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" AB; but things which are equal to the same are equal to one another... "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Side 7
av Euclides - 1853
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The Moral Philosophy of Aristotle: Consisting of a Translation of the ...

Aristotle, Walter Mooney Hatch - 1879 - 589 sider
...instincts resulting from education. (lJ 'Induction' or 'mental association' applies to such cases as that 'things which are equal to the same are equal to one another' — a truth which we can prove by bringing forward certain numbers and quantities. Induction being...
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Christian evidence lectures

Christian evidence society - 1879
...things, this maxim we apply to the actual material of this world. Did we apply, eg, the axiom that things which are equal to the same are equal to one another to actual things, we should first have to ascertain the fact that the two things were exactly equal,...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 sider
...BC is equal to BA. [Definition 15. But it has been shewn that CA is equal to AB ; therefore CA and CB are each of them equal to AB. But things which are equal to the same thing are equal to one another. [Axiom I. Therefore CA is equal to CB. Therefore CA, AB, BC are equal...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...the circle BCD, AC is equal (Def. 15) to AB. And because the point B is the centre of the circle ACE, BC is equal to BA. But it has been proved that CA is equal to AB. Therefore the two straight lines CA, CB, are each of them equal to AB. But things which are equal to the same...
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Works, Volum 3

Herbert Spencer - 1881
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — "Things which are equal to the same are equal to one another," can, by multiplied application, do more than establish the equality of some series of magnitudes. But...
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Macmillan's Magazine, Volum 43

1881
...always begin with an invocation to the Pleiades, thus fixing the original November date of the feast. " Things which are equal to the same are equal to one another." I have already adduced evidence to show that the Serbian Christmas feast is substantially a more primitive...
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Pamphlets, Religious: Miscellaneous, Volum 14

1881
...premises, the science of mathematics is " fundamentally wrong," and that it is an error to believe that things which are equal to the same, are equal to one another, or that the whole is greater than its parts. Accordingly, were it true that Freethinkers differed from...
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Unitary Arithmetic: Embodying the First Book of Arithmetic of the Irish ...

Alexander Kennedy Isbister - 1882
...B ig the centre of the circle ACE, therefore BC is equal to В A. But it has been proved that С A is equal to AB ; therefore CA, CB are each of them...equal to AB ; but things which are equal to the same thing are equal to one another ; (ax. 1) therefore CA is equal to CB i wherefore С A, AB, BC, are...
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The Principles of Psychology, Volum 2

Herbert Spencer - 1882
...knowledge beyond that of the coexistence of an indefinite number of things ; any more than the axiom — " Things which are equal to the same are equal to one another," can, by multiplied application, do more than establish the equality of some series of magnitudes. But...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 sider
...ACE, BC is equal to BA. [Definition 15. But it has been shewn that CA is equal to AB; therefore CA and CB are each of them equal to AB. But things which are equal to the same thing are equal to one another. [Axiom 1. Therefore CA is equal to CB. Therefore CA, AB, BC are equal...
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