ABSTRACT
Itmayberestatedasfollows:(1)thediscoveryoftheirrationalityofthe squarerootoftwowhichledtothebreakdownofthePythagorean programmeofreducinggeometryandcosmology(andpresumablyall knowledge)toarithmetic,producedacrisisinGreekmathematics;(2) Euclid'sElementsisnotatextbookofgeometry,butratherthefinal attemptofthePlatonicSchooltoresolvethiscrisisbyreconstructing thewholeofmathematicsandcosmologyonageometricalbasis,inorder todealwiththeproblemofirrationalitysystematicallyratherthanadhoc, thusinvertingthePythagoreanprogrammeofarithmetization;(3)itwas PlatowhofirstconceivedtheprogrammelatercarriedoutbyEuclid:itwas Platowhofirstrecognizedtheneedforareconstruction;whochose geometryasthenewbasis,andthegeometricalmethodofproportionas thenewmethod;whodrewuptheprogrammeforageometrizationof mathematics,includingarithmetic,astronomy,andcosmology;andwho becamethefounderofthegeometricalpictureoftheworld,andthereby alsothefounderofmodernscience-ofthescienceofCopernicus,Galileo, Kepler,andNewton.
