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[Euclid Elements, entry directory]
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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:
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