[99] _Quesiti et Inventioni_, p. 125. [100] "Non ha datta fora tal opera come cose composto da sua testa ma come cose ellette raccolte e copiate de diverse libri a penna."--_Quesiti et Inventioni_, p. 127. [101] Cardan repeats the remark in the first chapter of the _Liber Artis Magnae_ (_Opera_, tom. iv. p. 222). "Deceptus enim ego verbis Lucae Paccioli, qui ultra sua capitula, generale ullum aliud esse posse negat (quanquam tot jam antea rebus a me inventis, sub manibus esset) desperabam tamen invenire, quod quaerere non audebam." Perhaps he wrote them down as an apology or a defence against the storm which he anticipated as soon as Tartaglia should have seen the new Algebra. [102] Subsequently Tartaglia wrote very bitterly against Cardan, as the latter mentions in _De Libris Propriis_. "Nam etsi Nicolaus Tartalea libris materna lingua editis nos calumniatur, impudentiae tamen ac stultitiae suae non aliud testimonium quaeras, quam ipsos illius libros, in quibus nominatim splendidiorem unumquemque e civibus suis proscindit: adeo ut nemo dubitet insanisse hominem aliquo infortunio."--_Opera_, tom. i. p. 80. [103] _Quesiti et Inventioni_, p. 129. [104] Montucla, _Histoire de Math._ i. 596, gives a full account of Ferrari's process. [105] In the _De Vita Propria_, Cardan dismisses the matter briefly: "Ex hoc ad artem magnam, quam collegi, dum Jo. Colla certaret nobiscum, et Tartalea, a quo primum acceperam capitulum, qui maluit aemulum habere, et superiorem, quam amicum et beneficio devinctum, cum alterius fuisset inventum."--ch. xlv. p. 175. [106] Prefixed to the _De Vita Propria_. [107] In a question of broken faith, Cardan laid himself open especially to attack by reason of his constant self-glorification in the matter of veracity. [108] Leonardo knew that quadratic equations might have two positive roots, and Cardan pursued this farther by the discovery that they might also have negative roots. [109] "Caput xxviii. De capitulo generali cubi et rerum aequalium numero, Magistri Nicolai Tartagliae, Brixiensis--Hoc capitulum habui a prefato viro ante considerationem demonstrationum secundi libri super Euclidem, et aequatio haec cadit in [Symbol: Rx]. cu v binomii ex genere binomii secundi et qunti [m~]. [Symbol: Rx]. cuba universali recisi ejusdem binomii."--_Opera_, tom. iv. p. 341. [110] Montucla, who as a historian of Mathematics has a strong bias against Cardan, gives him credit for the discovery of the _fictae radices_, but on the other hand he attributes to Vieta Cardan's discovery of the method of changing a complete cubic equation into one wanting the second term.--Ed. 1729, p. 595. [111] _Opera_, tom. i. p. 66. CHAPTER VI