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" LET it be granted that a straight line may be drawn from any one point to any other point. "
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 44
by Euclides - 1858
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...are such as are in the same plane, and which, being produced eyer i so far both ways, do not meet. POSTULATES. 1. Let it be granted that a straight-...may be drawn from any one point to any other point. 3. And that a circle may be described from any centre, and with any radius. AXIOMS. 1. Things which...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...are in the same plane, and which, being produced ever so far both ways, do not meet. V POSTULATES. 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. Anil that...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 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 from any one point to any other point. II. That a terminated straight line may be produced to any length in at straight line. III. And that...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...TRAPEZIUM. [The straight line joining the opposite angles of a quadrilateral figure is called a DIAGONAL.] POSTULATES. 1. Let it be granted, that a straight...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. • 3....
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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 from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. Ill And that...
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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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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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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 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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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 may...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...lines are such as are in the same plane, and which, being produced ever so far both ways, do not meet. 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...
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