The monsters of Greek mythology who don't appear prominently in FF enough to warrent their own pages (and yes, I know that my definition of "prominent" is a tad hard to fathom, so sue me :P)
For more Greeciness, read up on gorgons, lamias, hydras, chimeras, classical giants, Scylla and Charybdis, bestiary monsters and Cerberus.
Arachne -- Centaur Knight -- Echidna -- Harpuiai -- Sphinx
In Greek mythology, Arachne was a woman who boasted that her weaving matched that of the goddess Athena. Athena was primarily a goddess of war and wisdom (that's a combination you don't see often) but was also connected with craftsmanship, including weaving. Athena responded by visiting Arachne in disguise and warning her agaisnt her boasting, but was brushed off. Angered, Athena challanged Arachne to a weaving contest, and, to her shock, found that Arachne was indeed as skilled a weaver. Ever a sore loser, Athena beat Arachne up and turned her into a spider.
FF4 mixes the two forms of Arachne - woman and spider - together.
Creatures from Greek mythology which are human from the wist up, but have horses' bodies from the waist down, the human body starting where the horse's neck would've been. While one centaur, Chiron, was wise and benign and served as a teacher to the heroes Achilles and Jason, the other members of his race were lecherous and drunken, quite unlike the popular modern-day conception of centaurs as noble beings. The centaurs used to live in Thessaly, but, aside from Chiron, they were banished after gatecrashing a king's wedding.
The centaur knight isn't ancient Greek in style. It's actually modelled around a Medieval European knight, making it an original Square creation.
According to Greek mythology, Echidna was a monster resembling a woman with a snake's tail instead of legs (FF3 mixed the two halfs up a bit). She and her consort Typhon became the parents of a number of monsters; precisely which ones is disputed, but amongst the children attributed to her are the gorgons, the hydra, the chimera, Orthos and Cerberus. Echidna was killed by the hundred-eyed Argos.
Plural of "harpy". According to Greek mythology, the harpuiai had the bodies of birds, but the heads and chests of women, and were sent by the gods to punish sinners. When King Phineas revealed too many of the gods' secrets in his prophecies, Zeus blinded him and sent the harpuiai to steal his food whenever he tried to eat. The harpuiai were eventually vanquished by the winged boreads who accompanied Jason and the Argonauts.
A creature from Greek mythology with the body of a lion, the head and chest of a woman and a bird's wings, the sphinx would wait by a road and ask passers-by a riddle. THAT riddle. For the sake of completism, I might as well put it here:
Being based around the D&D manticore, FF1's sphinx replaces the bird's wings with a bat's and adds a scorpion's tail.
IMAGE: Ancient Greek carving of the sphinx
Back to...ARACHNE

CENTAUR KNIGHT

ECHIDNA

HARPUIAI

SPHINX

"What has four legs in the morning, two legs in the noon and three legs in the evening?"
The answer is... a Sellafield sheep.
Ehh, alright then. The answer is a man - he crawls as a baby and has a walking stick as an old man.
Anyone who failed to answer was eaten by the sphinx. When Oedipus gave the correct answer, the sphinx killed herself.
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