| 1883
...are : — (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.** In the first proposition the third postulate is required in describing the circles and they.-'; .>•.'... | |
| Joseph Hughes - 1883
...are :— (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.** In the first proposition the third postulate is required in describing the circles and theßrsi in... | |
| Euclides - 1883 - 96 sider
...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.** These Postulates are Requests to be allowed to construct certain figures, and evidently require the... | |
| 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... | |
| Euclides - 1884
...one point to any other point. IL That a terminated straight line may be produced to any length in a **straight line. III. And that a circle may be described...centre, at any distance from that centre. AXIOMS. I.** Magnitudes which are equal to the same magnitude, are equal to one another. II. If equals be added... | |
| Stewart W. and co - 1884
...other point. II. That a terminated straight line may be produced to any length in a straight line. III. **That a circle may be described from any centre, at any distance from that centre. AXIOMS. I. Things** equal to the same are equal to one another. II. If equals be added to equals, the wholes are equal.... | |
| 1884
...any length in a straight line [plane through intersecting lines may be produced beyond these lines]. **III. And that a circle may be described from any centre at any distance from that centre** [a cone about any axis with any angle at the vertex]. AXIOMS. X. Two straight lines cannot inclose... | |
| Euclides - 1884
...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.** In Postulate 2, ' produced ' means lengthened out. In Postulate 3, ' described ' means drawn. After... | |
| 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.... | |
| 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,... | |
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