Plutarch, Brutus 5.3: 3 It is said also that when the great conspiracy of Catiline, which came near overthrowing the city, had come to the ears of the senate, Cato and Caesar, who were of different opinions about the matter, were standing side by side, and just then a little note was handed to Caesar from outside, which he read silently [τὸν μὲν ἀναγινώσκειν σιωπῇ]. But Cato cried out that Caesar was outrageously receiving letters of instruction from the enemy.
Augustine, Confessions 6.3.3: 3 Nor did I now groan in my prayers that You would help me; but my mind was wholly intent on knowledge, and eager to dispute. And Ambrose himself I esteemed a happy man, as the world counted happiness, in that such great personages held him in honor; only his celibacy appeared to me a painful thing. But what hope he cherished, what struggles he had against the temptations that beset his very excellences, what solace in adversities, and what savoury joys Your bread possessed for the hidden mouth of his heart when ruminating on it, I could neither conjecture, nor had I experienced. Nor did he know my embarrassments, nor the pit of my danger. For I could not request of him what I wished as I wished, in that I was debarred from hearing and speaking to him by crowds of busy people, whose infirmities he devoted himself to. With whom when he was not engaged — which was but a little time — he either was refreshing his body with necessary sustenance, or his mind with reading. But while reading, his eyes glanced over the pages, and his heart searched out the sense, but his voice and tongue were silent [sed cum legebat, oculi ducebantur per paginas et cor intellectum rimabatur, vox autem et lingua quiescebant]. Ofttimes, when we had come — for no one was forbidden to enter, nor was it his custom that the arrival of those who came should be announced to him — we saw him thus reading to himself, and never otherwise; and, having long sat in silence — for who dared interrupt one so intent? — we were fain to depart, inferring that in the little time he secured for the recruiting of his mind, free from the clamour of other men’s business, he was unwilling to be taken off. And perchance he was fearful lest, if the author he studied should express anything vaguely, some doubtful and attentive hearer should ask him to expound it, or to discuss some of the more abstruse questions, as that, his time being thus occupied, he could not turn over as many volumes as he wished; although the preservation of his voice, which was very easily weakened, might be the truer reason for his reading to himself. But whatever was his motive in so doing, doubtless in such a man was a good one.
Augustine, Confessions 8.12.29: 29 I was saying these things and weeping in the most bitter contrition of my heart, when, lo, I heard the voice as of a boy or girl, I know not which, coming from a neighbouring house, chanting, and oft repeating, Take up and read; take up and read. Immediately my countenance was changed, and I began most earnestly to consider whether it was usual for children in any kind of game to sing such words; nor could I remember ever to have heard the like. So, restraining the torrent of my tears, I rose up, interpreting it no other way than as a command to me from Heaven to open the book, and to read the first chapter I should light upon. For I had heard of Antony, that, accidentally coming in while the gospel was being read, he received the admonition as if what was read were addressed to him, “Go and sell that you have, and give to the poor, and you shall have treasure in heaven; and come and follow me” (= Matthew 19.21). And by such oracle was he immediately converted unto You. So quickly I returned to the place where Alypius was sitting; for there had I put down the volume of the apostles, when I rose thence. I grasped, opened, and in silence read that paragraph on which my eyes first fell [arripui, aperui, et legi in silentio capitulum quo primum coniecti sunt oculi mei], “Not in rioting and drunkenness, not in chambering and wantonness, not in strife and envying; but put on the Lord Jesus Christ, and make not provision for the flesh, to fulfil the lusts thereof” (= Romans 13.13-14). No further would I read, nor did I need; for instantly, as the sentence ended — by a light, as it were, of security infused into my heart — all the gloom of doubt vanished away.
Bernard M. W. Knox, “Silent Reading in Antiquity,” in Greek, Roman, and Byzantine Studies, volume 9 (1968), pages 432-433: 432-433 In the Sappho of Antiphanes (Kock 196, Athenaeus 1O.450c) a riddle is proposed. “What is it that is female in nature and has children under the folds of its garments, and these children, though voiceless, set up a ringing shout... to those mortals they wish to, but others, even when present, are not permitted to hear?” A second speaker suggests a wrong answer (which has, however, satiric political point and is probably the reason the scene was written in the first place), and then Sappho gives the correct solution. The answer is ἐπιστολή, a letter; it is a feminine noun, and its children are the letters of the alphabet. “Though voiceless, they speak to those far away, those they wish to, but for anyone who happens to be standing near the man who is reading (ἀναγινώσκοντος) they are inaudible.” This piece of evidence could hardly be bettered, for it is the essential characteristic of a riddle that the answer to the puzzle it presents must be immediately and universally recognized as right — it must be based on common fundamental assumptions.
Dirk Schenkeveld, Times Literary Supplement, volume 22 (March 1991), page 13, apud Frank D. Gilliard, “More Silent Reading in Antiquity: Non Omne Verbum Sonabat,” in the Journal of Biblical Literature, volume 112, number 4, page 691:
Knox adduced two examples from fifth-century Attic drama in which silent reading actually takes place on stage before the audience. In Euripides’ Hippolytus, Theseus notices the letter which is tied to the hand of his now dead wife. He opens it, the chorus proceeds to sing several lines, and then Theseus bursts out in a cry of grief and anger (lines 856-74). As Knox says, “Clearly he has read the letter and read it silently — the audience watched him do so.”
The other passage comes from the prologue of Aristophanes’ Knights. There, a Demosthenes opens a writing-tablet containing an oracle and while looking at it he continuously expresses his amazement at its contents, asks for more drink but does not tell what he is reading. His partner presses him with demands for information, which Demosthenes finally gives (lines 116-27). Both passages make sense only if we infer that both Theseus and Demosthenes are reading silently.
ETA: Thanks to mbuckley3 for the references from the Testaments of the Twelve Patriarchs and from Jubilees:
Jubilees 8.3-4 (translation by VanderKam): 3 He found an inscription which the ancients had incised in a rock. He read what was in it, copied it, and sinned on the basis of what was in it, since in it was the Watchers’ teaching by which they used to observe the omens of the sun, moon, and stars and every heavenly sign. 4 He wrote (it) down but told no one about it because he was afraid to tell Noah about it lest he become angry at him about it.
Testament of Simeon 5.4: 4 “For I have seen it inscribed in the writing of Enoch that your sons will be corrupted with you in fornication, and they will do harm to Levi by the sword.” / 4 «Ἑώρακα γὰρ ἐν χαρακτῆρι γραφῆς Ἐνὼχ ὅτι υἱοὶ ὑμῶν μεθ' ὑμῶν ἐν πορνείᾳ φθαρήσονται, καὶ ἐν Λευὶ ἀδικήσουσιν ἐν ῥομφαίᾳ.»