Lexical Definition

‎προσέρχομαι‎ prosérchomai (pros-er'-khom-ahee) to come near/agree ^G:V
from ‎πρός‎ and ‎ἔρχομαι‎ (including its alternate)

(as soon as he) come (unto), come thereunto, consent, draw near, go (near, to, unto).

• to approach, i.e. (literally) come near, visit, or (figuratively) worship, assent to

Abbott-Smith

προσ-έρχομαι, [in LXX for קרב, נגשׁ, etc.;]
to approach, draw near: absol., Mt 4:11, Lk 9:42, al.; c. infin., Mt 24:1, al.; c. dat. loc., He 12:18, 22; dat. pers., Mt 5:1, and freq., Jo 12:21, al.; ptcp., προσελθών, c. indic., Mt 8:2, and freq., Mk 1:31, Lk 7:14, al.; π. αὐτῷ, c. indic., Mt 4:3, Mk 6:35. Metaph.,
(a) of approaching God: absol. (Le 21:17, De 21:5, al.), He 10:1, 22; τ. θεῷ, He 7:25 11:6; τ. θρόνῳ τ. χάριτος, He 4:16; πρὸς Χριστόν, I Pe 2:4;
(b) in sense not found elsewhere (Field, Notes, 211), to consent to: ὑγιαίνουσι λόγοις, I Ti 6:3.

Abbott-Smith References

Liddell-Scott-Jones

προσέρχομαι,

imperfect -ηρχόμην[Refs 5th c.BC+]: future -ελεύσομαι[Refs 2nd c.BC+]aorist -ήλυθον, -ῆλθον: perfect -ελήλυθα:—come or go to, with dative, [Refs 5th c.BC+]; π. Σωκράτει visit him as teacher, [Refs 5th c.BC+]; τινὶ ὥσπερ ἀθλητῇ Th. [prev. cited] (see. προσάρχομαι); αἷς ἂν προσέλθω [γυναιξί] [Refs 5th c.BC+]: with adverbs, π. δεῦρο [Refs 5th c.BC+]; ἐγγύθεν, ὄπισθεν, [Refs 5th c.BC+]: absolutely, approach, draw nigh, [Refs 5th c.BC+]; of pain, pleasure, etc., to be nigh at hand, [Refs 5th c.BC+]

__2 in hostile sense, attack, π. πρὸς τοὺς ἱππέας [Refs 5th c.BC+]
__3 come in, surrender, capitulate, [Refs 5th c.BC+]
__4 come forward to speak, π. τῷ δήμῳ [Refs 4th c.BC+]; π. πολιτείᾳ enter political life, [Refs 1st c.AD+]; π. πρὸς τὰ κοινά come forward in public, [Refs 4th c.BC+]; π. πρὸς τὸ πολιτεύεσθαι, πρὸς τὴν πολιτείαν, [Refs 4th c.BC+]; ὑμῖν (i.e. Ἀθηναίοις) [Refs 5th c.BC+]
__5 appear before a tribunal, προσελθὼν εἶπεν [Refs 2nd c.AD+]; π. τῷ δικαστηρίῳ κατ᾽ αὐτοῦ [Refs 4th c.AD+]; approach an official, π. διὰ βιβλιδίων τῷ λαμπροτάτῳ ἡγεμόνι [Refs 3rd c.AD+]; π. τοῖς θεοῖς in supplication, [Refs 2nd c.AD+]
__6 π. τῇ φιλοσοφίᾳ, τοῖς νόμοις, apply oneself to.. , [Refs 1st c.BC+]; π. τῇ τούτου κληρονομίᾳ enter upon his inheritance, [Refs 2nd c.AD+]; have recourse to, τοῖς ἀνασκευαστικωτέροις [Refs 2nd c.AD+]
__7 of things, to be added, [Refs 4th c.BC+]
__II come in, of revenue, [Refs 5th c.BC+]
__III have sexual intercourse, [Refs 5th c.BC+]