11 Apr 2014

Euclid, Elements [B1, D2] Book 1, Definition 2

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[Euclid Elements, entry directory]

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Euclid

The Elements
Στοιχεῖα

Book 1
Βιβλίον I

Definitions
Ὅροι

Definition 1

Definition 2:
D2. A line is length without breadth.

(Byrne, p.xviii)

[In the introduction Byrne describes a line using a colored rectangle]

(Byrne p.xiv)

A line is length without breadth. With the assistance of colours, nearly in the same manner as before, an idea of a line may be thus given :—

Let two colours meet and cover a portion of the paper; where they meet is not red, nor is it blue; therefore the junction occupies no portion of the plane, and therefore it cannot have breadth, but only length: from which we can readily form an idea of what is meant by a mathematical line. For the purpose of illustration, one colour differing from the colour of the paper, or plane upon which it is drawn, would have been sufficient; hence in future, if we fay the red line, the blue line, or lines, &c. it is the junctions with the plane upon which they are drawn are to be understood.

(Byrne, p.xiv, emphases mine)

Sources:

Euclid; Oliver Byrne. The First Six Books of The Elements of Euclid, in which Coloured Diagrams and Symbols are Used Instead of Letters for the Greater Ease of Learners. London: William Pikering, 1847.

Available at:

https://archive.org/details/firstsixbooksofe00byrn

https://archive.org/details/firstsixbooksofe00eucl

Euclid; J.L. Heiberg; Richard Fitzpatrick. Euclid’s Elements of Geometry. Ed. Richard Fitzpatrick. Online edition. 2007. Available at:

http://farside.ph.utexas.edu/euclid/elements.pdf

Euclid; Heath.  The Thirteen Books of the Elements. Vol. 1. Books I-II. 2nd Edition. Ed. and Trans. Thomas L. Heath. Cambridge: Cambridge UP, 1968.

Euclid; Heath.  The Thirteen Books of the Elements. Vol. 1. Books I-II. 2nd Edition. Ed. and Trans. Thomas L. Heath. New York: Dover, 1956.

Available at:

https://archive.org/details/euclid_heath_2nd_ed

Euclid; Heath.  The Thirteen Books of the Elements. Vol. 1. Books I-II. 1st Edition. Ed. and Trans. Thomas L. Heath. Cambridge: Cambridge UP, 1908.

Available at:

https://archive.org/details/thirteenbookseu02heibgoog

Euclid; Heath.  The Thirteen Books of the Elements. Vol. 2. Books III-IX. 2nd Edition. Ed. and Trans. Thomas L. Heath. New York: Dover, 1956.

Available at:

https://archive.org/details/euclid_heath_2nd_ed

Euclid; Heath.  The Thirteen Books of the Elements. Vol. 2. Books III-IX. 1st Edition. Ed. and Trans. Thomas L. Heath. Cambridge: Cambridge UP, 1908.

Available at:

https://archive.org/details/thirteenbookseu00heibgoog

Euclid; Heath.  The Thirteen Books of the Elements. Vol. 3. Books X-XIII. 2nd Edition. Ed. and Trans. Thomas L. Heath. New York: Dover, 1956.

Available at:

https://archive.org/details/euclid_heath_2nd_ed

Euclid; Heath.  The Thirteen Books of the Elements. Vol. 3. Books X-XIII. 1st Edition. Ed. and Trans. Thomas L. Heath. Cambridge: Cambridge UP, 1908.

Available at:

https://archive.org/details/thirteenbookseu03heibgoog

Mendell, Henry. Euclid. In Vignettes of Ancient Mathematics:

http://web.calstatela.edu/faculty/hmendel/Ancient%20Mathematics/VignettesAncientMath.html

Joyce, David E. Euclid Elements. With diagrams, java applets.
http://aleph0.clarku.edu/~djoyce/java/elements/toc.html

Online Greek. Dimitrios E. Mourmouras:

http://www.physics.ntua.gr/~mourmouras/euclid/index.html