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" 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. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Página 304
por Euclides - 1814
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 páginas
...are equal to one another in area. CONSTRUCTION. — Draw BE and CH. DEMONSTRATION. Syllogism 1. Da (Things which are equal to the same) ARE equal to one another. [Ax. 1.] ii The straight lines BC and EH ARE equal to the same FG. [Hypoth. and I. 34] i Therefore...
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The British Journal of Homoeopathy, Volumen20

1862 - 724 páginas
...dilutions, and the pure ideal. The result would determine whether the dictum of opponents be just, that things which are equal to the same are equal to one another. So much by way of exordium. I now proceed to the subject in hand. The propriety of alternating medicines...
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The British Journal of Homoeopathy, Volumen20

John James Drysdale, Robert Ellis Dudgeon, Richard Hughes, John Rutherfurd Russell - 1862 - 722 páginas
...dilutions, and the pure ideal. The result would determine whether the dictum of opponents be just, that things which are equal to the same are equal to one another. So much by way of exordium. I now proceed to the subject in hand. The propriety of alternating medicines...
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The Cincinnati Lancet & Observer, Volumen5;Volumen23

1862 - 792 páginas
...insisted on by Mr. Lewes and others : namely, that alcohol replaced a certain amount of food ; and " as things which are equal to the same are equal to one another," he inferred that if a glass of ale was equal to a slice of mutton, in its satisfying effect, and that...
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Instinct and Reason; Or, The First Principles of Human Knowledge

George Ramsay - 1862 - 170 páginas
...in the first place, what are called the Axioms of Mathematics or the Science of Quantity, such as " Things which are equal to the same, are equal to one another." " If equals be added to equals, or subtracted from equals, the wholes, or the remainders, will be equal."...
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The Negeb: Or, "South Country" of Scripture

Edward Wilton - 1863 - 306 páginas
...etymologically, and with the latter, territorially ; and not forgetting the timehonoured axiom of Euclid, that " things which are equal to the same are equal to one another :" the conclusion seems irresistible, that lim and Azem are but component parts of a single proper...
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Rules and Proceedings, Volumen1

Oxford Architectural & Historical Society - 1864 - 808 páginas
...assailants should find such difficulty in grasping so palpahle a truism as the first axiom of Euclid, that " things which are equal to the same are equal to one another," or should refuse to apply it to lines and curves and geometrical figures. They even reverse it when...
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God's Week of Work: Being an Examination of the Mosaic Six Days in Relation ...

Evan Lewis - 1865 - 150 páginas
...Euclid are felt to be true in every age, and among every people : "The whole is greater than its part." "Things which are equal to the same, are equal to one another." There may be truths which reason can neither discover nor comprehend; but nothing can be true which...
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An Examination of Mr. J.S. Mill's Philosophy: Being a Defence of Fundamental ...

James McCosh - 1866 - 424 páginas
...principle in all such cases is either, ' Things are the same which are the same with a third,' or ' things which are equal to the same are equal to one another.' Much confusion is avoided by allotting reasoning of this description to a separate head. As there is...
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Biography: Or, Third Division of "The English Encyclopedia", Volumen1

Charles Knight - 1866 - 552 páginas
...mentions that Apollonius attempted to prove the axioms, and cites his investigation of the theorem, that things which are equal to the same are equal to one another, in which, as may be supposed, propositions are assumed not more obvious than the theorem itself. Vitruvius...
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