4802. ] 
75. De Beaune illuftrated with notes 
the moft difficult paflages of that great 
work, all the mytteries of which he under- 
ftood ; and he propofed a problem which 
gave rife to the inverle method of tangents. 
76. Schooten attempted a more exten- 
five undertaking. He faw that the Geo- 
metry of Defcartes, the work of a man’ 
of genius, who defpifed little explana- 
tions, was iil-adapted to the capacity of 
the generality of readers, and that it re- 
quired a commentary. He accordingly 
publifhed one, which was juftly inticled 
to the general approbation which it receiv- 
ed; for it includes every thing neceffary for 
underftanding his author, without being 
prolix*, } 
77- Hudde applied himfelf particularly 
te the analyfis of equations. One of his 
two letters, inferted in the Commentary of 
Schooten, contains a very ingenjous me- 
thod for difcoverine whether an equation 
of any dimenfion has equal roots, and for 
determining thofe roots. In the fame 
letters we find. Hudde’s methods of 
_ drawing tangents to curves, and of invef- 
tigating the Maxima and Minima. 
78. Van Heuraet, by purfuing the ana- 
lytis of Defcartes, recommended himfelf 
to notice, by his invention. for rectifying 
acurve. In this, however, he was: anti- 
cipated by the Englith geometrician Neil, 
who had diicovered fome years before the 
* Note by the Tranflator.—* Who fhall decide 
when doétors difagree?’Our author is of opinion, 
that Schooten’s commentary on the Geometry 
of Defcartes includes every thing neceflary for 
underftanding that refined and dificult perfor- 
mance. But Chriftian Wolfius, a firft-rate 
mathematician, and who of courfe will be fol- 
lowed in this inftance by all ordinary men, 
tells us, that Schooten’s work, excellent 
though it be, does not contain thofe full and 
perfpicuous elucidations which we have a 
right to expe@ in a commentary; for that 
Schooten himfelf often requires a commenta- 
tor. Elem. Math. Uniostom.v. p. 53, Ed. 
Yale, 1741. . This reminds me of the opi- 
nion, which a Quaker-teacher gave of a cer- 
tain elementary work on algebra, which was 
| publifhed as an introduétion to higher-and 
_ more difficult performances.—*‘‘Friend,(quoth 
he tothe author) thou wovld’ft haye us* be- 
_ lieve thy book to be an introduétion to the 
| works of Newton, Maclaurin, and other 
| great men; but I rather think that their 
| works may be confidered as introduétions to 
| thy book.” And the Quaker was in the 
maght 5 for the performance in queftion, under 
the humble guife of a fchool-book, contains 
\fome very difficult problems, without any fo- 
\lutions, or a fingle hint where folutions are 
| fo be found, 
Cheering Views of the National Debt. 
(597 
rectification of the femi-cubical parabola. 
But it is very probable, that Van Heuraet 
knew nothing of Neil’s difcovery ; and 
befides the two methods are very different 
from each other. 
( Algebra tobe continued. ) ; 
ee But |. 
To the Editor of the Monthly Magazine. : 
SIR, 
HE narrow limits of the human un- 
derftanding are never more apparent 
than in the prediétions of eminent men. 
Hume and Bolingbroke are names diftin- 
guifhed for attainments and fagacity ; 
but when they attempted, by virtue of 
thofe attainments and that fagacity, to 
penetrate into futurity, they afforded us a 
proof of the infufficiency of human wif- 
dom to the tafk they undertook. Long 
before the national debt had accumulated 
to its prefent gigantic fize, thefe philofo-) 
phers inform us, that the government 
would be deftroyed, and the country in | 
ruins. A train of followers, little lefs 
refpectable than they, have predi¢ted the 
fame thing, and live to view, with afto- 
nifhment, the Dedt and the Taxes in con- 
nection with the (ability of the government, 
and the tranquillity of the country. In the 
times of Bolingbroke and Hume, the re~ 
fources which England fhould draw from 
Eaft and the Welt Indies, the riches which 
fhe fhould devive from taking the lead in 
Europe in mechanicak invention, and the 
application of that invention to the pur- 
pofes of manufactures and commerce, 
could not be forefeen. Thefe philofophers 
faw, and could in fome degree eftimate, 
the productive powers of Britifh induftry; 
but that induftry has received aids which 
they did not live to contemplate. Even 
their followers, who live to fee whatever 
is to be feen in the complex mechanifin of 
Britifh profperity, have been dazzled and 
confounded by its fplendour and magni- 
tude, fo as to believe that all was artifi- 
cial and delufive. You talk of your prof-_ 
perity, fay they, and yet the nation is in 
debt tothe amount of more than five hundred 
millions! The nationis in debt. To whom? 
To herfelf. This is the grand fecret why 
fhe is profperous, and yet thus invelved. 
It is a fatt which is admitted by all par- 
ties, that the balance of debt between. 
England and all other countries is in her 
favour. Other countries are indebted to 
England a fum infinitely fuperior to that 
which fhe owes to them. Europe’ and 
America trade with the capital of England, 
and owe her a balance of ineftimable - 
amount. This fact, which, when ftated, 
will not be queftioned, is yet fo feldom 
adverted 
