 | Euclid, James Thomson - 1837 - 410 σελίδες
...definition 30.) to AB; and because the point B is the centre of the circle ACE, BC is equal (I. def. 30.) to BA. But it has been proved that CA is equal to...AB: but things which are equal to the same are equal (I. axiom 1.) to one another ; therefore CA is equal to CB; wherefore CA, AB, BC are equal to one another;... | |
 | John Playfair - 1837 - 332 σελίδες
...Definition) to AB ; and because the point B is the centre of the cir-' cle 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. (1. Axiom) ; therefore CA is equal... | |
 | Andrew Bell - 1837 - 290 σελίδες
...to AB ; and because the point B is the centre of the circle ACE, BC is equal to BA ; but it has teen proved that CA is equal to AB ; therefore CA, CB, are each of them equal to AB ; therefore (Axiom I) CA is equal to CB ; wherefore CA, AB, BC, are equal to one another ; and the... | |
 | Edward Tagart - 1837 - 156 σελίδες
...individual comprehended in it ; which is analogous to the axiom, or common notion of equality, that things which are equal to the same are equal to one another, or that the whole is made up of all the parts. A syllogism, to make a homely simile, is a kind of two-pronged... | |
 | William Josiah Irons - 1837 - 160 σελίδες
...proof. Our minds perceive all such truths by a direct glance. If any man should require proof that ' things which are equal to the same are equal to one another,' he would never get any such proof. If he should find by experience that it had been so, in a million... | |
 | Robert Simson - 1838 - 434 σελίδες
...BCD, AC is equal (15. Definition.) to AB; and because the point B is the centre of the circle ACE, BC is equal to BA : but it has been proved that CA is...which are equal to the same are equal to one another; (1st. Axiom.) therefore CA rs equal to CB ; wherefore CA, AB, BC are eqnal to one another ; and the... | |
 | Euclides - 1838 - 264 σελίδες
...circle BCD, AC is equal* to AB; and because the point B is the cenfiu'uim" tre of ^e c'rcle ACE, BC is equal to BA: But it has been proved that CA is...equal to AB; but things which are equal to the same thing are equal* to one another; A*'i'lm. therefore CA is equal toCB: wherefore CA, AB, BC are equal... | |
 | Richard W. Green - 1839 - 156 σελίδες
...dividing the 1st, x= — >£ Transposing and dividing the 2d, x= — —Jr. 5 Now, as it is evident that things which are equal to the same, are equal to one another ; one value of x is equal to the other value of x ; thus, ^. * 23— 3y _10+2y ~2~ ~~" ~5~ Destroying... | |
 | Euclides - 1841 - 378 σελίδες
...AB; and because the point B is the Bullion. centre O f tn e c i rc i e ACE, BC is equal to BA: hut it has been proved that CA is equal to AB; therefore CA, CB, are each of them equal to AB; but things * 1st which are equal to the same thing are equal* to one Axiom. anot her; therefore CA is equal to... | |
 | Francis Bacon - 1841 - 616 σελίδες
...similar to that of music termed the declining of a cadence. Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.... | |
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AB; but things which are equal to the same are equal to one another... 
