 | John Greig - 1816 - 224 sider
...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 sider
...the circle BCD, AC is equal 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...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... | |
 | John Playfair - 1819 - 350 sider
...circle BCD, AC is equal (11. Definition) to AB ; and because the point B is the centre of the circle ACE, BC is equal to AB : But it has been proved that CA is equal to AB ; therefbre'CA, CB are each of them equal to AB ; now things which are equal to the same are equal... | |
 | George Townsend - 1819 - 156 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... | |
 | Euclid, Robert Simson - 1821 - 514 sider
...(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 is equal to AB; therefore CA, CB are each of them equal to AB; but things which are equal to the same are equal to one another; (1st Axiom.J therefore CA is equal... | |
 | Henry Aldrich - 1821 - 300 sider
...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 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... | |
 | Peter Nicholson - 1825 - 1046 sider
...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, John Playfair - 1826 - 326 sider
...eirele BCD, AC is equal (11. Definition) to AB; and beeause the point B is the eentre of the eirele ACE. BC is equal to AB : But it has been proved that CA is equal to AB; therefore CA, CB are eaeh of them equal to AB; now things whieh are equal to the same are equal to one another, (1. Axiom)... | |
 | Euclid - 1826 - 234 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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AB; but things which are equal to the same are equal to one another... 
