The next important quote of Papias on Mark (and Matthew) is found in Eusebius, Ecclesiastical History 3.39.15-16. Again, it is interesting to look at the interpretive decisions of the translators and in what they insert in brackets: who is the one doing the remembering (Peter or Mark), did Peter adapt his teaching according to the needs of his audiences or in a certain literary form (chreiai or anecdotes), what does it mean that Mark did not write in order(taxis - literary arrangement, chronology, completeness) or only wrote down some things as he (Mark or Peter?) remembered them, what does it mean that Matthew put the sayings/logia/oracles into a Hebrew dialect (the Hebrew or Aramaic language or style?) and that each (who?) interpreted them as were able?
καὶ τοῦθ’ ὁ πρεσβύτερος ἔλεγεν· Μάρκος μὲν ἑρμηνευτὴς Πέτρου γενόμενος, ὅσα ἐμνημόνευσεν, ἀκριβῶς ἔγραψεν, οὐ μέντοι τάξει τὰ ὐπὸ τοῦ κυρίου η λεχθέντα ἢ πραχθέντα. οὔτε γὰρ ἤκουσεν τοῦ κυρίου οὔτε παρηκολούθησεν αὐτῷ, ὕστερον δὲ, ὡς ἔφην, Πέτρῳ· ὃς πρὸς τὰς χρείας ἐποιεῖτο τὰς διδασκαλίας, ἀλλ’ οὐχ ὥσπερ σύνταξιν τῶν κυριακῶν ποιούμενος λογίων, ὥστε οὐδὲν ἥμαρτεν Μάρκος οὕτως ἔνια γράψας ὡς ἀπεμνημόσευσεν. ἐνὸς γὰρ ἐποιήσατο πρόνοιαν, τοῦ μηδὲν ὧν ἤκουσεν παραλιπεῖν ἢ ψεύσασθαί τι ἐν αὐτοῖς. ταῦτα μὲν οὖν ἱστόρηται τῷ Παπίᾳ περὶ τοῦ Μάρκου· περὶ δὲ τοῦ Ματθαῖου ταῦτ’ εἴρηται· Ματθαῖος μὲν οὖν Ἑβραΐδι διαλέκτῳ τὰ λόγια συνετάξατο, ἡρμήνευσεν δ’ αὐτὰ ὡς ἧν δυνατὸς ἕκαστος.
“And the Elder said this also: ‘Mark, having become the interpreter of Peter, wrote down accurately everything that he remembered, without however recording in order what was either said or done by Christ. For neither did he hear the Lord, nor did he follow Him; but afterwards, as I said, (attended) Peter, who adapted his instructions to the needs (of his hearers) but had no design of giving a connected account of the Lord’s oracles. So then Mark made no mistake, while he thus wrote down some things as he remembered them; for he made it his one care not to omit anything that he heard, or to set down any false statement therein.’ Such then is the account given by Papias concerning Mark. But concerning Matthew, the following statement is made (by him): ‘So then Matthew composed the oracles in the Hebrew language, and each one interpreted them as he could.’” (JB Lightfoot and JR Harmer, Fragment II)
“And the elder was saying this: ‘On the one hand, Mark, becoming Peter’s interpreter, wrote accurately as many things as he remembered. On the other hand, [he did] not [write] in order the things either said or done by the Lord. For he had neither heard the Lord nor followed him. But later, as I said, [he had followed] Peter, who was teaching in accord with the anecdotes yet not as it were arranging the Lord’s oracles, so that Mark did nothing wrong by writing some things as he related [them] from memory. For he was thinking one thing beforehand of one thing, [i.e.] to omit not a single one of the things that he had heard or to falsify anything in them.’ Therefore, on the one hand, these things are related by Papias [or 'to Papias' as the one who heard the tradition] concerning Mark. Concerning Matthew, on the other hand, these things were said: ‘On the one hand, therefore, Matthew did arrange the oracles in Hebrew ‘dialect.’ On the other hand, each one interpreted them as he was able.’” (Robert Gundry, “The Apostolically Johannine Pre-Papian Tradition concerning the Gospels of Mark and Matthew,” page 49-50)
“And this is what the elder used to say, ‘when Mark was the interpreter [or translator] of Peter, he wrote down accurately everything that he recalled of the Lord’s words and deeds – but not in order. For he neither heard the Lord nor accompanied him, but later, as I indicated, he accompanied Peter, who used to adapt his teachings for the needs at hand, not arranging, as it were, an orderly composition of the Lord’s sayings. And so Mark did nothing wrong by writing some of the matters as he remembered them. For he was intent on just one purpose: to leave out nothing that he had heard or to include any falsehood among them… And this is what he says about Matthew: And Matthew composed the sayings in the Hebrew tongue, and each one interpreted [or translated] them to the best of his ability.’” (Bart Ehrman, Loeb, pg. 103)
“The Elder used to say: ‘Mark, in his capacity as Peter’s interpreter, wrote down accurately as many things as he [Peter?] recalled from memory – though not in an ordered form – of the things said or done by the Lord. For he [Mark] neither heard the Lord nor accompanied him, but later, as I said, [he heard and accompanied] Peter, who used to give his teachings in the form of chreiai, but had no intention of providing an ordered arrangement [suntaxin] of the logia of the Lord. Consequently Mark did nothing wrong when he wrote down some things just as he [Peter?] related them from memory. For he made it his one concern not to omit anything he had heard or to falsify anything. This, then, is the account given by Papias about Mark. But about Matthew the following was said: ‘Therefore Matthew put the logia in an ordered arrangement [sunetaxato] in the Hebrew language [hebraidi dialectō], but each person interpreted them as best he could’” (Richard Bauckham, Jesus
and the Eyewitnesses, pg. 203)
“And the presbyter would say this: ‘Mark, who had indeed been Peter’s interpreter [hermēneutēs], accurately wrote as much as he remembered, yet not in order, about that which was either said or did by the Lord. For he neither heard the Lord nor followed him, but later, as I said, Peter, who would make the teachings anecdotally but not exactly an arrangement of the Lord’s reports, so that Mark did not fail by writing certain things as he recalled. For he had one purpose, not to omit what he heard or falsify them.’ Now this is reported by Papias about Mark, but about Matthew this was said, ‘Now Matthew compiled the reports in a Hebrew manner of speech, but each interpreted them as he could.’” (Stephen Carlson)