, 310 
.n the fcience of fluxions and integrals of 
Mmcrements; whoever would fee them 
enumerated, may confult the prefaces of 
the different books, trom which they feem 
more in number than perhaps given by 
any other writer whatever; but it may be 
added that feveral new additions to the 
algebra, properties of curve lines and 
folids, filuents and fluxions, integrals and 
increments, feriefes have been given fince 
their publications in the addenda, printed 
feveral years paft, or in the Philofophical 
‘Tranfactions. han 
Some inventions are giver in my 
pamphlet on the tranflation of algebraic 
quantities into probable relations, and 
fome in the paper, inferted in the Phi- 
lofephical Tranfactions on central for- 
cés, attractions, &c. treated in a more | 
general manner than before given by any 
writer. Mr. Le Grange has fmce pub- 
hifhed fomething fimilar on the fame 
fubject, and alfo applied the principles 
to centers of gravities, ofcillations, &¢. 
On the whole, let the name of any 
French writer be mentioned, who has dif: 
covered a greater number of inventions in 
pure mathematics ; he may fee much the 
greater part of them enumerated in the 
re{pective books; about fifty or fixty are 
publifhed in the addenda, &c. which are 
not contained in the enumeration above- 
mentioned. I have no mathematical 
books at prefent in my poffeflion; but 
perhaps, I could from memory enu— 
merate the principal inventions, given by 
the different authors, before the publica- 
tion of iny books. 
General affertions without proof af- 
ford no conviction, and merit no re- 
gard; and particularily, when made by 
perfons ignorant of the truth or falfhood 
ef the propofition afferted; for then they 
deferve filence and contempt. 
T know that Mr. Lalande isa firft rate 
aftronomer, and writer of aftronomy ; 
but I never heard that he was much con- 
verfant in the deeper parts of mathematics 
for which reafon I take the liberty to atk 
him the following queftions : 7 

Original Letter of the late Dr. Waring: 
[May 
Has he ever read or underftood the 
writings of the Englifh mathematicians = 
and,as the queftion comes from me, I 
fubjoin particularly of mine? If the 
anfwer be in the negative, as it is m 
opinion, if his anfwer be the truth, that — 
it will; then there is an end of all further 
controverfy ;—but, if he afferts that he 
has, which is more than Condorcet did by 
his own acknowledgment, then he may 
know, from the enumeration of inventions 
made in the prefaces, with fome fubfe- 
quent ones added, that they are faid te 
amount to more than four hundred of one. 
Kind or other; let him try to reduce 
thofe to as low a number as he can, with 
the leaft appearance of candour and truth ; 
and then let bim compare the number, 
with the number of inventions of any 
French mathematician or mathematicians, 
either in the prefent or paft times, and 
there will refult a comparifon (if I mi 
take not) not much to his liking; and, 
further, let him compare fome of the firft 
inventions of the French mathematicians, 
with fome of the firft contained in my 
works, both as to utility, generality, 
novelty, difficulty and elegance, but wife- 
ly as to utility, there is little contained in 
the deep parts of any {cience ; he will find 
their difficulty and novelty, from his 
difficulty of underftanding them, and his 
never having read any thing fimilar be- 
fore; their generality, by the application 
of them; principles of elegance will dif 
fer in different perfons.—I muft fay, that 
he will probably not find the difference: 
expected. After or before this enquiry 
is inftituted for mine, let him perform the 
fame for the other Englith mathematicians,. 
and when he has completed fuch en- 
quiries, and not before, he-will become a 
judge of the juftice of his affertion; but 
Iam afraid, that he is not a fufficient 
adept in thefe ftudies, to inftitute fuch 
enquiries; and if he was, fuch enquiries 
are invidious, troublefome, and of fmall 
‘utility. Iam, Sir, with very great regard 
and efteem, Yours affectionately, 
E. WARING. 
TO CORRESPONDENTS. 
The veriters on controverfial points, and anfwerers of queries, are refpetfully apprized, that 
our readers generally think topics fully difcuffed long before all the letters we receive under 
thefe heads are inferted; whence we find it neceffary to exclude fome communications, per- 
hans fully as valuanle as thofe we have admitted, merely to avoid tedious repetitions. Several 
defences of the principles of th: Quakers, and explanations of the word ditch, are now under 
this predicament. 
We have determined to clofe all difcuifion relative to the Northampton Academy, and 
Diflenting Ordinations.~ 
Long political difcuffions are at no time well fuited to our Mifcellany, and are at prefent 
what we would peculiar] y avoid. Some communications under this head lie ready for return 
‘go their refpective writers. 
We beg leave to decline engaging in a controverly relative to Collier’s patent Sltermg 
machine. x 
W. H. is informed that a letter for sing is lyimg at Ne. 7a, St. PauPs Church-yard, con- 
Oath >, wing 
