▁fleet ▁as ▁they ▁approached ▁Sy rac use , ▁a ▁question ▁still ▁in ▁debate . ▁The ▁book ▁went ▁beyond ▁this ▁purpose ▁and ▁also ▁expl ored ▁con ic ▁sections , ▁ref lections ▁of ▁light , ▁and ▁the ▁properties ▁of ▁par ab olas . ▁In ▁this ▁book ▁he ▁developed ▁the ▁theory ▁of ▁mirror s ▁sh aped ▁into ▁par ab olas , ▁hyper bol as , ▁and ▁elli ps es , ▁and ▁various ▁combinations ▁of ▁these ▁mirror s . ▁He ▁demonstrated ▁that ▁if , ▁as ▁was ▁later ▁shown , ▁light ▁has ▁a ▁finite ▁and ▁determin ate ▁speed , ▁there ▁is ▁minimal ▁inter ference ▁in ▁the ▁image ▁at ▁the ▁focus ▁of ▁a ▁par abol ic , ▁hyper bol ic ▁or ▁elli ptic ▁mirror , ▁though ▁this ▁was ▁theoretical , ▁since ▁the ▁mirror s ▁required ▁could ▁not ▁be ▁constructed ▁using ▁contemporary ▁technology . ▁This ▁would ▁produce ▁better ▁images ▁than ▁the ▁teles cop es ▁that ▁existed ▁at ▁the ▁time . ▁ ▁He ▁also ▁demonstrated ▁some ▁properties ▁of ▁curves . ▁The ▁first ▁is ▁that , ▁for ▁a ▁light ▁ray ▁parallel ▁to ▁the ▁axis ▁of ▁a ▁par ab ola ▁and ▁reflected ▁so ▁as ▁to ▁pass ▁through ▁the ▁focus , ▁the ▁sum ▁of ▁the ▁incident ▁angle ▁and ▁its ▁reflection ▁is ▁equal ▁to ▁that ▁of ▁any ▁other ▁similar ▁ray . ▁He ▁then ▁demonstrated ▁similar ▁results ▁for ▁hyper bol as ▁and ▁elli ps es . ▁The ▁second ▁result , ▁useful ▁in ▁the ▁design ▁of ▁reflect ing ▁teles cop es , ▁is ▁that ▁if ▁a ▁line ▁is ▁extended ▁from ▁a ▁point ▁outside ▁of ▁a ▁par ab