| Euclides - 1885
...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... | |
| 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... | |
| H. Freeman Wood - 1888 - 398 sider
...B, at the distance BC, I describe the circle CGH, meeting DF at G, inasmuch as postulate 3 declares **that a circle may be described from any centre, at any distance from that centre.** I next, from the centre D, at the distance DG, describe the circle GKL, meeting DE at L. Now it follows... | |
| James McCosh - 1889 - 360 sider
...such that all straight lines drawn from a certain point within the figure are equal to one another ; " **and that " A circle may be described from any centre at any distance from that centre."** I shall have occasion, in speaking of the application of the principles laid down in this treatise... | |
| 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
...other point. 2. That a Terminated Straight Line may be produced to any length in a straight line. 3. **And that a Circle may be described from any centre, at any distance from that centre.** 1 ie Elementary Problems whose construction it is to be taken for granted we can effect. AXIOMS.1 1.... | |
| 1891
...must presuppose the admission of certain postulates on the part of both dramatist and audience. If **that a circle may be described from any centre, at any distance from that centre,** is matter of opinion, we can prove no mathematical proposition ; and, without some appropriate conceded... | |
| Louis Mallet - 1891 - 356 sider
...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... | |
| Euclid, Robert Simson - 1892 - 518 sider
...that is to say, a terminated straight line may be produced to any length in that straight line. 3. **That a circle may be described from any centre, at any distance from that centre,** that is, with a radius equal to any finite straight line drawn from the centre. It is important to... | |
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