Can someone please explain this?!
Given these basic aspects of Epicurean physics:
1) Things are not divisable into infinity.
2) Things are made up of indivisable minima. All larger magnitudes, including atoms themselves, consist of a finite number of these minima.
3) Any perceived magnitude can be analysed into an exact number of minima, i.e. a minimum is an exact submultiple of any larger magnitude (there cannot be "bits" of minima leftover).
4) Minima are never in motion, only the magnitudes they make up move because minima are indivisable and cannot be "traversing" from point A to B - it is either in A or in B since it has no "parts".
SO, how is THIS evident?: "One further consequence should be the falsity of conventional geometry. If, for example, the perfect geometrical square could exist, its side and diagonal would be incommensurable - incompatibly with the theory of minima, in which, as we have seen, all magnitidues share a common submultiple. there is good historical evidence that Epicurus accepted this consequence, but none that he worked out in detail an alternative geometry." (Long and Sedley, The Hellenistic Philsophers, vol. 1)
Why please? I have a vague notion that this has something to do with the Pythagorean theorem, e.g. sides = 1, diagonal = Root 2... And has anyone worked out an alternative geometry?