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Teokset Teokset 1 - 10 / 180 haulle Again ; the mathematical postulate, that " things which are equal to the same are....
" 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 Oedipus Romanus; or, An attempt to prove, from the principles of ... - Sivu 25
tekijä(t) George Townsend - 1819 - 147 sivua
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 sivua
...magnitudes, unto ratios, viz. that a magnitude cannot be both greater and less than another. That those things which are equal to the same are equal to one another, is a most evident axiom when understood of magnitudes ; yet Euclid does not make use of it to infer...

The Monthly Anthology, and Boston Review, Nide 5

David Phineas Adams, Samuel Cooper Thacher - 1808
...confound our two articles. " In the Celtic" says he, " the article an signifies the and that." But as things, which are equal to the same, are equal to one another, it is easy to prove, since an means that, and //•.- means that, that an and the are in the English...

Easy Introduction to Mathematics, Nide 2

Charles Butler - 1814
...ACE, BC is equal to BA, by the \5th definition; therefore CA,.CB are each of them equal to AB ; but things which are equal to the same are equal to one another, by the 1st' axiom; wherefore CA and CB are equal to one another, being each equal to AB ; consequently...

The Scots Magazine and Edinburgh Literary Miscellany, Nide 76

1814
...contrary, they are such 35, considered separately, do not afford room for a single inference. — That things which are equal to the same, are equal to one another, and that the whole is greater than its part, considered in themselves, are mere barren truisms. The...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sivua
...magnitudes, unto ratios, viz. that a magnitude cannot be both greater and less than another. That those things which are equal to the same are equal to one another, is a most.evident axiom when understood of magnitudes ; yet Euclid does not make use of it to infer,...

An introduction to the use of the globes

John Greig - 1816
...because they divide the globe into unequal parts, called segments, as o C b and A ob B D. 2. Axioms.* 1. Things which are equal to the same, are equal to one another. * Axiom, implies a plain, self-evident troth or proposition, which is no sooner proposed but understood....

The Edinburgh monthly review

...indeed so very surprising, that if I had time to prosecute the inquiry, I might prove, that as tilings which are equal to the same, are equal to one another, the Patriarchs are the Casars, and the Cinsars the sons of Jacob, because they are both synonymous with the /Jodiac !" Pp....

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sivua
...But it has been proved that CA is equal to AB ; therefore CA, CB are each of them equal to AB ; now things which are equal to the same are equal to one another .I. Axiom) ; therefore CA is equal to CB ; wherefore CA, AB, B are equal to one another ; and the triangle...

Artis logicæ rudimenta, with illustrative observations [and a transl. By J ...

Henry Aldrich - 1821
...reared, and as the final appeal in argument. They benr some slight analogy to the mathematical axioms, Things which are equal to the same are equal to one another ; and, Things of which one is equal and the other not equal to the same, are not equal to one another....

The First Six Books with Notes

Euclid - 1822 - 179 sivua
...a circle may be described from any centre, /&, ff, at any distance from that centre. M o 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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