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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: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 256
av Euclid, Robert Simson - 1838 - 416 sider
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The British Millennial Harbinger, Volum 5

1852
..."Yes." " And the three baskets three days too?" "Yes." Well, thought I, if it be a true axiom that things which are equal to the same are equal to one another, then a grape vine and a basket are identical ! So, finding the rabbinical logic of this poor deluded...
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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 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 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: A Popular Treatise on the ...

John 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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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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Francisci Baconi de Verulamio novum organum, sive indicia vera der ...

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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