Hi. In definition 4 and 7, Euclid uses:
"ἐξ ἴσου" :
δʹ. Εὐθεῖα γραμμή ἐστιν, ἥτις ἐξ ἴσου τοῖς ἐφ ̓ ἑαυτῆς σημείοις κεῖται.
ζʹ. ̓Επίπεδος ἐπιφάνειά ἐστιν, ἥτις ἐξ ἴσου ταῖς ἐφ ̓ 6. And the extremities of a surface are lines.
ἑαυτῆς εὐθείαις κεῖται.
Here is what one commentator says, "A (straight) line is a curve that lies symmetrically with the points on itself.
[The commonly quoted Heath's translation says "...lies evenly with the points...", but in his notes he says "we can safely say that the sort of idea which Euclid wished to express was that of a line ... without any irregular or unsymmetrical feature distinguishing one part or side of it from another."] "
Can anyone hep me understand this phrase? It is important so I can understand what Euclid is seeing and saying. Is the line moving out of "ἴσου" as if ἴσου were a phenomenon or is is he saying because of ἴσου, it is lying on itself?
Perplexing...