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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 geometry; or, The first six books, with the eleventh and ... - Page 5
by Euclides - 1855
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A Dictionary of Science, Literature, & Art: Comprising the ..., Volume 3

William Thomas Brande, George William Cox - Science - 1867 - 1088 pages
...assumed, or taken for granted. Euclid has constructed his Elements on the three following postulates: 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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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...certainly be convenient if this restriction were universally adopted.] 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...
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A Dictionary of Science, Literature, & Art: Comprising the ..., Volume 3

William Thomas Brande - Encyclopedias and dictionaries - 1867 - 1092 pages
...assumed, or taken for granted. Euclid lias constructed his Elements on the three following postulates: 1. That a straight line may be drawn from any one point to any other point. 2. That a terminated straight lino may be produced to any length in a straight line. 3. That a circle...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...parallel: and the diameter, or the diagonal is the straight liue joining two of its opposite angles. POSTULATES. I. LET it be granted 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. m. AXIOMS. I....
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The ratio between diameter and circumference in a circle demonstrated by ...

James Smith - 1870 - 634 pages
...that his first problem (Prop. I, Book 1) should be based upon the simplest of the postulates, viz. : " Let it be granted, that a straight line may be drawn from any one point to any other point" Thus, Euclid begins by showing us how to construct an equilateral triangle. There can be no doubt that...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871
...construction of figures and the properties of geometrical mag--tudes. POSTULATES. Let it be granted I. 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...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...which is contained an exact number of times in each of them. BOOK V PROBLEMS Postulates. 1 A a'.raight 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. From the greater...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...construction of figures and the prqperties pf geometrical magnitudes. POSTULATES. Let it be granted I. 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...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873
...lines are such as are in the same plane, and which, 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...
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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
...sin. A = VR 2 — 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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