In Greek philosophy, it is generally taken that the line and the circle form a contrary. For example in Aristoteles Physics generally takes that motion can be formed out of this contrary, and this is affirmed in Newtonian Mechanics where the general motion of a body is decomposed into rotational and linear motions.

In the Platonic dialogue, Parmenides, he defines the circle and straight line as:

a. The round is that which all the extreme points are equidistant from the centre.

b. The straight is that in which the centre intercepts the view of the extremes.

In this picture, the straight line appears as a 'degeneration' of the circle; this to me at least appears implicitly, given the language that Parmenides uses; is there definite textual evidence that this is the case?

  • How do you understand "the centre intercepts the view of the extremes"? – Ram Tobolski Feb 16 '15 at 18:57
  • @tobolski: consider the Line; not as the Euclidean Line; which is synthetic; but as the Real Line, which has an originary point; from there one sees'the extremes' - the limits. – Mozibur Ullah Feb 17 '15 at 16:33
  • Secondly it ties in with Aristotles notion of linear motion which moves along an axis, through degrees of potency understood as up/down; ie imagine yourself at the centre of the earth and throw a stone up; it goes up in a vertical direction - to its limit - and then back down, through the centre, and to its other limit. – Mozibur Ullah Feb 17 '15 at 16:36
  • @MoziburUllah Wy do you consider the extremes as infinitary? To me the round as defined above is more like a disc and the straight is a star shaped set (considering them as subsets of some euclidean space). – Alp Uzman Jan 7 '16 at 9:13

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