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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The Elements of Euclid - Side 8
av Euclid - 1838 - 416 sider
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sider
...point. V H. . That a terminated straight line may be produced to any length in a straight line. HI. And that a circle may be described from any centre,...centre. AXIOMS. I. THINGS which are equal to the same thing are equal to one anotheii II. If equals be added to equals, the wholes are equal. HI. If equals...
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The Oedipus Romanus; Or, An Attempt to Prove, from the Principles of ...

George Townsend - 1819 - 147 sider
...circumstance indeed so very surprising, that if I had time to prosecute the inquiry, I might prove, that as things which are equal to the same, are equal to one another, the Patriarchs are the Caesars, and the Caesars the sons of Jacob, because they are both synonymous...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1821 - 516 sider
...any one point to any other point. That a terminated straight line may be produced to any length in a straight line. III. And that a circle may be described...which are equal to the same are equal to one another. If equals be added to equals, the wholes are equal. III. If equals be taken from equals, the remainders...
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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....
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The First Six Books with Notes

Euclid - 1822 - 179 sider
...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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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. That a circle may be described from any centre, at any distance from that centre. AXIOMS. 1. Thingi which ate equal to the same are equal to one another. 2. If equals be added to equals the...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...continually produced shall meet on that side where the angles are less than two right angles. 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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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 sider
...but it has been shown that CA is equal to AB : therefore CA, св, are each of them equal to AB. And things which are equal to the same are equal to one another. Whence CA is equal to св ; wherefore the three, CA, AB, вс, are equal to one another ; and, consequently,...
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Alma Mater, Or, Seven Years at the University of Cambridge, Volum 1

John Martin Frederick Wright - 1827
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous ?" " Things which are equal to the same, are equal to one another." " Very good, Sir. What the second, and what the third?" "If equals be added to equals the sums are...
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Outline of a New System of Logic

George Bentham - 1827 - 298 sider
...which a syllogistic conclusion can be founded ? Such may, perhaps, be found the four following : 1. Things which are equal to the same, are equal to one another. 2. When of two things, one only is equal to a third, and the other is not equal to that third, these...
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