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The mathematics of periodic anthyphairesis as a basis for the full understanding of Plato's philosophy
Stelios Negrepontis, Athanase Papadopoulos
Even though Plato's philosophy in ancient times was always closely associated with mathematics, modern Platonic scholarship, during the last five centuries, has moved steadily towa…
The restoration of Book X of the Elements to its original Theaetetean form
Stelios Negrepontis, Dimitrios Protopapas
In the present work, we aim to restore Book X of the to its original Theaetetean, pre-Eudoxean form in two separate ways. First, we restore the considerable mathema…
The Reconstruction of Theaetetus' Theory of Ratios of Magnitudes
Stelios Negrepontis, Dimitrios Protopapas
In the present chapter, we obtain the reconstruction of Theaetetus' theory of ratios of magnitudes based, according to Aristotle's Topics 158b, on the definition of proportion in t…
The anthyphairetic reconstruction of the original Pythagorean proof of incommensurability, by means of the restoration of Book II of the Elements to its original Pythagorean form
Stelios Negrepontis, Vassiliki Farmaki
Unquestionably the greatest discovery of the Pythagoreans is the existence of incommensurable magnitudes, most probably the incommensurability of the diameter to the side of a squa…