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The numerical citations refer to page number. The source's text-space (including footnote region) is divided into four equal portions, a, b, c, d. If the citation is found in one such section, then for example it would be cited p.15c. If the cited text lies at a boundary, then it would be for example p.16cd. If it spans from one section to another, it is rendered either for example p.15a.d or p.15a-d. If it goes from a 'd' section and/or arrives at an 'a' section, the letters are omitted: p.15-16.

11 Apr 2014

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

by Corry Shores
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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