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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 London Magazine - Page 455
by John Scott, John Taylor - 1827
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 318 pages
...But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; now things which are equal to the same are equal to one another. (1. Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, CB are equal to one another ; trtrmgte...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 390 pages
...referred to (he work itself. It may be farther remarked, that the author adopts only the one axiom, " that things which are equal to the same, are equal to one another ;" deriving from this, as corollaries, such of the other axioms, as he requires in his subsequent reasonings....
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Remarks on Mathematical Or Demonstrative Reasoning

Edward Tagart - Logic - 1837 - 135 pages
...individual comprehended in it ; which is analogous to the axiom, or common notion of equality, that things which are equal to the same are equal to one another, or that the whole is made up of all the parts. A syllogism, to make a homely simile, is a kind of two-pronged...
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Parochial lectures

William Josiah Irons - 1837
...proof. Our minds perceive all such truths by a direct glance. If any man should require proof that ' things which are equal to the same are equal to one another,' he would never get any such proof. If he should find by experience that it had been so, in a million...
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The Elements of Euclid

Euclid - Geometry - 1838 - 416 pages
...III. And that a circle may be described from any centre, at any distance from that centre. AXIOMS. I. THINGS which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equals. m. If equals be taken from enuals, the remainders...
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Gradiations in Algebra: In which the First Principles of Analysis are ...

Richard W. Green - Algebra - 1839 - 148 pages
...dividing the 1st, x= — > Transposing and dividing the 2d, x= — —Jr. 5 Now, as it is evident that things which are equal to the same, are equal to one another ; one value of x is equal to the other value of x ; thus, ^. * 23— 3y _10+2y ~2~ ~~" ~5~ Destroying...
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Works, Volume 3

Francis Bacon - 1841
...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 Works of Francis Bacon, Lord Chancellor of England, Volume 3

Francis Bacon - 1841
...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 Dublin Review, Part 2

Nicholas Patrick Wiseman - 1841
...arrangement, how can the celebrated demand in the theory of parallels rank under the same head as that " things which are equal to the same are equal to one another." The misplacement of this axiom about parallels has cost many a trial at this old difficulty, and procured...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; now things which are equal to the same are equal to one another, (1. Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, CB are equal to one another ; and the...
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