He discovered New York Bay and sailed his boat some distance up the river in 1524. * For some years after this French navigators sailed up the river to trade with the Indians , and while history does not record where they stopped , one naturally concludes that they could hardly have avoided stopping at Croton Point . They did not settle here , however , as did the Dutch and English later . The Advent of Henry Hudson The popular history of our com- munity begins on September 3 , 1609 . On that day Henry Hudson , an Eng- lishman , in a ship named the " Half- Moon , " flying the Dutch Flag of the Dutch East Indies Company of Holland , entered the New York Har- bor and sailed up the river . He be- lieved he had found à new route to China and Asia . His exploit later gave the river its name , the Hud- son . The Indians had previously called the river " Shatamuc " which means " The river that flows both ways . " The colored glass portrayal of the " Half - Moon " on the entrance to the Pierre Van Cortlandt Ele- Encyclopedia Brittanica , Vol . 23 , 1945 : p . 90B . ** Alvin McCaslin Higgins , The Story of Croton , Quarterly Bulletin , Westches- ter County Historical Society , Vol . 16 , No. 3 , July 1940 , pp . 55-57 . mentary School commemorates this event . The point of land which we call Croton Point was known to the In- dians as Senasqua . After the Dutch came it was called Teller's Point for over a hundred years . The Van Cortlandts In the year 1681 , Stephanus Van Cortlandt built the Van Cortlandt Manor House on the Albany Post Road at the Croton River .