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hind his brother in this glorious career. 
Like James he participated in the folu- 
tion of the fineft problems which were agi- 
tated among the geometricians of that pe- 
riod. He propoled feveral himfelf, and 
Keill had fome reafon to repent of having 
called forth his powers. In 1698, John 
Bernoulli publifhed the rules and the ule 
of the exponential calculus, which Leib- 
nitz and he had invented, each in his turn ; 
and to the geometrician of Bafil France is 
indebted for her firft knowledge of the 
new calculus. He made a journey to Pa- 
ris, in 1691, when he became acquainted 
with ZL’ Ho/pital*, initiated him in the new 
geometry, and for his ufe he compofed 
his Legons dé Calcul Differentiel et de Cal- 
cul Integral (Lectures on the Differen- 
tial and the Integral Calculi). The care 
of Bernoulli was not loft; for L’ Hopital 
foon became one of the frtt geometricians 
in Europe. The work which he (L’ Ho- 
pital) publifed under the title of Aza- 
lyfe des Infiniment Petits (the Analyfis of 
Infinitefimals) was received with univerfal 
applaufe*. 
of preceptor, conferred on him; and the 
younger brother forgetting the obligations 
of gratitude; an open rupture was the confe- 
quence, and their tharp difputgs were only 
terminated by the death of James. The in. 
finitefimal geometry, however, was perhaps 
as much promoted by the illuftrious Ber- 
-noullis as by Leibnitz himfelf. They were 
both geniufes of the firft order, and it would 
be difficult to fettle the point of pre-eminence 
between them. 
* The Marquis de Hopital or Hofpital, 
who was born in 1661, had in his childhood 
an extreme pailion snd decided talents for 
the mathematics. - Scarcely had he attained 
his fifteenth year, when he gave proofs of 
his fagacity, by the folution of fome very diffi- 
cult problems. He ferved fome time in the 
army, but the weaknefs of his fight obliged 
him to abandon a piofefiion in which he ne- 
ver could have fignalized himfelf. ‘The ma- 
thematics then took entire poffeffion of his 
mind; and L’Hofpital faw himfelf placed 
nearly on a level with Newton, Leibnitz, 
and the Bernoullis. He was carried off by 
an apoplexy, in February, 1704. 
Note by the Tranflator. _The Marquis de 
L’ Hofpital’s excellent Analyfe des Infiniment 
Petits contains only the Differential Calculus, 
or what we call the direé&t method of fluxions ; 
for, when the author was proceeding to the 
integral calculus, or inverfé method of flux- - 
lions, Leibnitz wrote him, that he was about 
to publifha work, De Scientia Infiniti, which 
would comprife that doétrine. The Marquis, 
in confequence, modeftly defifted, and Leib- 
nitz néver publithed his intended perfor- 
mance, any more than his dvaly/is Situs, and 
Sketch of the Hiflory of Pure Mathematics. 
123 
95- It is the lot of all great inventors 
to be oppofed by contradiétion. The 
fome other works which he promifed to the 
world. Thus was the public deprived of the 
fecond part of the Analyfe des Infiniment Petits, 
which, it is fair to fuppofe, would have been 
as well executed as the firft, 
The Marquis was, undoubtedly, a great 
mathematical genius; but he enjoyed otium 
cum dignitate \eifure and fortune, and, as 
our author tells us, had for his preceptor one 
of the greateft mathematicians in Europe, 
who wrote a book (The New Calculus) pur- 
pofely for his ufe. What then are we to 
think of the Scotch gardener, Stone, who, 
having been only taught his alphabet, pene- 
trated, by mere dint of genius and folitary 
ftudy at his leifure hours, into all the arcana 
of the higher geometry, began where the 
Marquis left off, and completed the moft ar- 
duous part of the plan, which, as we have 
feen, the great author was prevented from 
executing ? And what are we to think of 
the Leicefterfhire weaver, Simpfon, who, 
with little more original inftru€tion than 
Stone, and no other help than the joint 
work of him ana L’Hofpital, juft mentioned, 
fat on his loom, and wrote a {till better 
book. Above all, what muft we think of 
Saunderfon, who, with ** wifdom from one 
entrance quite fhut out,” and labouring under 
many other difadvantages, wrote, or rather 
diétated, ably'on fome of the moft abftrufe 
parts of the mathematics; and, without any 
idea of light or colours, lettured learnedly on op= 
tics !—Vide Wolfi Elem. Math. Univ. tom ve 
p- 603 Saverien’s Dict. Math. et Phys. Arte 
Calcul. Integral; T. Simpfon’s Life in the 
Biograph. Dict. ; Stone’s Life, prefixed to his 
Euclid, by his learned countryman, the Che- 
valier Ramfay ; and Saunderfon’s Life, inthe 
4to edition of his Algebra. 
I cannot help thinking, that our author 
fhould have taken fome fhort notice of thefe 
aftonifhing phenomena of genius, particularly 
as all the three, but efpecially Simpfon, had 
rights to be confidered as inventors. Nor, in 
my humble opinion, fhould he have negleét- 
ed to name Matthew Stewart and (Glafgow) 
Simfon, as diftinguifhed reftorers and cultivae 
tors of the ancient geometry; or M‘Laurin, 
to whom the method of fluxions, fometimes 
called the modern geometry, owes its fecu- 
rity from all future metaphyfical affailants, 
unlefs we can fuppofe, that fome more formi- 
dable one than the very acute Bifhop of 
Cloyne fhould make a fecond attempt to fap 
its immoveable foundations. Having men- 
tioned that great mathematician, virtudus ci- 
tizen, and amiable man, it may not be amifgs 
if, like our author, who has givén us the end 
of Newton’s Epitaph, I infert a fimilar ex- 
traét from the equally admired one of his 
friend M‘Laurin, which 1 copied in 1786, 
from his monument, in the Grey Friar’s - 
Church-yard, Edinburgh, Is is faid to have 
Q 2 beca 
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