"Quite the contrary," said the bachelor; "for, as stultorum infinitum est numerus, innumerable are those who have relished the said history; but some have brought a charge against the author's memory, inasmuch as he forgot to say who the thief was who stole Sancho's Dapple; for it is not stated there, but only to be inferred from what is set down, that he was stolen, and a little farther on we see Sancho mounted on the same ass, without any reappearance of it.

The early writers on Algebra used numerus for the absolute or known term, res or cosa for the first power, quadratum for the second, and cubus for the third. The signs + and

We meet, indeed, with more refinement, and more generally with those amiable courtesies which are its proper fruits: those vices also have become less frequent, which naturally infest the darkness of a ruder and less polished age, and which recede on the approach of light and civilization: Defluxit numerus Saturnius, & grave virus Munditiæ pepulere: But with these grossnesses, Religion, on the other hand, has also declined; God is forgotten; his providence is exploded; his hand is lifted up, but we see it not; he multiplies our comforts, but we are not grateful; he visits us with chastisements, but we are not contrite.

Maledicat illum sanctus Michael, animarum susceptor sa- os crarum. Maledicant illum omnes angeli et archangeli, principatus et potestates, omnisque militia coelestis. os Maledicat illum patriarcharum et prophetarum laudabilis numerus.

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.

But even these, and much more other things not so good as they, compose in regard to the scheme of such a book as this the numerus, the crowd, which, out of no disrespect, but for obvious and imperative reasons, must be not so much neglected as omitted.

The receipt of this letter seems to have disquieted Tartaglia somewhat; for he has added a note to it, in which he says that Cardan has placed him in a position of embarrassment. He had evidently wished for an introduction to D'Avalos, but now it was offered to him it seemed a burden rather than a benefit. He disliked the notion of going to Milan; yet, if he did not go, the Marchese d'Avalos might take offence. But in the end he decided to undertake the journey; and, as D'Avalos happened then to be absent from Milan on a visit to his country villa at Vigevano, he stayed for three days in Cardan's house. As a recorder of conversations Tartaglia seems to have had something of Boswell's gift. He gives an abstract of an eventful dialogue with his host on March 25, 1539, which Cardan begins by a gentle reproach anent his guest's reticence in the matter of the rule of the cosa and the cubus equal to the numerus. Tartaglia's reply to this complaint seems reasonable enough (it must be borne in mind that he is his own reporter), and certainly helps to absolve him from the charge sometimes made against him that he was nothing more than a selfish curmudgeon who had resolved to let his knowledge die with him, rather than share it with other mathematicians of whom he was jealous. He told Cardan plainly that he kept his rules a secret because, for the present, it suited his purpose to do so. At this time he had not the leisure to elaborate farther the several rules in question, being engaged over a translation of Euclid into Italian; but, when this work should be completed, he proposed to publish a treatise on Algebra in which he would disclose to the world all the rules he already knew, as well as many others which he hoped to discover in the course of his present work. He concludes: "This is the cause of my seeming discourtesy towards your excellency. I have been all the ruder, perhaps, because you write to me that you are preparing a book similar to mine, and that you propose to publish my inventions, and to give me credit for the same. This I confess is not to my taste, forasmuch as I wish to set forth my discoveries in my own works, and not in those of others." In his reply to this, Cardan points out that he had promised, if Tartaglia so desired, that he would not publish the rules at all; but here Messer Niccolo's patience and good manners gave way, and he told Messer Hieronimo bluntly that he did not believe him. Then said Cardan: "I swear to you by the Sacred Evangel, and by myself as a gentleman, that I will not only abstain from publishing your discoveries if you will make them known to me but that I will promise and pledge my faith of a true Christian to set them down for my own use in cypher, so that after my death no one may be able to understand them. If you will believe this promise, believe it; if you will not, let us have done with the matter." "If I were not disposed to believe such oaths as these you now swear," said Tartaglia, "I might as well be set down as a man without any faith at all. I have determined to go forthwith to Vigevano to visit the Signor Marchese, as I have now been here for three days and am weary of the delay, but I promise when I return that I will show you all the rules." Cardan replied: "As you are bent on going to Vigevano, I will give you a letter of introduction to the Marchese, so that he may know who you are; but I would that, before you start, you show me the rule as you have promised." "I am willing to do this," said Tartaglia, "but I must tell you that, in order to be able to recall at any time my system of working, I have expressed it in rhyme; because, without this precaution, I must often have forgotten it. I care naught that my rhymes are clumsy, it has been enough for me that they have served to remind me of my rules. These I will write down with my own hand, so that you may be assured that my discovery is given to you correctly." Then follow Tartaglia's verses: "Quando chel cubo con le cose apresso Se agualia

"Men's names should not only distinguish them. A man should be something that all men are not, and individual in somewhat beside his proper name. Thus, while it exceeds not the bound of reason and modesty, we cannot condemn singularity. Nos numerus sumus is the motto of the multitude, and for that reason are they fools." Peak laughed his approval.

Quanto plus propinquorum, quo major affinium numerus, tanto gratiosior senectus, nec ulla orbitatis pretia. XXI. Suscipere tam inimicitias, seu patris, seu propinqui, quam amicitias, necesse est: nec implacabiles durant.

Compare our word seek. Nulla affectione animi. Numerus. Greater number and consequently less relative value of the silver coins. On quia, cf. note, H. 1, 31. VI. Ne quidem. Not even, i.e. iron is scarce as well as gold and silver. The weapons found in ancient German graves are of stone, and bear a striking resemblance to those of the American Indians. Cf. Ukert, p. 216.