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. The Elements of Euclid - Página 246por Euclid - 1838 - 416 páginasVista completa - Acerca de este libro
| Euclides - 1884 - 182 páginas
...angles CBE, EBA, ABD. But the angles CBE, EBD have been proved equal to the same three angles ; and **things which are equal to the same are equal to one another** ; therefore the angles CBA, ABD are equal to the angles CBE, EBD. ' (Ax. 1) But CBE, EBD are two right... | |
| Euclides - 1885 - 340 páginas
...AB . BE is equal to the figure AE. Hence the rectangle AB . CB is equal to the figure AE. And since **things which are equal to the same are equal to one another,** the rectangle AC . CB, together with the square, on CB, is equal to the rectangle AB . CB. , Or thus... | |
| Euclid, John Casey - 1885 - 340 páginas
...is the centre of the circle ACE, BC is equal to BA. Hence we have proved. AC = AB, and BC = AB. But **things which are equal to the same are equal to one another** (Axiom i.) ; therefore AC is equal to BC ; therefore the three lines AB, BC, CA are equal to one another.... | |
| Henry James Clarke - 1885 - 332 páginas
...the unreasonableness of such a desire. What then am I to do ? I need not ask how I am to prove that **things which are equal to the same are equal to one another** : this truth is one of which I have a clear perception ; I feel sure that I know it by immediate intuition,... | |
| 1886 - 436 páginas
...same time be and not be ; (2) that if equals be added to equals the wholes are equal ; and (3) that **things which are equal to the same are equal to one another.** It so happens that each of these propositions which he has assumed to be true is, if true, much more... | |
| Alfred James Swinburne - 1887 - 224 páginas
...middle terms is called the minor premiss. The former always comes first. Unless the principle that " **things which are equal to the same are equal to one another** " were true, it would not follow that " Socrates " and " mortal," which are equal to the same (" man... | |
| Michael William Meagher - 1889 - 226 páginas
...says the trunk lines of railroads unite to raise rates, just as robbers unite to plunder in concert. **Things which are equal to the same are equal to one another.** If, then, railroad companies unite to raise rates, and workingmen unite to raise rates of wages, and... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 páginas
...ie Elementary Problems whose construction it is to be taken for granted we can effect. AXIOMS.1 1. **Things which are equal to the Same are Equal to One Another.** 2. If equals te Added to equals, the Wholes are equal. 3. If equals be Taken from equals, the Remainders... | |
| Louis Mallet - 1891 - 398 páginas
...Mill's " Principles of Pol. Econ.," cap. 21. exports exchange for the same quantity of money. And since **things which are equal to the same are equal to one another,** the imports and exports which are equal in money price would, if money were not used, precisely exchange... | |
| Francis Bacon - 1893 - 268 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. Lastly... | |
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