556 
and Gottingen, and councellor of the 
great chamber of the late parliament of 
Paris. _ ide was born in this capital, 
January 1ith, 1734, and ftudied at the 
college of Jefuits, from 1743 to 1750. 
He was admitted in the Academy as an 
affociate in 1765, at which time, his 
brethren in the parliament pretended he 
could only fit as an honorary member ; 
but he defpifed the fuggeftion$ of 
vanity, and deemed himfelf honored by 
belonging to a body of learned men, 
under any denomination. 
On this cccafion, he undertook a feries 
of labours, which he followed up during 
thirty years, with equal affiduity and 
fuccefs ; this was the application of the 
algebraic analyfis to all the branches of 
aftronomy, and efpecially to eclipfes. 
Aftronomers have always neglected ana- 
lyfes too much; the obfervations and 
calculetions neceflary to produce refults, 
demanding fo much time, that they 
would have little or no leifure for ab- 
ftract fpeculations.. Du Scjour is the 
firtt whe addiéted himfelf entirely to this 
branch of {cience, and he mace en im- 
portant application of it, in determining 
the longitudes of a great number of towns, 
by means of the eclipies of #764 aad 
4769... “ 
Tn confequence of a Memoir, written 
y ine, ref{pe€ting the comets which had 
alfsichted al! France in 2773, he drew 
; ke pup- 
] 
np.a Treatife on this fubject. 
G . - J 
€ 
ee 
= 
( 
(ay) 
jah) 
=) 
Y 
) 
Lm) 
et 
La) 
a} 
(q") 
ta») 
© 
(om 
= 
oD 
Le) 
<a 
bad} 
at, 
(@) 
= 
wa 
we 
cr 
Se 
Yu 
iS 
a) 
of the moft dificule problems in altre- 
nomy. In this work, he demonitrated, 
how difficult it was. to ‘conceive th 
counter of a comet, with the earth, in 
the order of probabilities, or even in 
pofibilities for he want fo fer as that. 
I know thatfuch an aflertion ought to 
be accompanied by reftridtions, but. it 
was neceflaryto difpel terror, and nothing 
= 
en 
Vlinm 
could be-more ufeful than a. publication 
of this kind,. in order to, comfort the 
public. . 
The difappearance of Saturn’s, ring, 
‘which happens once every fittecn years, 
induced Du Scjour to publish a volume 
in Svo, in 1776, on this fubject. In 
1786 and 1789, he completed two large 
4to volumes of his works, under the 
title of *§ Traité Azalytique des Mouvenens 
apparens des corps cclefles.”” 
~ Tt was in the midft of labours fuch as 
thefe, notwithitanding every eppearance 
‘6r axobuft confitution, that he was. at- 
. Mr. -Frend’s Algebra. 
(Aug. 
tacked by a malignant. fever, which his 
conftant uneafinefs fince the death of ci- 
tizen Freteau, rendered more dangerous. 
He died on the sth Fruétidor (22nd Aug.) 
in the 6oth year of his age, at his country 
houfe, at Angerville, near Fontainbleau, 
which had formerly belonged to the 
famous Lord Bolingbroke. 
lis fimplicity was correfpondent to 
his learning ard virtues, for there was 
nothing in his drefs or manners, that 
announced the poffeflion of great know- 
ledge, an exacted fituation, or a large - 
fortune. 

MATHEMATICAL CORRESPONDENCE, 
To the Editor of ibe Monthly Magazine. 
STR, 
te. ltters of your corref{pondents 
A. SrearcHand No CONJUREK, res 
yived fome early impreffions made on my 
mind, in the coarfe of my youthful ftudies, 
and 1 was excited to re-examine the 
difficulties, which 1 had encountered in 
a {cience, inthe endeavour to obtain the 
comprehenfion of a mode of reaioning, 
by which fuch wonders are faid to be 
performed. 
In the courfe of this purfuit, Mr. 
Frewxop’s Algebra.was lately put mte 
*< through a few chapters of Maclaurin’s 
& Algebra; but frightened, and with 
oS 74 S ~ : 
eood reafon, at Cardan’s Rule,” and, 
¢ ;, unable to preceed: farther 
By 2 me ai 2 = 
ia. that part of my mathematical frudies. 
FEN +e es | = = Se 
There was no great G fheulty, indeed, 
in compreheading Cardan’s precefs: bur 
when d came to the application of 1: to 
practice, 1 do net Know whether it fuc- 
ceeded once in the equations which I 
[ 1 at randcm; and I was told by 
ted, that it would not do unleds 
Ablc roots were in the equa- 


Se 
tion! hew to make thefe impofiible roots, 
cr to difcover whether they were in any 
propofed equation, 1 was totally at a 
lofs. 
As the rule was. demonfirated to me, 
a xvas made cqual to a4, and then I 
was teld, that as only one fuppofition 
had been, another might be made, 
namely, that 3a might be equal to ¢. 
Mr. Frend denies this; and fays, that 
326 can be equal to g only in particular 
cafes; and brings as a proof, the equar 
tion «3-274--28=0, in which, ¢=s35 
confequently, apicer; and, thercfore, 
Mr, 
