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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 ... - Side 262
av Euclides - 1834
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The Elements of Euclid [book 1] for beginners, by J. Lowres

Euclides - 1852
...a circle may be described from any centre, with any distance from that centre as radius. 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 - 1853 - 147 sider
...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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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 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 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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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 Principles of animal and vegetable physiology

J. Stevenson Bushnan - 1854 - 234 sider
...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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Orr's Circle of the Sciences: Organic nature, v.1] The principles of physiology

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

Francis Bacon - 1855 - 385 sider
...of 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 in...
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The Novum Organon: Or, A True Guide to the Interpretation of Nature

Francis Bacon - 1855 - 338 sider
...of 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 in...
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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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