| Andrew Bell - 1837 - 240 páginas
...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... | |
| William Josiah Irons - 1837 - 160 páginas
...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... | |
| Edward Tagart - 1837 - 156 páginas
...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... | |
| Robert Simson - 1838 - 434 páginas
...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...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 páginas
...the 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...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 páginas
...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 páginas
...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 - 618 páginas
...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.... | |
| Nicholas Patrick Wiseman - 1841 - 628 páginas
...arrangement, how can the celebrated demand in the theory of parallels rank under the same head as that " **things which are equal to the same are equal to one another."** The misplacement of this axiom about parallels has cost many a trial at this old difficulty, and procured... | |
| Francis Bacon - 1841
...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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