Complex sentence: Ptolemy rode to the center encouraging his phalanx to attack, Polybius tells us "with alacrity and spirit", while on the Ptolemaic far right, Ptolemy's cavalry was routing their opponents.
Split into simpler sentences: Ptolemy rode to the center encouraging his phalanx to attack, Polybius tells us "with alacrity and spirit". On the Ptolemaic far right, Ptolemy's cavalry was routing their opponents.