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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The philosophical and mathematical commentaries of Proclus ... on the first ... - Page 6
by Proclus (Diadochus.) - 1789
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 588 pages
...being produced ever so far both ways, do not meet. POSTULATES. I. Let it be granted that a straight line may be drawn from any one point to any 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...
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The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1873 - 238 pages
...— cos. 2 A, And cos. A — ± VR 2 — sin. 2 A. 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. And that a...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...straight line joining two of its opposite angles. 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 line may be produced to any length in a straight line. 3. And that a...
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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
...cos. 2J.t And cos. JL === ± 1/12 2 — 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 may be produced to any length in a straight line. 3. And that a...
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874 - 120 pages
...quadrilateral which has two of its sides parallel. 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 line may be produced to any length in a straight line. 3. And that a...
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The Intuitions of the Mind Inductively Investigated

James McCosh - Intuition - 1874 - 484 pages
...in the propositions founded on them, such as the following, 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...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 426 pages
...All other four-sided figures are 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 line may be produced to any length in a straight line. 3. And that a...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...straight line is one which lies evenly between its extremities. It is 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...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...arc is hence called an angls of ninety 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 line may be produced to any length in a straight line. 3. That a circle...
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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
...straight line has one and only one point of bisection. 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...
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