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" Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one... "
The Elements of Euclid [book 1] for beginners, by J. Lowres - Page 10
by Euclides - 1852
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Orr's Circle of the Sciences: Organic nature, v.1] The principles of physiology

William Somerville Orr - Science - 1854 - 422 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 arc...
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Francisci BAconi de Verulamio, ...: Novum organum, sive Indicia vera de ...

Francis Bacon - 1855 - 386 pages
...Music called " sliding from the close or cadence." In like manner, the Mathematical Postulate, " those things which are equal to the same, are equal to one another," is Conformable to the construction of the Syllogism in Logic; for it unites those Terms which agree...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...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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The Popular Educator, Volume 6

1855 - 424 pages
...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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The Novum Organon: Or, A True Guide to the Interpretation of Nature

Francis Bacon - Science - 1855 - 388 pages
...Music called "sliding from the close or cadence." In like manner, the Mathematical Postulate, " those things which are equal to the same, are equal to one another," is Conformable to the construction of the Syllogism in Logic; for it unites those Terms which agree...
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Locke's Writings and Philosophy Historically Considered: And Vindicated from ...

Edward Tagart - Hume, David, 1711-1776 - 1855 - 524 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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Liber Cantabrigiensis, an Account of the Aids Afforded to Poor Students, the ...

Robert Potts - Scholarships - 1855 - 588 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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Intuitive Calculations: The Most Concise Methods Ever Published, Designed ...

Daniel O'Gorman - Ready-reckoners - 1856 - 186 pages
...the truth or falsity of propositions. AXIOMS. 1. — Those things which are equal to the same thing are equal to one another. 2. — If equals be added to equals, the whole shall be equal. 3. — If equals be taken from equals, the remainder will be equal. 4. — If...
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...means the square-root of the product of A and B. AXIOMS. 1. Things which are equal to the same thing, are equal to one another. 2. If equals be added to equals, the wholes will be 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals,...
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The Works of Francis Bacon, Volume 3

Francis Bacon, Basil Montagu - 1857 - 612 pages
...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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