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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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The Atlantic Monthly, Volume 4

1859
...in his hand, before commencing his artistic and scientific achievements upon the black-board, says': "Let it be granted that a straight line may be drawn from any one point to any other point," I invariably answer, " Of course, — by all manner of means," — although you know, dear Don, that,...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...being applied the one to the other, coincide throughout their whole extent, are equal POSTULATES. 1. Let it be granted, that a straight line may be drawn from one point to another point. 2. That a terminated straight line may be prolonged, iu a straight line,...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...straight line are necessary to fix the position of a plane." — Pott's Euclid, p. 44. 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...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...line which is contained an exact number of times in each of thsm. BOOK V. PROS LEM.S. Postulates. 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. From the greater...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...parallel : and the diameter, or the diagonal is the straight line 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. n. That a terminated straight line may be produced to any length in a straight line. in. And that a...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...line joining two of the opposite angular pomts of a quadrilateral is called a diagonal. 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...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 443 pages
...two given points. XIV. Straight lines which are parallel to the same line are parallel to each other. POSTULATES. I. Let it be granted that a straight line may be drawn from any point to any other point. II. That a terminated straight line may be produced, in either direction,...
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The Intuitions of the Mind Inductively Investigated

James McCosh - History - 1860 - 512 pages
...definitions and 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 as...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...PROP. 1. — PROK. To find the centre of a given circle. SOL. — Pst. 1. Let it be granted that a st. line may be drawn from any one point to any other point. 10, I. To bisect a given finite st. line. 11, I. To draw a st. line at rt.s to a given st. line from...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...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. AXIOMS....
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