▁of ▁opt ics ▁and ▁motion , ▁work ▁on ▁ind iv is ibles , ▁the ▁prec urs ors ▁of ▁inf init es imal ▁calculus , ▁and ▁the ▁introduction ▁of ▁log arith ms ▁to ▁Italy . ▁Caval ieri ' s ▁principle ▁in ▁geometry ▁partially ▁anticip ated ▁integral ▁calculus . ▁ ▁Life ▁ ▁Born ▁in ▁Milan , ▁Caval ieri ▁joined ▁the ▁Jes u ates ▁order ▁( not ▁to ▁be ▁confused ▁with ▁the ▁Jes uits ) ▁at ▁the ▁age ▁of ▁fifteen , ▁taking ▁the ▁name ▁Bon av ent ura ▁upon ▁becoming ▁a ▁nov ice ▁of ▁the ▁order , ▁and ▁remained ▁a ▁member ▁until ▁his ▁death . ▁He ▁took ▁his ▁v ows ▁as ▁a ▁full ▁member ▁of ▁the ▁order ▁in ▁ 1 6 1 5 , ▁at ▁the ▁age ▁of ▁sevent een , ▁and ▁shortly ▁after ▁joined ▁the ▁Jes u at ▁house ▁in ▁P isa . ▁By ▁ 1 6 1 6 ▁he ▁was ▁a ▁student ▁of ▁geometry ▁at ▁the ▁University ▁of ▁P isa . ▁There ▁he ▁came ▁under ▁the ▁t ute lege ▁of ▁Bened etto ▁Cast elli , ▁who ▁probably ▁introduced ▁him ▁to ▁Gal ile o ▁Gal ile i . ▁In ▁ 1 6 1 7 ▁he ▁briefly ▁joined ▁the ▁Med ici ▁court ▁in ▁Florence , ▁under ▁the ▁patron age ▁of ▁Card inal ▁Feder ico ▁Bor rome o , ▁but ▁the ▁following ▁year ▁he ▁returned ▁to ▁P isa ▁and ▁began ▁teaching ▁Mathemat ics ▁in ▁place ▁of ▁Cast elli . ▁He ▁applied ▁for ▁the ▁Chair ▁of ▁Mathemat ics ▁at ▁the ▁University ▁of ▁Bolog na , ▁but ▁was ▁turned