▁on ▁his ▁method , ▁would ▁treat ▁' all ▁the ▁lines ' ▁and ▁' all ▁the ▁plan es ' ▁as ▁equivalent ▁or ▁equal ▁to ▁the ▁area ▁and ▁volume , ▁but ▁Caval ieri , ▁in ▁an ▁attempt ▁to ▁avoid ▁the ▁question ▁of ▁the ▁composition ▁of ▁the ▁continu um , ▁ins isted ▁that ▁the ▁two ▁were ▁compar able ▁but ▁not ▁equal . ▁ ▁These ▁parallel ▁elements ▁are ▁called ▁ind iv is ibles ▁respectively ▁of ▁area ▁and ▁volume ▁and ▁provide ▁the ▁building ▁blocks ▁of ▁Caval ieri ' s ▁method , ▁and ▁are ▁also ▁fundamental ▁features ▁of ▁integral ▁calculus . ▁ ▁He ▁also ▁used ▁the ▁method ▁of ▁ind iv is ibles ▁to ▁calculate ▁the ▁result ▁which ▁is ▁now ▁written ▁, ▁in ▁the ▁process ▁of ▁calculating ▁the ▁area ▁en closed ▁in ▁an ▁Arch im ede an ▁Sp iral , ▁which ▁he ▁later ▁general ised ▁to ▁other ▁figures , ▁showing , ▁for ▁instance , ▁that ▁the ▁volume ▁of ▁a ▁cyl inder ▁is ▁one ▁third ▁of ▁the ▁volume ▁of ▁a ▁circ ums cribed ▁cyl inder . ▁ ▁An ▁immediate ▁application ▁of ▁the ▁method ▁of ▁ind iv is ibles ▁is ▁Caval ieri ' s ▁principle , ▁which ▁states ▁that ▁the ▁volumes ▁of ▁two ▁objects ▁are ▁equal ▁if ▁the ▁areas ▁of ▁their ▁corresponding ▁cross - sections ▁are ▁in ▁all ▁cases ▁equal . ▁Two ▁cross - sections ▁correspond ▁if ▁they ▁are ▁inter sections ▁of ▁the ▁body ▁with ▁plan es ▁equ id istant ▁from ▁a ▁chosen ▁base ▁plane . ▁( The ▁same ▁principle ▁had ▁been ▁previously ▁used ▁by ▁Zu ▁G eng z hi ▁( 4