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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The first six books of the Elements of Euclid, with numerous exercises - Seite 4
von Euclides - 1853 - 147 Seiten
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The London University Magazine, Band 1

1829
...convenient to substitute for it. How do you reconcile the admission of Euclid's postulate, " that a straight line may be produced to any length in a straight line, 1 ' with the neces-, I. «*_ xy — x + y, II. 3x* — 2xy + y 3 — 4>x — 4y + 3 = 0. III. x>=xy...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 Seiten
...piece of paper for a plane, with a pen,* a ruler, and a pair of compasses, it is evident, that, first, a straight line may be drawn from any one point to any other point ; 2ndly, a terminated straight line may be produced to any length in a straight line ; 3dly, from the...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...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...may be produced to any length in a straight line. BOOK I. — AXIOMS. AXIOMS. I. THINGS which are equal to the same thing, are equal to one another....
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...of paper for a plane, •with a pen,* a ruler, and a pair of compasses, it is evident, that, first, a straight line may be drawn from any one point to any other point ; 2ndly, a terminated straight line may be produced to any length in a straight line ; 3dly, from the...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 Seiten
...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 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 a...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 Seiten
...supplementary. So also are two angles which are together equal to two right angles. POSTULATES.* 1. Let it be granted, that a straight line may be drawn from any one point, to any other point :.). writers rather improperly use urcb) and chord receive their names from the bow (in Latin arcvs),...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 Seiten
...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- line 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
...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...be produced to any length in a straight line. III. Anil that a circle may be described from any centre, at any distance from that centre. AXIOMS. THINGS...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 Seiten
...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...terminated straight line may be produced to any length in at straight line. III. And that a circle may be described from any centre, at any distance from that...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...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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