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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 451
1827
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An introduction to mental philosophy

sir George Ramsay (9th bart.) - 1853
...intervention of any general axiom, that the side AB is equal to the side A C. The general axiom, that things which are equal to the same are equal to one another, cannot make the conclusion one whit more evident than it was before. We see at once from the particular...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...But it has been proved that CA is equal to AB; therefore CA, CB, are each of them equal to AB; but things which are equal to the same are equal to one another (Ax. 1.) ; therefore 3. CA is equal to CB. Wherefore CA, AB, BC, are equal to one another ; and therefore...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...3. And that a circle may be described from any centre, at any distance from that centre. 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 first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...but it has been proved that ca is equal to ab; therefore ca, cb, are each of them equal to ab ; but things which are equal to the same are equal to one another (1 ax.); therefore ca is equal to cb; wherefore ca, ab, bc are equal to one another; and the triangle...
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Orr's Circle of the Sciences: Organic nature, v.1] The principles of physiology

William Somerville Orr - Science - 1854
...truths — also such propositions as that, when equals are taken from equals, equals remain ; that things which are equal to the same are equal to one another ; that things which are doubles or halves of the same, are equal to one another ; that twice four arc...
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The Principles of Animal and Vegetable Physiology: A Popular Treatise on the ...

John Stevenson Bushnan - Physiology - 1854 - 234 pages
...truths — also such propositions as that, when equals are taken from equals, equals remain ; that things which are equal to the same are equal to one another ; that things which are doubles or halves of the same, are equal to one another; that twice four are...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...that the evidence of the conclusion is manifest.—Dr Whewell. 199. 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.—Bacon....
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Liber Cantabrigiensis, an Account of the Aids Afforded to Poor Students, the ...

Robert Potts - 1855 - 554 pages
...that the evidence of the conclusion is manifest.—Dr Whewett. 199. 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.—Bacon....
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The Popular Educator, Volume 6

1855
...art equal to ta<A other. (Euclid 11, 5.) This is nothing more than an application of the axiom, that things which are equal to the same are equal to one another. And с : d : : m : n 2. If a :.* : : m : я And m : n : : с : d Cor. If a : 6 : : m : я l m : п>...
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Locke's writings and philosophy historically considered, and vindicated from ...

Edward Tagart - 1855 - 517 pages
...of nature and fact. In mathematical reasoning, no axiom is more constantly employed than this — ' things which are equal to the same are equal to one another.' Are the ideas of equality and inequality in the mind of a child before things have been observed, measured,...
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