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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 intellectual sciences; outline lects, Volume 1

Barzillai Quaife - 1873 - 260 pages
...capable of being infinitely and eternally extended. 4. It is a Postulate of Geometry, that a given straight line may be produced to any length in a straight line ; which is the same thing as saying, that a straight line may be infinitely and eternally produced....
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 424 pages
...called trapeziums. Postulates. 1. Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight...centre. Axioms. 1. Things which are equal to the same thing are equal to one another. 3. If equals be taken from equals the remainders are equal. 4. If equals...
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The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1874 - 207 pages
...— sin. 2A 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. 3. And that a circle may be described from any center, and with any radius. 4. That no part of the circumference of a circle is straight. 5. That...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 234 pages
...degrees. 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, with a radius equal to any finite straight line. AXIOMS....
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...taken for granted : That a straight line may be drawn from any one point to any other point; And also that a terminated straight line may be produced to any length in a straight line. A superficies has length and breadth but not thickness. The extremities of superficies are lines. A...
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The Intuitions of the Mind Inductively Investigated

James McCosh - Intuition - 1874 - 484 pages
...put in the form of maxims : "A straight line may be drawn from any one point to any other point ;" "A straight line may be produced to any length in a straight line ;" " There may be such a figure as a circle, that is, a plane figure such that all straight lines drawn...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...called trapeziums. Postulates. 1. Let it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight...centre, at any distance from that centre. Axioms. lual to the 2. If equals be added to equals the wholes are equal. 1. Tilings which are equal to the...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 pages
...POSTULATES. 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 described from any centre, with a radius equal to any finite straight line. THEOREMS...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...POSTULATES. 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 described from any centre, with a radius equal to any finite straight line. SECTION...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1876 - 446 pages
...I. LET it be granted that a straight line may be drawn from any one point to any other point. n. . That a terminated straight line may be produced to any length in straight line. in. And that a circle may be described from any center, at any distance from that...
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