| W. J. C. Miller - 1885
...that it " lies evenly between its extreme points "; but in Postulate ii. he says, " Let it be granted, **that a terminated straight line may be produced to any length in a straight line,"** and this gives us the idea of an infinite straight line. But do we require more than two infinite straight... | |
| 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,... | |
| 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... | |
| Euclid, John Casey - 1885 - 312 sider
...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.... | |
| 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
...DAB., producing the straight lines DA, DB, to E and F; in accordance with postulate 2, which states **that a terminated straight line may be produced to any length in a straight line.** From the centre B, at the distance BC, I describe the circle CGH, meeting DF at G, inasmuch as postulate... | |
| 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 it... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...POSTULATES. Let it be granted 1. That a straight line may be drawn from any one point to any other point. 2. **That a terminated straight line may be produced to any length in a straight line.** 3. That a circle may be described from any centre at any distance from that centre. In practice this... | |
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