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" Let it be granted 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. And that a circle may be described from any centre, at any distance from... "
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Page 11
by John Playfair - 1855 - 318 pages
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The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884 - 214 pages
...POSTULATES. Let it be granted I. That a straight line may be drawn from any 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 from any centre, at any distance from that centre. AXIOMS....
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...CONSTRUCTION. Let it be granted that 1. A straight line may be drawn from any one point to any other point. 2. A terminated straight line may be produced to any length in a straight line. 3. A circle may be drawn with any centre, with a radius equal to any finite straight line. H 2 BOOK II....
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An introduction to the Elements of Euclid, being a familiar explanation of ...

Stephen Thomas Hawtrey - 1884 - 184 pages
...Postulate 1.—That a straight line may be drawn from any one point to any other point: Postulate 2.—That a terminated straight line may be produced to any length in a straight line: Postulate 3.—That a circle maybe described from any centre at any distance from that centre. In other...
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Mathematical Questions and Solutions, from the "Educational Times ..., Volume 42

W. J. C. Miller - Mathematics - 1885 - 154 pages
...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...
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The Passenger from Scotland Yard

H. Freeman Wood - Police - 1888 - 412 pages
...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...
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First and Fundamental Truths: Being a Treatise on Metaphysics

James McCosh - Metaphysics - 1889 - 390 pages
...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...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...of the circle. 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...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 amounts...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...(42). POSTULATES. 45. 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 distance in a straight line. 3. That a circle may be described with any centre, at any distance from...
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The Nineteenth Century, Volume 30

Nineteenth century - 1891 - 1150 pages
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...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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