ola ▁to ▁the ▁focus , ▁then ▁the ▁reflection ▁of ▁this ▁line ▁on ▁the ▁outside ▁surface ▁of ▁the ▁par ab ola ▁is ▁parallel ▁to ▁the ▁axis . ▁Other ▁results ▁include ▁the ▁property ▁that ▁if ▁a ▁line ▁passes ▁through ▁a ▁hyper bol a ▁and ▁its ▁external ▁focus , ▁then ▁its ▁reflection ▁on ▁the ▁interior ▁of ▁the ▁hyper bol a ▁will ▁pass ▁through ▁the ▁internal ▁focus ; ▁the ▁reverse ▁of ▁the ▁previous , ▁that ▁a ▁ray ▁directed ▁through ▁the ▁par ab ola ▁to ▁the ▁internal ▁focus ▁is ▁reflected ▁from ▁the ▁outer ▁surface ▁to ▁the ▁external ▁focus ; ▁and ▁the ▁property ▁that ▁if ▁a ▁line ▁passes ▁through ▁one ▁internal ▁focus ▁of ▁an ▁el lipse , ▁its ▁reflection ▁on ▁the ▁internal ▁surface ▁of ▁the ▁el lipse ▁will ▁pass ▁through ▁the ▁other ▁internal ▁focus . ▁While ▁some ▁of ▁these ▁properties ▁had ▁been ▁noted ▁previously , ▁Caval ieri ▁gave ▁the ▁first ▁proof ▁of ▁many . ▁ ▁Lo ▁Spec chio ▁U st orio ▁also ▁included ▁a ▁table ▁of ▁reflect ing ▁surfaces ▁and ▁modes ▁of ▁reflection ▁for ▁practical ▁use . ▁ ▁Caval ieri ' s ▁work ▁also ▁contained ▁theoretical ▁designs ▁for ▁a ▁new ▁type ▁of ▁teles cope ▁using ▁mirror s , ▁a ▁reflect ing ▁teles cope , ▁initially ▁developed ▁to ▁answer ▁the ▁question ▁of ▁Arch im edes ' ▁Mir ror ▁and ▁then ▁applied ▁on ▁a ▁much ▁smaller ▁scale ▁as ▁teles cop es . ▁He ▁illustrated ▁three ▁different ▁concepts ▁for ▁incorpor ating ▁reflect ive ▁mirror s ▁within ▁his ▁teles cope ▁model . ▁Plan ▁one ▁consisted ▁of ▁a ▁large , ▁con ca ve ▁mirror