Name this classical order which chronologically came after Doric and Ionic.
This style of architecture is exemplified by the Choragic Monument of Lysicrates in Athens and the Temple of Bacchus at Baalbek in modern-day Lebanon, and many buildings in this style have a fleuron on each side of an abacus.  An example of this style in Rome is the Column of Phocas, and, like the Composite order, this style often used acanthus leaves in its capitals. It also uses flat roofs and fluted columns. Name this classical order which chronologically came after Doric and Ionic.
This style of architecture is exemplified by the Choragic Monument of Lysicrates in Athens and the Temple of Bacchus at Baalbek in modern-day Lebanon, and many buildings in this style have a fleuron on each side of an abacus.  
Corinthian order