| 1883
...straight and crooked would have no more meaning to him than red and blue to the Wind. The axiom, that **things which are equal to the same are equal to one another,** is only a particular case of the predication of similarity ; if there were no impressions, it is obvious... | |
| Stewart W. and co - 1884
...triangle. Because A is the centre of BCD, AC is equal to AB ; and because B is the centre of ACE, BC'is **equal to BA, but it has been proved that CA is equal to** AR ; therefore CA, CB, are each of them equal to AB , but things which are equal to the same are equal... | |
| Euclides - 1884
...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
...because B 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.... | |
| Euclid, John Casey - 1885 - 312 sider
...because B 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 - 265 sider
...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
...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 - 188 sider
...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 - 193 sider
...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 - 515 sider
...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... | |
| |