Abstract
I HAVE read the passage referred to, but for many reasons cannot admit that the argument is conclusive. In the first place, the quotation from Aristotle's “Ethics” has no authority whatever; it has no grammatical connection with the previous context, and shows every mark of being a marginal annotation which has been wrongly incorporated with the text. Then the use of the same symbol for different points (AA, BB, ΓΓ denoting segments) is very unusual, and is not what we should expect from a competent mathematician, so it is rash to infer that the use of Γ, Δ in the sense “of which Γ, Δ are the extremities” was a current technical practice at the time of the writer. But even if this be admitted, it does not follow that Euclid means the same thing in his definition of a straight line; all the evidence, it seems to me, points in another direction. Euclid has just defined points, and stated that the extremities of lines are points; if he had intended what the current English translation makes him say, would he not have written, “A straight line is a line which lies evenly () with respect to its extremities”? Again, in i. 9 he says, “on AB let any point D be taken” (); now if D is taken “on” AB, surely it is included in “the points on AB” (). Moreover, Euclid explicitly recognises infinite, or indefinitely long, straight lines; the enunciation of i. 12 is , &c.; see also the scholia in Heiberg's edition of the “Elements,” v. 78–83, 136–9.
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Euclid's Definition of a Straight Line. Nature 69, 489 (1904). https://doi.org/10.1038/069489c0
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DOI: https://doi.org/10.1038/069489c0
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