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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 - Página 246
por Euclid - 1838 - 416 páginas
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The New quarterly review, and digest of current literature, Volumen7

1858
...have a gayer or gladder aspect. Mr. Smith's only justification here is a mathematical one : that as things which are equal to the same are equal to one another, and both blossoms and tears have been likened to a shower of rain, therefore blossoms may always be...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...compasses. Having these, the reader will be able to draw any of the figures in this book.] AXIOMS. I. THINGS which are equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal. III. 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 - 176 páginas
...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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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 - 146 páginas
...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 - 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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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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The Principles of animal and vegetable physiology

J. Stevenson Bushnan - 1854 - 234 páginas
...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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Francisci BAconi de Verulamio, ...: Novum organum, sive Indicia vera de ...

Francis Bacon - 1855 - 385 páginas
...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 - 386 páginas
...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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