Phoebus was the name used in classical mythology for Apollo in his role as god of the sun. His son was Phaeton. Under the alternate spelling Phevos and together with Athena, he is a mascot of the 2004 Summer Olympics in Athens.
... the square" is to add a constant (i.e., in this case, a quantity that does not depend on x) to the expression to the left of "=", that will make it a perfect square ...