8 0 – 5 2 5 ) ▁of ▁China , ▁in ▁the ▁specific ▁case ▁of ▁calculating ▁the ▁volume ▁of ▁the ▁sphere .) ▁▁ ▁The ▁method ▁of ▁ind iv is ibles ▁as ▁set ▁out ▁by ▁Caval ieri ▁was ▁powerful , ▁but ▁was ▁limited ▁in ▁its ▁useful ness ▁in ▁three ▁respect s . ▁First , ▁while ▁Caval ieri ' s ▁proofs ▁were ▁intuit ive ▁and ▁later ▁demonstrated ▁to ▁be ▁correct , ▁they ▁were ▁not ▁rig orous ; ▁second , ▁his ▁writing ▁was ▁dense ▁and ▁op aque ; ▁third , ▁the ▁treatment ▁of ▁the ▁continu um ▁as ▁being ▁composed ▁of ▁inf init es im als ▁was ▁at ▁the ▁time ▁condem ned ▁in ▁Italy ▁by ▁the ▁Jes uit ▁order ▁as ▁a ▁feature ▁of ▁atom ism , ▁a ▁forb idden ▁doctrine . ▁While ▁many ▁contemporary ▁mathemat icians ▁further ed ▁the ▁method ▁of ▁ind iv is ibles , ▁often ▁with ▁little ▁regard ▁for ▁the ▁limitations ▁that ▁Caval ieri ▁im posed ▁on ▁the ▁use ▁of ▁inf init es im als ▁in ▁order ▁to ▁avoid ▁controvers y , ▁the ▁Ge omet ria ▁ind iv is ibil ius ''' ▁critical ▁reception ▁was ▁severe . ▁Andre ▁Ta quet ▁and ▁Paul ▁G uld in ▁both ▁published ▁responses ▁to ▁the ▁Ge omet ria ▁ind iv is ibil us . ▁G uld in ' s ▁critique , ▁which ▁was ▁particularly ▁in - depth , ▁suggested ▁that ▁Caval ieri ' s ▁method ▁was ▁derived ▁from ▁the ▁work ▁of ▁Johannes ▁Ke pler ▁and ▁Bar th ol ome w ▁S over , ▁attacked ▁his ▁method ▁for ▁a ▁lack ▁of