How did early chemists determine which substances were elements

Chemistry deals with the study of elements-- their properties, chemical reactions and their compounds. This science includes the study of how these elements or compounds are formed. The history of chemistry is divided to 4 periods. 
Black Magic, Alchemy, Traditional Chemistry and Modern Chemistry comprised these periods.
How did the early chemists determine which of the substances are elements? Long time ago, chemists knew which substances could not be broken down and that mixtures are broken down through chemical means. Through the said process, they were able to identify which are elements from the substances they have tested.