| Euclid - 1810 - 518 páginas
...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 - 558 páginas
...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 - 1814 - 528 páginas
...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 - 568 páginas
...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... | |
| 1814 - 1026 páginas
...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 - 528 páginas
...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 páginas
...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 - 317 páginas
...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 páginas
...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 páginas
...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... | |
| |