▁directed ▁towards ▁the ▁sun ▁as ▁to ▁reflect ▁light ▁into ▁a ▁second , ▁smaller , ▁convex ▁mirror . ▁Caval ieri ' s ▁second ▁concept ▁consisted ▁of ▁a ▁main , ▁trunc ated , ▁par abol oid ▁mirror ▁and ▁a ▁second , ▁convex ▁mirror . ▁His ▁third ▁option ▁illustrated ▁a ▁strong ▁res embl ance ▁to ▁his ▁previous ▁concept , ▁replacing ▁the ▁convex ▁secondary ▁l ens ▁with ▁a ▁con ca ve ▁l ens . ▁ ▁Work ▁in ▁Ge ometry ▁and ▁the ▁Method ▁of ▁Ind iv is ibles ▁▁ ▁In sp ired ▁by ▁earlier ▁work ▁by ▁Gal ile o , ▁Caval ieri ▁developed ▁a ▁new ▁geomet rical ▁approach ▁called ▁the ▁method ▁of ▁ind iv is ibles ▁to ▁calculus ▁and ▁published ▁a ▁treat ise ▁on ▁the ▁topic , ▁Ge omet ria ▁ind iv is ibil ibus ▁continu orum ▁nova ▁quad am ▁r ation e ▁prom ota , ▁or ▁Ge ometry , ▁developed ▁by ▁a ▁new ▁method ▁through ▁the ▁ind iv is ibles ▁of ▁the ▁continu a . ▁This ▁was ▁written ▁in ▁ 1 6 2 7 , ▁but ▁was ▁not ▁published ▁until ▁ 1 6 3 5 . ▁In ▁this ▁work , ▁Caval ieri ▁cons iders ▁an ▁entity ▁referred ▁to ▁in ▁the ▁text ▁as ▁' all ▁the ▁lines ' ▁or ▁' all ▁the ▁plan es ' ▁of ▁a ▁figure , ▁an ▁in defin ite ▁number ▁of ▁parallel ▁lines ▁or ▁plan es ▁within ▁the ▁bounds ▁of ▁a ▁figure ▁that ▁are ▁compar able ▁to ▁the ▁area ▁and ▁volume , ▁respectively , ▁of ▁the ▁figure . ▁Later ▁mathemat icians , ▁impro ving