## 16 Apr 2014

### Euclid, Elements [B1, D4] Book 1, Definition 4

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# Euclid

The Elements
Στοιχεῖα

Book 1
Βιβλίον I

Definitions
Ὅροι

Definition 4

Definition 4:
D4. A straight line is that which lies evenly between its extremities.

(Byrne, p.xviii)

4. A straight-line is (any) one which lies evenly with points on itself.

(Fitzpatrick 6)

4. A straight line is whatever lies equally with the points on it,

(Mendell)

δʹ. Εὐθεῖα γραμμή ἐστιν, ἥτις ἐξ ἴσου τοῖς ἐφ᾿ ἑαυτῆς σημείοις κεῖται.

(Heiberg)

[From Mendell’s commentary:]

The meaning of this definition is very unclear.  It is common to translate 'ex isou', here 'equally' as 'evenly', cf. def. 7.

(Mendell)

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