Fowler argues that a good reconstruction must offer a rationale for these blocks as coherent wholes, and he finds that the standard story doesn't offer such an interpretation. For example, the standard story would suggest that the crucial distinction would be between commensurable and incommensurable lines, but that isn't the way Book X organizes the world at all. Fowler's counterproposal is very interesting. This is perhaps what makes it so hard for us to think mathematics in the Greek way. The idea that a length is a number is so deeply ingrained in our thought that it takes a conscious effort to conceive of an approach to geometry that does not make such an assumption.
Fowler argues that Greek geometry was completely non-arithmetized.
Most historians would agree with this description of Greek geometry, I think. Many, however, see this characteristic as something to be explained . Fowler turns this on its head, and argues that in fact the non-arithmetized nature of Greek geometry should be read as evidence that Greek geometry does not derive from Babylonian sources. There are two important consequences. This is a crucial distinction.