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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 Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Page 5
by Robert Simson - 1762 - 466 pages
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...space between the lines is always of the same breadth. POSTULATES. i Let it be granted, that a straight line may be drawn from any one point to any other point. When a straight line is drawn from one point to another point, the points are said to be joined. The...
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Practical carpentry, joinery, and cabinet-making [by P. Nicholson. by P ...

Peter Nicholson - Cabinetwork - 1856 - 518 pages
...POSTULATE signifies something which may be assumed as granted. Hence it may be granted, 1st, That a right line may be drawn from any one point to any other point : 2dly, That a line may be produced, that is, continued or lengthened at pleasure : 3dly, That a circle...
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Mensuration of Lines, Areas, Surfaces, and Volumes ...

Robert Rawson - 1856 - 178 pages
...being produced ever so far both ways, do not meet. POSTULATES. r 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. And that a circle...
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The Atlantic Monthly, Volume 4

1859 - 802 pages
...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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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...length in a st. line. P. 3. Prom the greater line to cut off a part equal to the less. Pst. 1. A st. line may be drawn from any one point to any other point. DEMONSTRATION. — P. 4. If two triangles have two sides and their included angle of one triangle equal...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...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 - 380 pages
...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
...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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The Intuitions of the Mind Inductively Investigated

James McCosh - History - 1860 - 512 pages
...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 - 464 pages
...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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