1797+] 
of man be direéted, in the field, by the 
obfervations of the philofopher and the 
naturalift. 
MonveE treada fable, the verfification 
of which was {mooth and pleafant. 
Coxicin d’HaRLEVILLE, and Fon- 
TANEs recited verfes, which were heard. 
with delight. 
There has been but one tranflation in 
French verfe of the Pharfalia of Lucan : 
it is by Brebeuf. It-was held in little 
eftimation in his time, and is not read at 
prefent. Several of our modern verfi- 
fiers have tranflated a few of the cantos; 
but no one has fucceeded in transferring 
to the French tongue the mafculine con- 
cifenefs and energetic eloquence of the 
poet who fung the laft ftruggles of Ro- 
map liberty. 
,To a republican, Lucan is the firft 
of poets. Heinfius has obferved that 
there is as much difference between the 
fublime majefty of the author of the 
Pharfalia and the fmooth elegance of 
Mathematical Correfpondence. 
33 
Virgil, as between the impetuous courfe 
of the horfe and the trot of the afs. 
This is the language of an enthufaft, 
not of a man of tafte. 
It belonged to LEGOUVE, who has fuc- 
ceeded fo well in exprefling the charac- 
ter of Lucan in his fine tragedy of Epi- 
charis and Nero, to attempt a verfion of 
his mafculine and fublime beauties. 
The firft canto of the Pharfalia, which 
he read, contains very fine verfes. What 
is not a {mall merit, it fometimes reaches 
the force of the original. We can rea- 
dily conceive that a tranflation of the 
magnificent pictures, the rich deferip- 
tions of Homer and Virgil, may be fuc- 
cefsfully made ; but it is far more diffi- 
cult to convey to French verfe the fen- 
tentious brevity of a writer who has hap- 
pily expreffed the profoundeft ideas in 
the feweft words. 
The affembly was extremely numerous. 
The five members of the Directory were 
prefent. 
ee 
MATHEMATICAL CORRESPONDENCE. 

Question XXV (No. XIII).—Anfwered by Mr. T. Hickman, Land-Surveyor, Woburn. 
ROM the given point A let fall the, line AH’ perpendicular to the 
From A, on this line, as a diameter, defciibe a femicircle 
AD, touching the given circle externally in P, which will be the point 
required: for it is well known, that a heavy body will defcend down any 
chord AP in a femicircle in the fame-fpace of time in which it would 
fall freely through the diameter AD; and it is evident, that AD is the 
diameter of the leaft circle that can teuch the given circle BP ; confe- 
quently, AP is the plane on which the body would defcend to the circle 
horizon. 
-in the /eaff time. 
Cor.) 2 
If another femicircle be defcribed on the line AH’ to touch 
the given circle internally in P’, then AP! is evidently the plane on 

which a heavy body would be the dongs? time in defcending to the 
given circle, 
Cor, 2. 
fame conftruction will hold. 
If BPP’, inftead of a circle, werea given right-line, or a given curve of any order, the 
I 
Cor. 3. If the time in which the body is to defcend to the given circle, or other given. curve, 


er line, inftead of a minimum or maximum had been a given quantity, we have only to take, on 
AH’, a lipe through which the body would fall freely in the given time, and thereon defcribe a 
femicircle, the interfections of which, with the given curve or line, would determine the points 
required. | 
Question XXIX (No. XV).——Anfwered by Mr. WM. Saint, of Norwich. 
Let x denote the leaft number that will anfwer the firft condition, Then, by the queftion, 
¥—Llo XI x—I . 
x w——T 
— >» > > &O. — — — — to = are whole numbers. Put '——— =f 5 then x 
2 3 II 2 
: |. af 3h 
==2p-++1; which put for x in the fecond term, gives Lh, and Eg iadees sey 
3 Tee oe uetine, 

Let x be the leaft number which will anfwer the firft condition, then, per queftion, ea 
2 
x—I 
x—I | 2 x—I 
» ———, &C, — — — — to — are whole numbers ; put 
3 4 II 2 
which put for x, in the fecond term, gives fee and Sane ge eit which put =r, 

=f, thenx=2/4-/-1, 
3 
vs ae “ie (ot gal jal Be ; and by proceeding, in like manner, with all the terms to 
the lait, we fhall have x==27720%ee2519, and by taking xx, 2 6 8.9, 10, I 
Mentuty Mac. Ne. XX, : PF 2 2) 39 4) 52 9) 72 9) 9 is 
