 | Alexander Smith (M.A.) - 1835 - 750 pages
...of mathematical axioms. Take such instances as these, " all the parts are equal to the whole," — " things which are equal to the same are equal to one another." Why must we at once affirm that these propositions are true, and that the contrary of them cannot be... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...ACE, BC is equal (I. def. 30.) 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 (I. axiom 1.) to one another ; therefore CA is equal to CB; wherefore CA, AB, BC are equal to one another;... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...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 to CB ; wherefore CA, AB, CB are equal to one another ; trtrmgte... | |
 | William Josiah Irons - 1837 - 160 pages
...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 - Logic - 1837 - 156 pages
...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 - Geometry - 1838 - 434 pages
...the circle ACE, BC 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.) therefore CA rs equal to CB ; wherefore CA, AB, BC are eqnal to one another ; and the... | |
 | Euclides - 1838 - 264 pages
...^e c'rcle ACE, BC 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 thing are equal* to one another; A*'i'lm. therefore CA is equal toCB: wherefore CA, AB, BC are equal... | |
 | Richard W. Green - Algebra - 1839 - 156 pages
...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... | |
 | Francis Bacon - 1841 - 616 pages
...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.... | |
 | Francis Bacon - 1841 - 616 pages
...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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But things which are equal to the same are equal to one another... 
