cepts on that feience iffued from the 
prefs. 
ar. Algebra, when tranfplanted into 
Italy, was foon augmented with new dif- 
coveries. Lucas de Burgo had gone no 
farther than equations as the fecond di- 
mention, or qnadratics; but the Italian 
analy fts enriched the f{cience with the re- 
folution of equations of the third and 
fourfh dimenfions, or cubics and biqua- 
dratics. 
AeA iy Alaa oe of Bologna, of 
the name of Scipio Ferrea, having Tolved a 
particular cafe of cubic equations, care- 
fully concealed this fecret, or at leaft im- 
narted it to noone but his fcholar Florido. 
The latter, with a view to humble Jar- 
talea,* propofed to him fome problems, 
which he thought it im pofhible for him to 
folve, on account of his ignorance of 
equations of the third dimenfion, © Tarta- 
Jea, ftung with the reproachful boafting 
of Florido, fet himfelf in earneft to the 
gefolution of cubic equations. Having 
fucceeded in his refearch, he accepted 
Floride’s-challenge, folved all his pro- 
blenis in a few hours, and covered him 
with confufion, which was the more deeply 
felt, as he could folve none.«of the pro- 
biems propofed by his antagonift. 
43. Tartalea, wifhing to keep his dif- 
covery to himfelf, ne huled to communicate 
it to Cardan,t till the latter {wore not to 
ties of that proportion appeared to bith fo 
aworderful, that he gave it the appellation of 
Divirre, in order to exalt, by a pompous 
name, a thing which partakes of nothing 
wonderful. The word Algebra, according to 
him, comes from the words dljabar v’ Al- 
niucalala, which, inthe Arabic, fignify Op- 
polition .nd Reftitution. 
* Nicolo Tartalea, or Tartaglia, was born 
at Brefcia, of a very poor family, and was 
in that town when the French plundered it, 
on their return from Naples. He received 
many wounds, feveral of them on the head, 
which caufed him to ftutter. _ No one knows 
how Tartalea learned to read; but, in order 
to acquire writing, he was ebieed to iteal 
from a teacher a fet of the fetter of the al- 
phabet. ence it is eafy to imagine ey what 
difaculttes he muft have faeiobnred in ac- 
quiring his knowledge. One of the i ingeni ous 
inventions of ‘Tartalea is h’s method of mea- 
faring the area of a triangle, having its three 
fides given, without inveftigating the perpen- 
dicular. That mathematician was born in 
3479 and died in 1557. He was-accufed of 
beng very vain 
+ Jerome Cardan, born at Pavia, in F§Of, 
received from mature an acute genius, but a 
Gneular charaG@er. After having made him- 
# 
Sketch of the Hiftory of Pure Mathematics. 
[May 1, 
impart if to any other perfon. But this 
engagement did not hinder Cardan from 
- publifhing the invention in his Algebra, 
which was printed in the year 1545. 
Tartalea, finding himfelf made a jalt of, 
complained bitterly of this treatment. 
But Cardan coolly replied, that the addi-~ 
tions which he had made to the method, 
and the demonttrations of it which he had 
difcovered, gave him the right of ufing it 
as his own invention. The death of Tar- 
talea terminated the difpute. The irrita- 
tion with which it agitated nie, appeared 
to have brcken his heart. + 
44. The refolution of equations of the 
fourth dimenfion, or biquadratics, foon 
followed that of the third, or of cubics~ 
This was the work of Lewis Ferrari, of 
Bologna, a young man of a pregnant ge- 
nius, and the fcholar of Cardan. 
AS. Raphael Bombelli, of Bologna, whofe 
Algebra was printed in 1579, unfolded, 
in a more perfpicuous manner what Car- 
dan had delivered on equations of the third 
and fourth dimenfions. He demonftrated, 
that the parts of the formula, which re- 
prefent a root, in the irreducible cafe, 
form, by their affemblage, a real refult. 
46. While thefe Italian mafters were 
carrying the art of folving’the higher 
equations, to a degree beyond which it is. 
not yet much extended, other geometri- 
cians were rendering important fervices to 
the mathematics. 
4.7. Commandini,* inhis numerous tranf- 
lations, gave proofs of his profound know- 
ledge of geometry. 
48. Maurolico,* who was converfant in 
Caen EEEEIEIEETEEEniad aetna” aeeeeitn nena ne ee 
felf confpicuous for his knowledge of the ma- 
thematics and medicine at Padua, Milan, 
and Bologna, he got himfe!f thrown into pri- 
fon in this laf city. As foon as he reco- 
vered his liberty he went to Rome, obtained. 
a penfion from the Pope, and allowed himfelf — 
to die of hunger in 1576, in order to fulGl 
his herofcope ; for, having been infected 
with judicial aftrology, be had predicted that 
he would not live above 75 years, and he 
was refolved to keep his word. In his Hiftory 
of his own Life, Cardan defcribes his bad 
qualities as frankly a3 his good ones, 
* Frederic Commandini, a mathematician 
and Doétcr in Medicine, was born at Urbino, 
in 1509, and died in 1575. He mdy be 
looked upon as a model to commentators, and | 
he performed the duties of an editor in fo fu- 
periora manner, that his. notes are not much~ 
thort of good originals. 
} Francis Maurolico, Abbot of St. Mary’ Si 
in Sicily, was born at Meilina in 1494, and 
died in 1575. He taught the mathematics 
with 
