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" Let it be granted that a straight line may be drawn from any one point to any other point. "
Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856) - Page 47
edited by - 1854
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...straight line joining the opposite angles of a quadrilateral figure 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 any terminated straight line may be produced or continued to any length in a straight line....
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...are in the same plane, and which, however far produced either way, do not meet. B 2 POSTULATES. I. Let it be granted, that a straight line may be drawn...point. II. That a terminated straight line may be produced to any length in a straight line. Ill And that a circle may be described from any centre,...
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The Philosophy of Necessity: Or, The Law of Consequences; as ..., Volume 1

Charles Bray - Cooperation - 1841 - 326 pages
...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 - Cooperation - 1841 - 694 pages
...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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Transactions of the Royal Scottish Society of Arts, Volume 11

Royal Scottish Society of Arts - Industrial arts - 1887 - 644 pages
...longness of a line, and so the definition conies to be a line is the length of a line ! Pass we to the postulates. Let it be granted that a straight line may be drawn between any two given points ; that a straight line may be continued both ways ; that a circle may...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...trapezium having two, 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...point. II. That a terminated straight line may be produced to any length in a straight line. III. That a circle may be described from any centre, at...
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Chambers's Information for the People, Volume 2

William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...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 - Geometry - 1844 - 268 pages
...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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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...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...point. II. That a terminated straight line may be produced to any length in a straight line. III. And that a circle may be described from any centre,...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...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...point. II. That a terminated straight line may be produced to any length in a straight line. III. And that a circle may be described from any centre...
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