Beseech - Vine's Expository Dictionary of New Testament Words
Beseech
[ 1,,G3870, parakaleo ]the most frequent word with this meaning, lit. denotes to call to one's side," hence, "to call to one's aid." It is used for every kind of calling to a person which is meant to produce a particular effect, hence, with various meanings, such as "comfort, exhort, desire, call for," in addition to its significance "to beseech," which has a stronger force than aiteo (See ASK). See, e.g., the RV "besought" in Mark 5:18; Acts 8:31; Acts 19:31; 1 Corinthians 16:12. See CALL, No. 6, Note
(2), COMFORT, DESIRE, EXHORT, INTREAT, PRAY.
[ 2,,G2065, erotao ]
often translated by the verb "to beseech," in the Gospels, is elsewhere rendered "beseech," in 1 Thessalonians 4:1; 1 Thessalonians 5:12; 2 Thessalonians 2:1; 2 John 1:5. See under ASK, No. 2.
[ 3,,G1189, deomai ]
"to desire, to long for," usually representing the word "need," is sometimes translated "beseech," e.g., Luke 5:12; Acts 21:39; 2 Corinthians 10:2; Galatians 4:12. It is used of prayer to God, in Matthew 9:38; Luke 10:2; Luke 21:36; Luke 22:32; Acts 4:31; Acts 8:22, Acts 8:24; Acts 10:2; Romans 1:10; 1 Thessalonians 3:10. See PRAY, REQUEST.
Note: Proskuneo is wrongly rendered "besought" in the AV marg. of Matthew 18:26. The word signifies "to worship."