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

Euclid - 1810 - 518 sider
...circle BCD, AC is equal c to AB; and because the point B is the centre of the circle c is. Defi. ACE, BC is equal to BA: but it has been proved that CA is equal nitionto AB; therefore CA, CB are each of them equal to AB; but things which are equal to the same...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...because the point B is the centre' 15 Definio/' the circle ACE, BC is equal to BA : But it has been don proved that CA is equal to AB; therefore CA, CB, are...things, which are equal to the same are equal to one anotherj; therefore CA is equal ' itt.\xiom. to CB; wherefore CA, AB, BC arc equal to one another;...
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An Easy Introduction to the Mathematics: In which the Theory and ..., Volum 2

Charles Butler - 1814
...and because the point B is the centre of the circle ACE, BC is equal to BA, by the 15«ft definition: therefore CA, CB are each of them equal to AB< but...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...
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Easy Introduction to Mathematics, Volum 2

Charles Butler - 1814
...point B is the centre of the circle 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...
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The Scots Magazine and Edinburgh Literary Miscellany, Volum 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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...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,...
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An Introduction to the Use of the Globes ... 3. Ed. Corr. and Enl

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

John Playfair - 1819 - 317 sider
...1. Definition) to AB ; and because the point B is the centre of ie circle ACE, BC is equal to AB : 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...
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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
...BCD, AC is equal (15. Definition.J to AB; and because the point B is the centre of the circle ACE, B^C is equal to BA: but it has been proved that CA...which are equal to the same are equal to one another; (1st Axiom.J therefore CA is equal to CB; wherefore CA, AB, BC are equal to one another; and the triangle...
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