FLUXIONS. 
of Newton’s letter of the 10th December 1672 had been 
385 
drawing tangents. Newton replied, that he conjectu- | History. 
red what the nature of that method was ; and he gave an (~~ 
example of it, which shews that he was in possession j.6n Leib 
of a method in effect the same as these two geome- nitz and 
ters had found. He adds, that this is only a parti- Newton. 
History. 
i person: That Newton was in possession 
i hake titers the year 1669; and that those who 
reputed Leibnitz the first inventor, knew little or no- 
thing of his sr —— cere ee 
Oldenbur; - before, nor ’s having that 
~ method irae me years before Mr Leibnita began 
to publish it in the Leipsic Acts: That for these reasons, 
they reckoned Newton the first inventor, and were of 
opinion that Mr Keill, in asserting the same, had been 
in nowise injurious to Mr Leibnitz. 
In this report, the committee cautiously avoided gi- 
ving any direct opinion upon the int on which 
seems to shew, that were of the latter opi- 
with care over E with a view to vindicate 
the claim of the British nation, to the most important 
discovery that has ever been made in abstract sci- 
ence. 
It was not to be that Leibnitz would quiet- 
ly submit to this decision, so unfavourable to his pre- 
arisen from the insinuation, that he had stolen the in- 
vention ; for, as to the right to priority of discovery, that 
is, beyond this dapat favour of wwe aS 
is dispute was originally agitated, the natu- 
ral feelings of patriotism, which protect nations against 
the encroachments and unjust pretensions of each other, 
dispute about a mat- 
of faith rather than of testimony. Even Newton 
himself, who, for a time, does not to have taken 
ata tatioer by Cotes and Bentley at, Conbeidge, while 
tainty, whether there were just for the suspici 
ows e i Ae suspicion 
Montucla, in his History of Mathematics, vol. ii 8 
2d edit. 2 Thanet - tay, he 
mercium m, which treat of fluxions in.so-clear- 
of Newton’s invention. . 
cular case, or rather a corollary to a method much 
more general, which, without a laborious calculation, 
applies to the finding of tangents to all sorts of curves; 
geometrical or ‘nochaniéal, and that without being 
obliged to free the equation from radicals. He repeats 
the same thing, without explaining himself farther, in 
another letter; and he conceals the principle of the 
method under tran: letters. The only place where 
Newton has allowed any thing of his method to trans- 
ire, is in his Analysis per equationes numero terminorum 
infinitas. He here discloses, in a very concise and ob- 
scure manner, his method of'fluxions ; but there is no 
certainty that Leibnitz saw this essay.. His opponente 
have never asserted, that it ®as communicated to him 
by letter; and they: have gone no-farther-than-to sus- 
pect that he had obtained a knowledge of it in his in- 
tercourse with Collins upon his second journey to Lon- 
don. Indeed, this suspicion is not entirely destitute of 
probability ; for Leibnitz admitted, that, in this Inter- 
view, he saw a part of the Epistolary Corr lence: - 
of Collins, However, I think it would be rash to:pro- 
nounce upon this circumstance. If Leibnitz had con- 
fined himself to a few essays of his new calculus;-there - 
might have been some ground for that suspicion. But 
the numerous pieces he inserted in the Leipsic Acts,’ 
prove the calculus to have received such improvements: 
from him, that probably he owed the invention to his 
ius, and to the efforts he made to discover a method . 
t had put Newton in possession of so many beauti- 
ful truths. This isso much the more likely, as from the. 
method of tangents discovered by Dr Barrow, the tran- 
sition to the differential caleulus was easy, nor was the: 
step too great for such a genius as that with which: 
- Leibnitz appears to have been endowed:” In this opi-: 
nion, we are di to agree with Montucla; and 
we consider that we add to its weight by the fol- 
lowing testimony in its favour, from one of the most». 
elegant writers and able critics of the present time: - 
The celebrated La Place having asserted, in his Philoso«> 
phical Essay on Probabilities, that Fermat was the true 
inventor of the Differential Calculus ; the writer to: 
whom we have alluded, in a review of La Place’s werk,’ 
says, “ Against the affirmation that Fermat is the real: 
inventor of the differential calculus, we must enter a 
strong and solemn protestation. The age in which that 
discovery was made has been unanimous in ascribing 
the honour of it either to Newton or Leibnitz; or, as . 
seems to us much the fairest and most le opi~ 
nion, to both, that is, to each independently of the other, . 
the priority in respect of time being soniewhat on the 
side of the English mathematician. The writers ef the- 
history of the mathematical sciences have given their: 
= ee to nome oe Montucla; for poe 
who has treated the subject with great impartiality, 
Bossut, with no eet a certainly im. favour: of: 
the English phi In the it controversy to 
which this invention gave rise, all the claims were like« 
ly. to.be well considered ;. and the ultimate and fair de~ 
cision in which -all sides seem..to have acquiesced, is 
that which < pees ject mentioned. . ae be on 
good , that a decision passed by such com 
Seat judges, ahd that hes hewn now-in force foe a con 
dred years, should all at once be reversed.” Edinburgh 
Review, vol, xxiii, p. 324. 
3c 
