ad Sketch of the Hiftory of Pure Mathematics. 
mew ones. ‘The difcoveries which he 
made in his early youth, would have fuf- 
fced to procure to any other man the re- 
putation of a confummate geometrician, 
One of his fir inquiries was to find a 
general method to folve equations, an im- 
portant part of analyfis, on which Leb- 
mitz* allo laboured, and which hath 
called forth the exertions of feveral other 
celebrated mathematicians. He did not 
find that folution; but he confiderably 
* Godfrey William, Baron of Leibnitz, 
was born at Leipzick in 1646. He begaa his 
ftudies in his native country, which afforded 
him but indifferent afliftance. He formed 
himfelf, fo to fpeak, by his aétiveand ardent 
genius, and at the age of fifteen he had pof- 
teffed himfelf, with incredible zeal, of all 
kinds of human knowledge. Poetry, hiftory, 
antiguities, jurifprudence, philofophy, ma- 
thematics, phyfic, &c. in a few years came 
under the dominion of his genius. ae 
In the beginning of the year 1673, Leib- 
nitz, having been in London, became ac- 
quainted with Mr. Oldenburg, the Secretary 
of the Royal Society, with-whom he opened 
an epiftolary correfpondence. After a ftay of 
fome months in the metropolis of England, 
he returned to Paris, where he had already 
been in 1672. Then it was that he began 
to apply to the higher geometry, a tafte 
for waich he had conceived from the convere 
fation of Huygens. 
In 1676 Leibnitz returned to Germany, by 
the way of London, where he ftaid but a 
few days, and repaired to the Court of the 
Ele&or of Hanover, who recalled him, and 
attached him to his interefts. ‘The bufinefs 
with which he was charged by that Prince 
did not hinder him from inferting in the 
Leipzick A&tsa number of memoirs, both 
payfical and mathematical, which all bear 
the ftamp of genius, and which leave us to 
regret that their author, diftracted between 
his laborious employments, and by his tafte 
for metaphyfics,} had not leifure to culti- 
vate, exclufively, the accurate fciences, and 
to give to the learned world a work, of which, 
according to his plan, ‘the difierential and 
integral calculi were to have formed the 
moft confiderable part. It was at the inftance 
of Leibnitz, that Frederick f. King of Prutia 
and Elector of Brandenburg, founded the 
Academy of Berlin in 1701. Leibnitz was 
appointed Prefident of that Inftitution, and 
continued in that place till his death, which 
happened on the 14th of November, 1716, 
when a fit of the gout feizing on his nobler 
organs, almof immediately deprived him of 
life. ‘ 
+ Leibnitz was a metaphyfician as well as 
a mathematician.—See his correfpondence 
with Dr. Samuel! Clarke, in which,’ hew- 
ever, that celebrated German makes, compa- 
vatively, but a poor figure. Tranflater. 
[ Aug. 1, 
enlarged the bounds of algebra. He dif- 
covered a method for decompofing, when 
poffible, an equation of any dimenfion, 
into commenfurable faétors, and he gave 
a rule for extrating the roots of quanti- 
ties, partly commeniurable and partly in- 
commenfurable. He alfo enriched alge- 
bra with the celebrated formula, com- 
monly known by the name of Newton's 
Binomial Theorem. , The infinite feries 
which this formula gives for the quadra- 
ture of the circle, was difcovered in an- 
other manner by James Gregory,* who was 
alfo the author of many other very curious 
feries. In one word, Newton invented the 
method of fluxions ;¢ Leibnitz vindicated 
his claim to the fublime difcovery ; and 
the pretenfions of thofe immortal men be- 
came the fubject of a long controverfy be- 
tween the English geometricians and thofe 
of the Continent. 
85. It appears that Newton firft dif- 
covered the method of fluxions; but it 
is not lefs certain that Leibnitz invented 
the differential calculus, wi:hout borrow- 
ing any thing from Newton. On this 
fubjec&t I believe we might: refer to the 
teftimony of Newton himlelf, who, in his 
Principia, has thus fpoken of the German- 
geometrician : 
86. ‘© About ten years ago (fays he) 
having exchanged fome letters with M. 
Leibnitz, and having fignified to him 
that I was in pofieflion of a method of de- 
termining the Maxima and Minima, and 
of drawing tangents, and which irrational 
quantities did not embarrafs, and having. 
concealed my method, by tranfpofing the 
letters; he returned me for anfwer, that 
he had fallen upon a fimilar method, 
which he communicated to me, and which 
differed from mine in nothing but the 
enunciation and notation, and the idea of 
the generation of quantities.” 
* james Gregory was born in Scotland in 
1636, and lived feveral years in Italy. On 
returning to his native country, in 1670, he 
was appointed Profeflor of the Mathematics 
at St. Andrews. He was advancing rapidly 
in the fteps of Newton, and was infpiring 
the greateft expe€tations, when a premature 
death carried him off in 1675. 
Dr. James Gregory was the brother of Dr. 
David Gregory, the great aftronomer. Their 
family has been remarkable for genius, efpe- 
cially in the mathematics. See the Encyclos 
pedia Britannica, article Gregory. Tranflator. 
+ What we call a differential, Newton 
calis a Fluxion ; and what we call an integral, 
he calls a fluent. The method of fluxions 
anfwers to the calculus differentialis; andthe 
inverfe method of fluxions, to the calculus 
jutegratis. 
$7. This 
