The inquiry begins with a courteously worded request from Messer Juan Antonio (speaking on behalf of Messer Hieronimo Cardano), that Messer Niccolo would make known to his principal the rule by means of which he had made such short work of Antonio Fiore's thirty questions. It had been told to Messer Hieronimo that Fiore's thirty questions had led up to a case of the _cosa_ and the _cubus_ equal to the _numerus_, and that Messer Niccolo had discovered a general rule for such case. Messer Hieronimo now especially desired to be taught this rule. If the inventor should be willing to let this rule be published, it should be published as his own discovery; but, if he were not disposed to let the same be made known to the world, it should be kept a profound secret. To this request Tartaglia replied that, if at any time he might publish his rule, he would give it to the world in a work of his own under his own name, whereupon Juan Antonio moderated his demand, and begged to be furnished merely with a copy of the thirty questions preferred by Fiore, and Tartaglia's solutions of the same; but Messer Niccolo was too wary a bird to be taken with such a lure as this. To grant so much, he replied, would be to tell everything, inasmuch as Cardan could easily find out the rule, if he should be furnished with a single question and its solution. Next Juan Antonio handed to Tartaglia eight algebraical questions which had been confided to him by Cardan, and asked for answers to them; but Tartaglia, having glanced at them, declared that they were not framed by Cardan at all, but by Giovanni Colla. Colla, he declared, had sent him one of these questions for solution some two years ago. Another, he (Tartaglia) had given to Colla, together with a solution thereof. Juan Antonio replied by way of contradiction--somewhat lamely--that the questions had been handed over to him by Cardan and no one else, wishing to maintain, apparently, that no one else could possibly have been concerned in them, whereupon Tartaglia replied that, supposing the questions had been given by Cardan to Juan Antonio his messenger, Cardan must have got the questions from Colla, and have sent them on to him (Tartaglia) for solution because he could not arrive at the meaning of them himself. He waved aside Juan Antonio's perfectly irrelevant and fatuous protests--that Cardan would not in any case have sent these questions if they had been framed by another person, or if he had been unable to solve them. Tartaglia, on the other hand, declared that Cardan certainly did not comprehend them. If he did not know the rule by which Fiore's questions had been answered (that of the _cosa_ and the _cubus_ equal to the _numerus_), how could he solve these questions which he now sent, seeing that certain of them involved operations much more complicated than that of the rule above written? If he understood the questions which he now sent for solution, he could not want to be taught this rule.