Disclaimer: All I own is about four copies of the play, a paltry familiarity with Latin (a far cry short of what I would need in an early Renaissance university) and a comparable amount of Greek (although a fondness for all the things listed).
The Leucorea library was, unsurprisingly, already inhabited by at least a dozen students when Horatio made his way there on an autumn afternoon. Most were seated at tables near the fire, poring over books or parchments or at least pretending to do so until the master presently in the room should decide to take himself off elsewhere, though one or two scholars wandered amongst the shelves. A couple of fellow Poles greeted him in their native tongue, albeit quietly, and Horatio responded in kind, but they did not press him to join them and he had no inclination to do so. He made his way to one of the wide-silled windows - a particular favorite of his, out of sight from the door but with an excellent view of the fireplace and its environs. Once settled in the embrasure, Horatio opened the book he had brought with him but did not immediately begin to read.
Rather, he gazed through the window panes - glass! this was the luxury of wealth bestowed more upon books than on men, though even that did not explain why the glass was so clear as it was, permitting vision to cross through it as well as light - looking down upon the world that passed below. A woman walked by, carrying a covered basket in one hand and leading a young girl by the other; two men - fellow students - passed, one gesticulating avidly and apparently discoursing with equal fervour while his companion strode at a safe distance from the flying hands and fidgeted with his coat or glanced about him; a young boy dashed past; another pair of men, folk of the town this time, engaged in conversation - a discussion, rather than the monologue the student seemed to have been delivering. Within the library, meanwhile, occasional whispers stirred the air - too quiet for Horatio to identify the languages - and heads furtively turned every now and then in the direction that Horatio had last observed the master, now hidden beyond two or three bookcases from Horatio's view. Lordlings, a handful of princes and men, as Horatio, of no noteworthy background all maintained a tactful hush in the presence of academic authority; nothing of especial note would occur while that man remained. Horatio fell at last to reading the book he had held open all the while that he had observed the worlds around him.
It was several pages before there was a slight clattering, two faint swishes and finally a quiet thud of wood as the door closed. One student who was perpetually keeping at least half an eye on the door returned the majority of his attention the book before him and the parchment on which he made an occasional note. The latest arrival presently appeared in Horatio's range of vision and crossed directly to the fireplace, where he set down the small bag he carried and crouched, warming first his bare hands, then shedding his coat and warming the rest of himself - a student perhaps from warmer climes, who did not find the local weather wholly agreeable. He would find it a good deal less pleasant when winter proper came, supposed Horatio, who had grown up in a climate very similar to that of Wittenberg.
He returned to his book, which he had never wholly left, and continued another few pages before he again heard the sounds of the door opening and shutting; this time the student who watched the room's single entrance continued to stare openly at the door. As others in the library noted this, the room became even quieter than it had been while the master remained. The fire persisted in crackling and the men already strolling amongst the shelves continued to do so, but the furtive whispers had ceased and most men waited tensely for whatever sign it was that determined they were safe from righteous academic wrath. Presently the signal was given - not visibly or audibly, but more by a common consent; the stops were released and a clamour broke out from most of the tables, until soon even the more cautious students were drawn into conversation. Horatio followed snatches of three discussions: one in German that seemed to be complaining loosely of the French - whether the students, the nation in general or some other aspect of that region, Horatio was unable to determine, for his command of the local vernacular was no better than serviceable; of the other two, both in Latin, one was a debate concerning Abelard - focusing more upon his personal affairs than his scholarly achievements - and the second a tirade against the Ancient Greek language. Some of the grievances aired in this last were ones with which Horatio at least sympathized, although he found the invective a trifle strong, for the very text he had brought with him was in that tongue; he continued to regard those once-alien letters but no longer read them, allowing his attention instead to drift between the three discussions.
At length, a debate further away surged up over those close to Horatio, and gradually all other conversations subsided to make way for it. Horatio lifted his eyes, even his head slightly, to better observe the participants. One man was the cold student, who still stood by the fireplace, his hand absently running along the mantelpiece, while the second man leaned back against a table; once or twice some others seated near these two joined in, but their contributions - and even the contributors themselves - had little lasting impact in what remained primarily a dialogue. The debaters continued, indifferent - perhaps even oblivious - to their surroundings, not even breaking off when several heads turned in the direction of the door. Horatio had not heard it open, but took the cue to return his evident interest to his book.
The students, however, soon relaxed, and Horatio was again surreptitiously observing the room when the newcomer emerged from behind a bookshelf. Horatio recognized him as the gesticulator from the street and further, as was now evident at closer range, the Danish prince. Horatio knew the man by sight, though certainly he had never spoken with him. If his reputation was accurate, then Hamlet - this prince - had an extremely quick mind and a sharper wit, especially in Latin, than most people could entirely appreciate; the Danish students assured everyone else that he was quite as clever in his own tongue as in the language of scholarship.
And so, indeed, it proved. The Danish prince stood poised, with one foot on a stool, leaning in to listen to the debaters. After a few of their exchanges, he shot a brief but incisive comment at an inconsistency in one of the men's arguments - not either of the faults Horatio had noted (which were minor enough: fools would not produce an impromptu discourse intelligent enough in either content or rhetoric to engage the attention of the populous of Leucorea's library), but a more subtle, yet also more pivotal matter.
It was not until the Dane commented again that Horatio realized he had lost the main thread of the debate to follow instead the implications of the prince's remark. He kept better heed of the conversation's path thereafter, noting to himself points that could be objectionable; he did not go so far as to venture a theory as to which of these the prince might raise, which was just as well, for his tentative supposition proved incorrect (though the comment at least transpired to concern one of the subjects Horatio had identified).
Though the prince had entered into the debate arguing as if he were the Devil's advocate, he gradually contrived to build a cohesive view from the various points he brought up. Horatio was unable to determine if the prince believed his own assertions or if he argued merely as the Sophist. He hoped - irrelevantly, to be sure, for what did his opinion matter? - that the former was the case, though he was inclined to doubt this. The man was a prince, after all, a courtier, and could not be expected ever to speak what he truly thought. He was, regardless of belief, a formidable speaker, for he had supplanted the second of the original speakers through sheer force of personality, and, thanks to a pair of witticisms backed by apparently solid logic, was well on his way to vanquishing the student still standing by the fireplace. Neither of these men appeared entirely pleased by the course their conversation had taken, but the remainder of the room gave every appearance of greatly enjoying the display. At last, the remaining original debater, flustered by the Dane's combination of jest and reason, made a grievous slip in judgement, and the prince delivered one concluding barb that finally silenced him, earning laughter or applause from their audience, most of all from the man previously ousted.
The prince and the cold student had evidently forgotten the people around them, for at the sudden outburst of noise they surveyed the room with astonished expressions. Horatio hastily dropped his own smile and returned his attention determinedly to his book, hoping to avoid notice. He thought, perhaps, that the Dane had glanced his way, but reasoned that it was unlikely, for when he risked another glimpse at the fireplace, the prince's back was to him and he was shaking hands with both men whose conversation he had intruded upon. It was, Horatio reflected, an event he was quite glad to have had the opportunity to witness.