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56. In Portugal we find the geometri- 
cian Noxius, or Nunez, ftriving to make 
the mathematics flourifh in his native 
country. But he was not the inventor of 
the ingenious divifion which bears his 
name.* 
57- Algebra, though cultivated in Italy, 
aflumed a new form in the hands of the 
celebrated Vieta,+ who alone did as much 
honour to his country, as all the Italian 
mathematicians together had done to 
their's. The moft celebrated authors, 
even among the Englifh, have done Vieta. 
the tuftice to remark, that his works have 
ferved as a light to all his fucceffors, and 
that to him they owe the moft important 
dilcoveries which have been made in the 
analytic art f. 
EE Ne See ek LO sev Oe ore OY Ye Wr een Le Eel SN 
rable inftrument in 1607, and it certainly re- 
ceived improvements from him, as well as 
from our countrymen Gunter, Fofter, and 
others, See Wolfi Elementa Mathefeos Uni- 
werfe, tom. 5, p. 49.—Saverien Diction. de 
Math, et de Phyf. Art. Compas——And Cunn 
On the Sector, publifhed by Stone, Preface. 
' % The divifion which bears the name of 
Nonius was the invention of Peter Vernier, 
Governor of the Caftle of Ornans, in Franche 
Comté, who publifhed it at Bruffels in 1631, 
in a little work intitled La Coafruéfion, 
PUfage et les Proprietes du Cadran Nouveau. 
Nonius died in 1577, aged 80 years, 
fT Francis Vieta was born at Fontenai, in 
Poitou, about the year 1540, and was Mafter 
of Requefts at Paris. The occupations of 
his office did not hinder him from finding 
leifure to devote to the mathematics. Simple 
and modeft, like other men of true merit, his 
application was fuch, that he fometimes 
pafied three days fucceffively in his ftudy, 
and could fcarcely be prevailed on to take his 
meals. During the wars between France and 
Spain, letters in cypher having been inter- 
cepted, on their way fiom the Court of 
Madrid to the Viceroy of the Low Countries, 
Vieta was the only man who could be found 
to decypher them, which he effected, not- 
withfianding their extreme complication. 
The Spaniards, whofe plans the ability ef 
Vieta had been confounding for two years, 
were fo much aflured of the impofiibility of 
unravelling their cypher, that when they 
heard that he had difcovered the key to it, 
‘they loudly exclaimed, that he had obtained 
his end by magic. Vieta. died in Paris in 
1603, aged 63 years. He printed {mall edi- 
tions of his writings, and gave them away 
to fuch of his friends as were capable of un- 
derftanding them. i 
I Nore by the Tranflator.—The Englith, as 
our ‘author intimates, readily acknowledge 
the merit of Vieta, as well, he might have 
adced, as that of his other great countrymen. 
Dr, Berrow, in bis firft Lecture in 1686, calls 
~ 
Skeich of the Hiftory of Pure Mathematics: 
fMay 1, 
58. Vieta fir introduced the letters of 
the alphabet, to denote, not only unknown, 
-but given quantities. “The utility of that 
practice- was eafily perceived by perfons 
converfant in algebra. In fa&, the me- 
thod of Vieta furn thee us with general 
folutions, while thofe of his predecefiors 
were confined to particelar ones ; and it 
afforded an eafy mode of penetrating into 
the nature and compofition of equations. 
\ 59. To Vieta we owe almof ali the 
transformations ufed to throw an equation 
into a more commodious form. He 
teaches us how to perferm on the roots of 
_equations all the operations of arithmetic, 
by adding, fubftraGting, multiplying, and 
dividing thofe roots; alfo how to deftroy 
the fecond term of an equation, and to 
clear it of fra€tions. He rhen proceeds 
“te the refolution of equations of all di- 
menfions, and, when an exa& refuit can- 
not be obtained, he gives a method of ap- 
proximation. He firft laid down a gene- 
ral method of .applying algebra to geo- 
metry, and it is to the mutual aid, which 
thoie fciences afford to each other, that we 
owe the progrefs of both. Vieta gave afhin- 
ing proof of his genius, when he remarked 
Vieta a confummate mafter of the analytic 
art (fummus artis analytice preceptor). But 
the ingenious author, in return, might have 
taken fome notice of our Qughtred, by whom, 
fays Dr. Wallis, ‘* The method of Vieta 
was followed and much improved,” (or as 
Dr. Harris has it, ¢* mightily improved’’) in 
his Clavis, firft publifhed in 1631, and other 
treatifes; and he doth therein, in a brief 
compendious metliod declare, what had be- 
fore been the fubjeét of large volumes 5; and 
doth, in a few {mall pieces of his, give us 
the fubftance and marrow of ail, or moft of 
the ancient geometry. The only copy (if 
indeed I fhould not rather call it a paraphrafe) 
of Vieta I have feen, was printed at Parisin 
1636, and intitled Algebre de Viete, d'une 
Methode neuvelle, claire et facile, par laquelle 
toute P Obfeurité de I’ Inventeur of? ojiée, et fes 
Termes, pour la plufpart inutiles, changez. ‘The 
dedication is in very elegant Latin, and figned 
Jac. Humius, Theagrius Scotus. Does not 
this ticle make it very probable, that. the 
editor, Mr. James Hume, alfo improved upon 
Victa? Be this as it may, it is not more cer- 
tain that Oughtred improved Vieta’s method, 
than that Harrict, whofe book alfo appeared 
in 1631, carried his difcoveries far beyond 
the limits of his great French precurfor. ] have 
never feen Harriot’s work, any more thaa~ 
Vieta’s original; but thufe who will compare | 
our author’s account of Vieta’s improvements 
with Dr. Wallis’s 53d chap. will have little 
doubt that he has afcribed fome difcoveries to 
Vieta which were made by Harriot. ae 
that 
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