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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The Elements of Euclid - Side 8
av Euclid - 1838 - 416 sider
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The Practical Teacher, Volum 2

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.-'; .>•.'...
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The Practical Teacher; with which is Incorporated the Practical ..., Volum 2

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...
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Geometry for schools, comprising books i. and ii. of Euclid, with some ...

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...
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The World's Cyclopedia of Biography, Volum 3

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...
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The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

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...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

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....
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The Living Age ..., Volum 161

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...
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An introduction to geometry, consisting of Euclid's Elements, book ..., Volum 1

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...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

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....
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The Fundamental Science

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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