before vowels angi-, word-forming element meaning "vessel of the body," now often "covered or enclosed by a seed or blood vessel," from Latinized form of Greek angeion "case, capsule, vessel of the body," diminutive of angos "vessel, jar, vat, vase," which is of unknown origin. Beekes says "Possibly a Mediterranean loanword ..., as kitchen utensils are often borrowed."
word-forming element meaning "birth, origin, creation," from Greek genesis "origin, creation, generation," from gignesthai "to be born," related to genos "race, birth, descent" (from PIE root *gene- "give birth, beget," with derivatives referring to procreation and familial and tribal groups).
<a href="https://www.etymonline.com/word/angiogenesis">Etymology of angiogenesis by etymonline</a>
Harper, D. (n.d.). Etymology of angiogenesis. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/angiogenesis