Note on Citations

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, D1] Book 1, Definition 1

by Corry Shores
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Euclid

The Elements
Στοιχεῖα

Book 1
Βιβλίον I

Definitions
Ὅροι

Definition 1

Definition 1:
D1. A point is that which has no parts.

(Byrne, p.xviii)

[In the introduction Byrne describes a point using a colored circle]

(Byrne p.xiii)

Let three colours meet and cover a portion of the paper, where they meet is not blue, nor is it yellow, nor is it red, as it occupies no portion of the plane, for if it did, it would belong to the blue, the red, or the yellow part; yet it exists, and has position without magnitude, so that with a little reflection, this junc-|-tion of three colours on a plane, gives a good idea of a mathematical point.

(Byrne, p.xiii-xiv)

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