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" LET it be granted that a straight line may be drawn from any one point to any other point. "
The text of Euclid's geometry, book 1, uniformly and systematically arranged ... - Side 72
av Euclides - 1884
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The Philosophy of Necessity: Or, The Law of Consequences; as ..., Volum 1

Charles Bray - 1841 - 326 sider
...no magnitude." " A line is length without breadth."* " Let it be granted," says the mathematician, " that a straight line may be drawn from any one point to any other point," that is, from that which has no parts and no magnitude, to that which has no parts and no magnitude;...
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The philosophy of necessity, or, The law of consequences: as applicable to ...

Charles Bray - 1841 - 694 sider
...no magnitude." " A line is length without breadth."* " Let it be granted," says the mathematician, " that a straight line may be drawn from any one point to any other point," that is, from that which has no parts and no magnitude, to that which has no parts and no magnitude;...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 sider
...only, of its sides parallel to one another is now called a trapezoid. 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 sider
...POSTULATES. 1. LET it be granted that a straight line may be drawA 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 that centre. AXIOMS. 1....
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Chambers's Information for the People, Volum 2

William Chambers, Robert Chambers - 1842 - 938 sider
...be done, or to be imagined to be done. The postulates given by Euclid are the following : — 1 . Л line may be drawn from any one point to any other point. 2. A line may be produced (that is, continued or lengthened) at pleasure to any length. 3. A circle...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - 1844 - 268 sider
...problems, while axioms are self-evident theorems. Geometers usually enumerate three 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 any circle...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 sider
...into which it is divided by a diameter, that are called semicircles. POSTULATES* 1. Let it be granted, that a straight line may be drawn from any one point, to any other point : f 2. That a terminated straight line may be produced to any length in a straight line : , 3. That...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 sider
...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. II. That a terminated straight line may be produced to any length in a straight line. III. And that...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 sider
...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. And that...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 sider
...such as arc in the same plane, and, being produced ever so far both ways, do not meet. POSTULATESLet it be granted, i. 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. That a...
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