▁to ▁each ▁side ▁at ▁the ▁side ' s ▁mid point . ▁M arden ' s ▁theorem ▁still ▁applies : ▁the ▁fo ci ▁of ▁the ▁Ste iner ▁in el lipse ▁are ▁zero es ▁of ▁the ▁derivative ▁of ▁the ▁polynomial ▁whose ▁zero es ▁are ▁the ▁vertices ▁of ▁the ▁n - gon . ▁ ▁References ▁ ▁Category : Tri angle ▁geometry ▁Category : Con ic ▁sections <0x0A> </s> ▁Johannes ▁E ch arius ▁Carol us ▁or ▁Jean ▁Eug ène ▁Charles ▁Al ber ti ▁( b apt . ▁ 2 0 ▁June ▁ 1 7 7 7 ▁- ▁after ▁ 1 8 4 3 ), ▁was ▁a ▁Dutch ▁painter ▁of ▁Italian ▁descent ▁who ▁worked ▁in ▁Paris ▁for ▁most ▁of ▁his ▁life . ▁ ▁Life ▁Al ber ti ▁was ▁born ▁in ▁Ma astr icht . ▁ ▁He ▁studied ▁first ▁in ▁Amsterdam , ▁where ▁he ▁had ▁moved ▁at ▁the ▁age ▁of ▁five , ▁and ▁then ▁at ▁Paris ▁under ▁David , ▁and ▁afterwards ▁in ▁Rome , ▁where ▁he ▁copied ▁the ▁works ▁of ▁Gu ido ▁Ren i ▁and ▁Anthony ▁van ▁Dy ck . ▁He ▁subsequently ▁returned ▁and ▁settled ▁in ▁Paris . ▁He ▁left ▁Paris ▁in ▁ 1 8 4 3 , ▁pres umably ▁returning ▁to ▁the ▁Netherlands , ▁but ▁the ▁date ▁of ▁his ▁death ▁is ▁not ▁recorded . ▁Mar ius ▁among ▁the ▁Ru ins ▁of ▁Car th age , ▁painted ▁in ▁ 1 8 0 5 , ▁gained ▁him ▁a ▁gold ▁medal . ▁ ▁Al ber ti ▁made ▁eng rav ings ▁both ▁from ▁his ▁own ▁works ▁and ▁from ▁those ▁of ▁the ▁Italian