"Although viewing lengths as numerical quantities is a relatively recent development in geometry, it has caught on quite well and is very much ingrained in the modern view of geometry. The previous chapters are a demonstration that geometry can get along quite well without numbers, and many geometrical ideas can be developed purely geometrically. Also, one obtains a more clear axiomatic development of geometry by asserting only geometric axioms
and avoiding a separate development of the real number system."
and avoiding a separate development of the real number system."
This explains it all.
