 | 1814 - 1032 σελίδες
...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... | |
 | Euclides - 1816 - 588 σελίδες
...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,... | |
 | John Greig - 1816 - 224 σελίδες
...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.... | |
 | John Playfair - 1819 - 354 σελίδες
...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... | |
 | George Townsend - 1819 - 156 σελίδες
...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... | |
 | Henry Aldrich - 1821 - 300 σελίδες
...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.... | |
 | Euclid - 1822 - 222 σελίδες
...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... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...is equal to BA : But it has been proved dial CA is equal to AB ; therefore CA, CB, are each of diem equal to AB ; but things which are equal to the same are equal to one another (1st Axiom.) tiierefore CA is equal to CB ; wherefore CA, AB, BC, are equal to one another j and the... | |
 | Euclid - 1826 - 234 σελίδες
...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,... | |
 | Euclides - 1826 - 226 σελίδες
...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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But things which are equal to the same are equal to one another... 
