When Casanova reentered the hall, a panelled chamber on the ground floor, there were seated at the well-furnished board, his host and hostess, their three daughters, and a young woman. She was wearing a simple grey dress of some shimmering material. She had a graceful figure. Her gaze rested on him as frankly and indifferently as if he were a member of the household, or had been a guest a hundred times before. Her face did not light up in the way to which he had grown accustomed in earlier years, when he had been a charming youth, or later in his handsome prime. But for a good while now Casanova had ceased to expect this from a new acquaintance. Nevertheless, even of late the mention of his name had usually sufficed to arouse on a woman's face an expression of tardy admiration, or at least some trace of regret, which was an admission that the hearer would have loved to meet him a few years earlier. Yet now, when Olivo introduced him to Marcolina as Signor Casanova, Chevalier de Seingalt, she smiled as she would have smiled at some utterly indifferent name that carried with it no aroma of adventure and mystery. Even when he took his seat by her side, kissed her hand, and allowed his eyes as they dwelt on her to gleam with delight and desire, her manner betrayed nothing of the demure gratification that might have seemed an appropriate answer to so ardent a wooing.
After a few polite commonplaces, Casanova told his neighbor that he had been informed of her intellectual attainments, and asked what was her chosen subject of study. Her chief interest, she rejoined, was in the higher mathematics, to which she had been introduced by Professor Morgagni, the renowned teacher at the university of Bologna. Casanova expressed his surprise that so charming a young lady should have an interest, certainly exceptional, in a dry and difficult subject. Marcolina replied that in her view the higher mathematics was the most imaginative of all the sciences; one might even say that its nature made it akin to the divine. When Casanova asked for further enlightenment upon a view so novel to him, Marcolina modestly declined to continue the topic, declaring that the others at table, and above all her uncle, would much rather hear some details of a newly recovered friend's travels than listen to a philosophical disquisition.