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 in