Buddhism
Contacts between Buddhism and Christianity
One one of the major Ashoka’s rock edicts, (the 13th), it is stated how a few ellenistic kings were followers of the Dhamma. One of them is Ptolemy II and his sister Arsinoe II.
In the apocryphal Gospel of Thomas, at verse 90, Jesus says:
Come unto me, for my yoga is natural and my lordship is gentle—and you shall find repose for yourselves.
thus literally naming Yoga in a text of very early Christianity. It is also stated by Dio Chrysostum and Clement (respectively 1st and 2nd century A.D.) that in Alexandria, Egypt, Indian scholars were a common sight (cit needed).
Similitudes between Buddhism and Western philosophies
Hegesians
Hegesias of Cyrene (fl. 290 BC) argued how happiness was impossible to achieve and the goal of life should be to avoid pain and sorrow.
He arguably wrote a book called Death by Starvation that persuaded so many people that death was more desirable than life that he was banned from teaching in Alexandria.
Hegesias was living before the edicts of Ashoka (268-232 BC) and the missionaries the Indian king sent to the Hellenistic world. Therefore the connection to Buddhism should have happened earlier, unrelated with Ashoka’s reign.
Dionysus in India
Fairly attested throughout the Greek texts is the belief that the God Dionysus travelled and subdued India (parts of). He was called Nysian/Nysean by the Indians.