Abarim Publications' online Biblical Greek Dictionary
The verb ευρισκω (heurisko) means to find (hence our English word "heuristic"). This verb is on a close par with our English equivalent, and holds no major mysteries. It may mean to discover or find out (Matthew 1:18, 13:46), to search for and find (Matthew 2:18, 7:7), to happen upon (Matthew 8:10), or to achieve (to find rest; Matthew 11:29). The passive subjunctive is often deployed to express a condition or situation in which one is hopefully found (Acts 5:39, 1 Corinthians 4:2, Philippians 3:9).
This verb occurs 177 times in the New Testament, see full concordance, and from it stems:
Together with the preposition ανα (ana), meaning on or upon and which in this case serves as an emphatic: the verb ανευρισκω (aneurisko), meaning to finally find by having searched diligently (Luke 2:16 and Acts 21:4 only).
Note the similarity with the otherwise unused adjective ευρυσ (eurus), meaning broad or wide. Our word "aneurysm" means "very wide."