It depends upon what you mean of sympathetic magic - but gods were of the spirit of elements and could call upon such powers of nature and magic.
Aphrodite
The Romans took their gods directly from the Greek pantheon. There was no god of dancing, but Terpsichore, one of the Greek muses, was the muse of dance.
Hestia was not more important than Vesta. At some point in their history, the Romans linked their divinities to the Greek ones. Vesta was the Roman equivalent of Hestia.
The Roman elites looked up to the Greeks. They received an education in both Latin and Greek and the pinnacle of their education was a stay in Greece to study Greek philosophy. The first professional teachers in Rome were Greek.The Romans adopted the architectural styles of the Greeks for temples and porticoes and coped Greek statues. They also adopted Greek medicine and the Greek catapult (which they improved). They adopted some Greek gods and many Greek myths and linked their gods to Greek ones.
Horace was referring to the great cultural influence which the Greeks had on the Romans. The Romans adopted some Greek gods and linked their gods to the Greek ones, adopted Greek myths, sculpture, medicine, philosophy, sports and siege machines. Latin literature started with translations of Greek epics, tragedies and comedies and their plays were originally modelled on Greek ones.
Pegasus is linked to the ancient Greek civilization
There is no evidence Egyptian and Greek mathematics are linked.
The owl.
no it isn't because Argos the shop is English and Argos the city is Greek
thebes
I suppose Arachne could be linked to Spiderman, since she is known as the mother of spiders.
Juliana (Roman/Latin) is "youthful; Jove's child". It has no Greek meaning. Jove is linked below.
parallel comes directly from Greek παράλληλος[paralleelos]
greek language and culture
The greek god for Mars is Ares
greek language and culture
Words with 'esthesia' are usually of Greek origin and are linked to feelings, sensation and perceptions.