be-hold'-ing: Many Hebrew and Greek words are so rendered in English Versions of the Bible, but epopteusantes, "your good works, which they behold" (1Pe 2:12); "beholding your chaste behavior" (1Pe 3:2), and epoptai, "We were eyewitnesses of his majesty" (2Pe 1:16) are peculiar to Peter. The fact that this word is used only by Peter and is used in both epistles is an argument for identity of authorship. The word epoptes denotes one who had been initiated into the innermost secrets of his faith and who enjoyed the highest religious privileges; but now in contradiction to the secrecy of all pagan "mysteries" (Eleusinian, etc.) the apostles would share with all the faithful every spiritual vision which they enjoyed ("we made known unto you").
⇒See the definition of beholding in the KJV Dictionary
In 2 Cor 3:18, for katoptrizomenoi, the English Revised Version gives "reflecting (as a mirror) the glory of the Lord," the American Standard Revised Version "beholding (as in mirror," etc.). Katoptron was a mirror of polished metal. We cannot clearly and fully behold the outshining of spiritual grandeur in Christ Jesus, but in the gospel God accommodates and adjusts the vision as we are able to bear it, and the glory beheld becomes glory imparted to (and reflected by) the beholder.
John's Gospel gives us theaomai ("to look closely at"), and theoreo ("to discern"). "We beheld (etheasametha) his glory" (Joh 1:14), "that they may behold (theorosin) my glory" (Joh 17:24). In classic literature, the former word is closely associated with theatrical spectacles, and the latter with athletic games, and they both convey the idea of unceasing interest, deepening in this connection into love and joy.
M. O. Evans