Vor. IV.]. | . Account of Vandermonde. | 553 
elevated, attentive mind; and which, monde, as well as of Fontaine, who firk 
blended with the fweets of tranquillity, initiated him into the my fteries of mathe- 
the charms of retreat, and the confciouf- matical fcience, to labour frequently upon, 
“nefs of fuccefs, becomes often a fort of fubjegts already handled by the greatett 
paffion, as felicitous as durable. All mafters. In his firft! memoir, he had 
that time, Fontaine, whofe attention was flarted, fo to peak, in competition with 
again direéted to the refearches which he Legrange and Euler; in bis fecond, with 
had ‘added to thofe of Jean Bernoulli, Euler and Letbnitz, ‘This laf was of 
relative to the then famovs queftion of opinion,-that the analyfis made ufe of in 
the tautocrones, had the glory to be van- his time, by the geometricians, was not 
guithed only by Delambert and La- applicable to all queftions in the phyfical 
grange. Vandermonde, a witnefs to this fcienccs ; and that a new geometry fhould 
combat, neceffarily illuitrious, animated be invented, to calculate the relations of; 
by the honour which he faw annexed to “pofitions of different bodies, in. fpace, 
that glorious defeat, enchanted with the this he called geometry of jituation.. Ex- 
fight of Fontaine, as happy, in fpite of cepting, however, one application, made 
his age, from his love of geometry, asa by Leibnitz himfelf, tothe game of /olitazre, 
youth of twenty could be with, a fenti- and which, under the appearance’ of an 
ment lefs tranquil, thought he fhould object of curiofity, {carcely worthy the 
infure ‘his happinefs forever, by yielding fublimity and ufefalnefs of geometry, Is 
to a paffion which the ice of age could not an example for fo'ving the moft elevated 
extinguith ; in a word, he devoted him- and important queftions, Euler was al- 
{elf to geometry. , moft the only one who had prastifed this 
His labours; however. were for fome geometry of fituation. He had reforted 
time fecret;. and perhaps the public to it for the folution of a problem called 
would never have enjoyed the benefit of the «avaliery which, alfo, appeared very 
any of his works, if another geometri- familiar at firft fight, and was alfo preg- 
cian (whofe name, fays Lacepede, cannot nant »with ufeful and important applica~ 
be pronounced, in this place, without a tions. This problem, with the vulgar, 
mixture of intereft and regret) had not confifted merely in running through all 
infpired him with a confcioufnefs of his the cafes of the chefs-board, with the kaight 
own ftrength, and courage to difplay it. of the game of chefs ; to, the profound 
Fontaine tad already devoted him to geo- geometrician, however, it was a precedent 
metry ; Dufejour exhorted him to pene- for tracing the route. which every body 
_trate even into its fan€tuary. In brief, mutt follow, whofe courfe is fubmitted to 
he prefented himfelf to the Academy of a known law, by conforming to certain 
Sciences, into which he was admitted, required conditions, through all the 
in'1771; and, im that very year, juftified . points difpofed over a fpace, in a pre- 
the fuffrages of his affociates, by a paper © fcribed order. Vandermonde was chiefly 
which he publifhed, relative to the refo- anxious to find in this {pecies of analyfis, 
lution of equations. _-. a fimple notation, likely to facilitate the 
‘From the fixteenth century, the method making of calculations; and he gave an 
of refolving equations of the four firft de- example of this, in a fhort.and cafy fo- 
grees has been known,. and fince that lution of the fame problem of the cavalier, 
. timie the ‘general theory of equations has which Euler bad rendered famous.. , 
received great improvements. In {pite, His tafte forthe high conceptions of the 
however, of the recent labours of many {peculative {cierces, as blended with that 
great geometticians, the folutions of which the amor potrig naturally infpires 
equations of the fifth degree had in vain for objeéts immediately ufeful to fociety, 
been attempted. Vandermonde wifhed | had led him to turn his thoughts towards 
to confolidate his labours with thofe of perfeéting the'arts converfant in weaving, 
other illuftrious analyfts, and he propofed by indicating a manner of noting the 
_a new theory of equations, in which he points through which are to pafs the 
feems to have made it particularly Kis threads intended to form the linés which 
bufinefs to fimplify the methods of calcu- terminate the furface of different regular 
“‘Jation, and to contraét the Jength of the bodies: accordingly, a great part of the 
formule which he confidered. as one of above memoir is taken up with this fub- 
the greateft difficulties of the fubjeét. je&t. 
- This work was quickly followed by In the year following (1772) he print- 
“another, on the problems called by eda third memoir; in’ which he traced 
= 
x 
.gsometricians, problems of . fituatiun, It out a new path for geometers, difcovering 
feems to have been the deftiny of Vander- by learned analytical refearches, srvatronat 
bye Faby ee a quantities 
