 | Euclid - Geometry - 1810 - 554 pages
...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... | |
 | Euclides - 1814 - 560 pages
...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;... | |
 | Charles Butler - Mathematics - 1814 - 528 pages
...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... | |
 | Charles Butler - 1814 - 582 pages
...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... | |
 | English literature - 1814 - 1032 pages
...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 pages
...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 pages
...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 pages
...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... | |
 | George Townsend - 1819 - 156 pages
...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... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...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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AB; but things which are equal to the same are equal to one another... 
