Is it farther or further?
c.1300, "to demonstrate, prove;" mid-14c., "to attest (something) with authority," from Old French aprover (Modern French approuver) "approve, agree to," from Latin approbare "to assent to as good, regard as good," from ad- "to" (see ad-) + probare "to try, test something (to find if it is good)," from probus "honest, genuine" (see prove).
The meaning extended late 14c. to "to sanction, endorse, confirm formally" then to "assent to (something) as good" (early 15c.), especially in reference to the actions of authorities, parliaments, etc. Related: Approved; approving.