement of Learning and Novum Organum

Francis Bacon - 1900
...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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