558
SrSir
3 MrWhen the Differential method began to be celebrated in Holland as the
Method of Mr Leibnitz Dr Wallis, in the introduction to his Works printed in the
year 1695, wrote that this method was the sam with the method of fluxions
from wchwhich Mr Newton had explained to Mr Leibnitz ten years b in his Letters
written 1676 & had invented ten years before that time or above. Mr Leibnitz
in the correspondence wchwhich followed thereupon between him & Dr Wallis
did not deny this nor contend for any thing more then that he had added something to Mr Newtons method and what he had added to
the Mr Newtons method was his own. Mr Newton in the Preface or IntroctionIntroduction to his Quadratura Curvarum
published some months after the death of Dr Wallis, about 12 years ago wrothe that he
had found the death of Dr W method of fluxions by degrees steps in the years
1665 & 1666. Dr Dr Wallis being dead Mr Leibnitz now pretends that Mr Newton was
did nonot the firs did not invent the it so early nor was the first
inventor & upon Dr Keills defending Dr Wallis against what has
been published to this purpose in the Acta L Eruditorum, has d
justified affirmed that what was there published, to be just was just & Nu & he has demanded that
Dr Keill should recant & that Mr Newton should declare his opinion in this
matter, that is, that he should retract what he had published in the
Introduction. r Newton's being thus accused of plagi
ary, the R. Society ordered the ancient Letters & papers to be
published, from the ancient MSS & But Mr Leibnitz has ever sindce refuseds to make good
his accusation,. huffs at what was published as trifling, complains of things
omitted omitting the suppressing what made for him, & particularly of hng suppressing what he
had seen in England in England in the hands of Mr Collins about Mr
Newton's ignorance has been suppressed, & appeales frōom the judgment of the Committee of
the R Society to the jugment of his scholar disciple & confederate Mr Iohn Bernoullei. Mr Leibnitz
having thus accused Dr Keill of what he durst not accuse Dr Wallis &
demanded that Dr Wallis Keill should recant & Mr Newton but the
be Questioned & Mr Newton for a what Mr published Mr Newton also should be questioned for what
he published to yethe same purpose (all wchwhich amuounts to an accusation of
Plagiary against Mr Newton) it lies upon Mr Leibnitz by the laws of
all nations either to provesprove his accusation, or esleelse to be deemed guilty of
calumny.
As for his sleighting
How little reason there is for Mr Leibnitz to sleight the ancient
papers printed by order of the R. Society or the interpretations put upon
them, may appear by this instance that there is a letter in the hand
writing of Mr Leibnitz dated from Paris May 1675, in answer to a Letter of
Mr Oldenburg dated 2415 April preceding he acknowledges the receipt of a Letter a Letter with several
from Mr Oldenburgh. This Letter was dated 15 April preceding
series in it & conteins one a series for findigng
chwhich series was invented by Mr Gregory four yearyears before. ButAnd Mr
Mr Leibnitz He the same year had he received it from
London published communicated ita but as appears by the Letter & yet the same year
to his friends at Paris as his own & afterwards published it at Paris
in Germany as as his own without ever acknowledging that he had received it from
London.
And as for his complaint that Mr Leibn what made for hism & particularly what he saw in the
hands of Mr Collins when he was in London the second time concerning Mr Newtons ignorance, has
been omitted suppressed in the Commercium; he is mistaken. it is uj unjust It That passag is there printed
pag 75, lin 10, 11. And by the statutes of the R. Society it is expulsion
to defame them.
Mr Leibnitz here tells us that Mr C when he was the second
time in England (wchwhich was in October 1676) Mr Collins shewed him
a part of the his correspondence wthwith Mr Gregory & Mr Newton
What he then saw in the hands of Mr Collins was in Mr
Newtons Letter of 24 October 1676. W Mr Leibnitz was in London
some part of that Month & saw before he left London saw that
Letter in the hands of Mr Collins but staied not to take a
copy of it amlong with him. He tells us that he Mr Collins then
shewed him a part of his correspondence with Mr Collins &
Mr Newton. I suppose he means the originals who from whence
their series had been taken.
36 Mr Newton Leibnitz tells us that it would have been easy for Mr
Newton to find the differential method, if it had been hinted to
him: & was it not as easy for Mr Leibnitz to find it by the
hints wchwhich Mr he received from Mr Newtons Letters of 10 Dec
1672, 213 Iune 1676 & 24 Octob. 1676.
He tells us that Mr Ne
7 He allows that Mr Newton preceded him in the method
of Series, but he saith that at length he invented a general
method of series, wchwhich m after which he had no further use
of Mr Newton's extractions. And yet his general method is
Mr Newton's. In his Letter of 13 Iune 1676 Mr Newton repre
sented that his method of Series was not general without some
other Methods: & in his Letter of 24 Octob. 21676
sented that his general method of Series depended upon became general by two
Methods: chwhich consisted in extracting equ fluents out
of equations involving their fluxions, the other in assuming the
terms of a series & determining them by the conditions of yethe
Probleme. The first method that shews demonstrates that Mr Newton was
then well aq acquainted wthwith fluxional Equations & had then
carried Analysis to a higher pitch in such Equations then r Leibnitz & his has
been able to do carry it in differential Equations to this day. The
second is theat very general method of Series which Mr Leibnitz published
Mr Newton. And it lies upon Mr Leibnitz to make it appear that
he kewknew either of those methods so early.
Mr Leibnitz was in London the first time in Feb. 1673 & then went to Paris in or about
the beginning of March following, & at that time knew nothing of the higher Geometry
but some time after began to be suppose in the year 1674
Paris by Mron Huygens as he represents in his Letter to you. He might begin to learn it there
fore in the year 1674. The same yeare he met with a series for finding any arc
of a circle whose sine was given & if the proportion of this arc to the whole circum
ference was known it gave him the whole circumference. The next year Mr Olden
burg sent him eight series in a letter dated 15 Apr 1675 & he acknowledged the receipt of them
in his Answer dated 20 May following & said he would compare them with
his own. The
1. Mr Newton gave an instance of his Differe method of fluxions in his Analysis
per Æquationes numero termin communicated by Dr Barrow to Mr Collings in the year 1669 & described
the universality of it in the his Letter to Mr Collins dated 10 Decem 1672 with an
example therof in drawing of Tangents, & desc a copy of wchwhich Letter was sent to Mr Leibnitz
at Paris in the year 1676, & in his Letters of 13 Iune & 24 Octob. 1676 described the
method further to Mr Leibnitz by as extending to Quadratures of Curves, invers Problems of Tangents & others more difficult &
there also gave an example of it in a general series wchwhich breake off for squaring of Curves.
Mr Leibnitz came from Paris to was in London in the same October began to learn the higher Geometry in the year 1674 & came from Paris to London in October abovemention 1676, & there saw this last Letter in the hand
of Mr Collins & by his Letter & that of 10 Decem 1672 knew that ✝ ✝ understanding that the method of new methods of Tangents were a Corollary of M branch of Mr Newtons general method, fell upon considering how to make Mr Newtons method of Tangents (wchwhich was the same wthwith that of Slusius, become general, & the next year & the next year wrote in a Letter from Hannover dated 21 Iune 1677 wrote bak
sent back Dr Barrows method of Tangents, as his own & with the name & charac
teristick changed to make it his own, & shewed how this method giave the method of Slusius
& became & might be improved much beyond his former method (that of Dr Barrow) so as to proceeded without taking away fractions & surds as like Mr Newtons had described
method & extended to Quadratures, like Mr Newton's method & then he took notice that
this method Mr Newton, having described that his method did the same
these performances being the same wthwith those wchwhich Mr Newton had ascribed
to his method, theis methods seemed he took this his his new method to be alike Mr Newtons. Thus was he ethen endeavouring to find out Mr Newtons method. But now he contends that Mr Newton. But how he contends that Mr
Newton had no such method in those days. Mr Newton in his Letter of 24 Octob
represented that his method iswas founded in solving this Probleme Data æquatione fluentes
quotcunque quantiatatesquantitates involvente fluxiones invenire & vice versa, & that his method of series
became universal by solving this Probleme Ex æquatione fluentes quotcunque
Fluentem ex æquatione fluxiones involvente extrahere. But Mr Leibnitz tells
us that Mr Newton had in those days had no method of fluxions no fluxional
equations, but the no characteristick for fluxions & moments. Dr Barrow
published his differential method of Tangents in the year 1670. Mr Newton knew that
method long some years before Mr Leibnitz & yet is accused of wanteding a differential Characteristic
24 When hMre Leibnitz first published his differential Method,Acta Erudit. pro Novem. 1684 he wrote that it
reacht to such difficult Problems as could not be solved
without it the method or another method like it. And what other method
he meant you may know by his Letter to Mr Newton dated 17 March 1693
& still extant in his own hand writing. His words are Mirifice ampliaveras
Geometriam tuis seriebus, sed etiam edito Principiorum opere ostendisti patere
tibi etiam quæ Analysi receptæ non subsunt. Conatus sum ego quoque, notis
commodis adhibitis quæ Differentias & Summas exhibeant, Geometriam
illam quam transcendentem appello Analysi quodammodo subjicere; nec res
male processit. And hitherto Mr Leibnitz forbore to contend wthwith Mr
Newton for the preference.
4 Afterwards in the year 1699 Mr Fatio contended th published
that Mr Newton was the oldest inventory by many years & Mr
Leibnits pub in his Answer published in the Acta Eruditorum for May 1700
did not dispute it but granted that Mr Newton was the first who by giving
a publick specimen of this method openly, had proved that he had it, & contended himselfor
nothing more then that each of them had found the method apart without receiving
light from the other.
5 In October 1704 Dr Wallis died, the last of the old men who corresponded with
Mr Oldenburg & Mr Collins in these matters. And then Mr Leibnitz began
to claim the precedency. For in Ianuary 1705 in giving an Account of Mr
Newton's Quadratura Curvarum it was presented in the Introduction of wchwhich Mr it was
in wchwhich Mr Newton had said that he found the Method of fluxion gradually in the
years 16765 & 1666, it was retorted upon him that he had substituted fluxions for the
differences of Mr Leibnitz the first Inentor. And this representation Mr Leibnitz
And when Dr Keill defended Dr Wallis & Mr Newton, Mr Leibnitz defended what had
been published in the Acta Eruditorum, & demanded that Dr Keill should recant & Mr
Newton exp de taxed Mr Newton with knowing that Dr Keill was in the wrong &
pressed that he should declare his opinion in theis matter, that is, that Mr
Newton should retract what had been publickly publickly affirmed by Dr Wallis Mr Fatio Dr Keill &
himself, & granted by Mr Leibnitz in his Letter of 21 Iune 1677 [See Commercium p 88
lin 14 & p. 8 89 lin penult. & p. 90 lin. 26, 27, 28] & in his c not disputed
in his correspondence with Dr Wallis & answer to Mr Fatio 559 The accusation against Mr Newton amountess to to plagiary, & if it be not made good
it ought to go for calumny, & Mr Leibnitz is the man who ought to make it
good.
118)560
the the
SrSir
It is now twenty years since I left off Mathematicks, & when
I medled not with these matters I was surprized to find my self
It was n
It is now 20 years since I left off the study of Mathema
When the R. Society upon a Question arising between r
Dr Keill wchwhich affected me gave order that appointed a Committee to seach out the ancient Letters & Papers
found in the Archives & Letter-books of the R. Society & Library of
Mr Iohn Colling & gaive their opinion thereupon that the same should
be printed with the opinion of the Committee thereupon that the matter
of fact might appear thereupon to the world: I instead of returning a
fair answer, a defamatory Libel was printed in Germany dated the of Iune
16 1713 & dispersed through Germany France & Italy
SrSir
When Ever since You know that the Commercium Epistolicum came abroad conteining the
ancient Letters & Papers found preserved in the Archives & Letter Books of the R. S.
& Library of Mr Collins came abroad call came abroad; I he relating to the dispute between Mr Leibnitz & MDr Keil. They were collected & pub
lished by order of the a Committee appointed by the R. Society for that pur
pose; & Mr Leibnitz has hither d avoided returning an Answer to the same. And
first a Libel for the Book is matter of fact & uncapable of an Answer.
First therefore a Libel d For avoiding an Answer he pretended at that he
had not seen it this Book nor head leasure to examin it, & but had desired an eminent
Mathematician to examin it. And the Answer of the MathematianMathematician or prettended Answer Mathematician was in
sertd into a defamatory Libel published in Germany dated &
published in Germany without the name of the author or publishedr or City
where it was published. And I have since seen some Letters written since by
Mr Leibnitz in all wchwhich he excuses himself from returning an Answer
And the Postscript which you shewed me is of the same kind. For He tells you
in it that the English shall not have the pleasure of seing him return
an Answer to their slender reasonings as he calls them,. A AIn the first part of the Postscript
he affirms many things without proving any thing as men in passion anger use to
do & are in the second part & the whole Postscript is reflecting & defamatory without proving any thing & he falls upon my Philosophy, chwhich is nothing
at all to the Question & in squabling about it calls those thin corrupts the significations of words calling those things miracles wchwhich happen constantly & is without & those things occult qualities wchwhich are not occult & contends for Hypotheses in opposition to Propositions proved from Experiments & observations & experiments by the argument of Induction, & ascribes opinions to me which are not mine. & inat the same time he has sent a Mathematical
Probleme to be solved by the English Mathematicians wchwhich is as little the
purpose. I
He complains of the Committee of the R. Soc. as if they had
acted partially asin omitting what made against me. but his com
plaint I take to growndless & But in proving the accusation he instances in a Paragraph wchwhich
he s concerning my ignorance wchwhich he says they omitted. The But
he injures them But he injures them. And yet For Theis Paragraph is not omitted. It is in my Letter of 24 Octob. 16
will find it in the Commercium Epistolicum pag lin . He saith that
he saw this Paragraph when he was in London th in the hands of Mr Colling
when he was in London yethe second time that is, in October 1676, & there
fore he then saw that Letter. & & And in that & some othersother Letters writ before that time I described the
method of fluxions, & in the same Letter I described two general methods
of Series one of wchwhich Mr Leibnitz no in the said ProstscriptPostscript
1 I expect I beleive you will think it reasonable that Mr Leibnitz be constant to himself & still acknowledge
what he acknowledge what he acknowledged above 15 years ago & I still forbeare to
s contradict what he forbore to contradict in those days.
May 16765 & conteining several series & with the several converging Series conteined therein & I expect that he still
acknowledge the receipt thereof.
2 In a Letter datd 12 May 1676 he acknowledged that he then wanted the method
for finding a Series for the Arc whose sine was given, & by consequence that when when he wrote his Letter of 26 Octob. 1674 he wanted that method. 3 In the Acta
Eruditorum for May 1700, he acknowledged that no body heSo
Fluxions or Differences before me & him, & that no body before me had proved
by a specimen made publick that he had the method: & I expect that he
continuecontinues to make the same acknowledgemtacknowledgement the same. 6 Dr Wallis in the Preface to the two first volumes of his works published in April or May 1695 wrote that I in my two Letters of written in the year 1676 had explained to Mr Leibnitz the Method (called by me the Method of fluxions & by him the method of fdifferen)differences written b invented by me ten years before or above, that is in the year 1666 or before, & in the Letters wchwhich followed between thisem, & Mr Leibnitz did not f contradic had notice of this Paragraph & did not con then contractcontradict it nor found any fault with it & I expect that he still forbears to contradict it But as as he has attaqued me wthwith an accusation wchwhich amounts to plagiary if he goes on to accuse me of plagiary it lies upon him by the laws of all nations to prove his accusation or be ion pain of being accounted guilty of calumny. or be decd
4. ② In his Letter to me dated 7. March 1693 & now in the custody of the R. S. he wrote that I Mirifice ampliaveras Geometriam tuis seriebus, sed edito Principiorum opere ostendisti patere tibi quæ Analysi receptæ non subsunt Conatus sum Ego quoque notis commodis adhibitis quæ differentias & summas exhibent, Geometriam illam quam transcendentem appello, Analysi quodammodo subjicere, nec res male processit. And ① in the Acta Eruditorum for October 1684, when he had described hi the differential methodelements of his method of tangents & Maxima & Minima he added that the method extended to the difficulter sort of Problems wchwhich without this method or ANOTHER LIKE IT could not be managed so easily. ③ And what he then acknowledged he ought still to acknowledge.
5 In his Letter of 21 Iune 1677 he acknowledged in answer to mine of 24 Octob 1676 that I had a method of d of Analysis wchwhich readily gave the M like that wchwhich he proposed wherein I had described my method partly in plane words & partly in cyphers he said that he agreed with me that the method of Slusius tangents of Slusius was not yet perfect & thenat he long ago then set down Dr Barrow's a differential method of tangents by Differences published by Dr Barrow in the year 1670 & then shewed how it might be improved to perform those things which I had attributed to my method & thence concluded that mine differed not much from his, especially since it faciliated Quadratesures: & in candor he ought still to acknowledge that he then understood that he had when I wrote my Letter of 24 Octob. 1676 I had such a method.
6 In his Letter of I 27 Aug. 1676 he represented that he did not beleive that my methods were so general as I had described them, because thre & affirmed that there were many Problemes so difficult that they could did not depend upon Quadratures Equations & Quadratures: such as (amongst many others) were the inverse Problemes of tangents. And by what these words that he had not yet found the DDiff reduction of Problems to Differential Equations & by. And what he then acknowledged he ought in candor to acknowledge still.
8 And when after this I beleive you will see that I described the extent & nature of this method in my Letter of 10 Decem 1672 & that I couched both the Differential & the Summatory Method in my Tract of Analysis communicated by Dr Barrow to Mr Collins in the Iuly 1669. At wchwhich time Mr Leibnitz had not yet begun to study Geometry learn Algebra & the higher Geometry.
But if he goes on still to accuse me of plagiary, S it lies upon him by the laws of all nations to accus prove his accusation on pain of being deemed guilty of calumny. He is the aggressor & it lies upon him to prove his charge.
9 I forbe descend not further into particulars [those being described in the Commercium Epistolicum & the Accoundt thereof to wchwhich] I but refer you to the Commercium Epistolicum. & the Account thereof where you will find them whole matter distinctly stated & represented.
I forbear to descend further into particulars. You have them reprethsented in the Commercium Epistolicum & the Extract thereof to both wchwhich I referr
561
He hadth hitherto written Letters fill to his correspondents full of affirmations & reflexions without proving any thing. But he is the aggressor & it lies upon him to prove his chanrge. But if he goes on still to
Hitherto he avoided staid at answ returning an sanswer to the Commercium EpistEpistolicum by pretending that he had not seen it being at Vienna, & that And he pretends And now he tells you that And he still avoids excuses his answering it, pretending telling you that the English shall not have the pleasure to see him answer the returne an answer to their slender reasoning as he calls them, & by endeavouring to engage me in disputes about Philosophy & about solving of Problems which are nothing to the Question in hand
I do not contend about skill in Mathematicks having left off that study 20 years ago & look upon solving of Problems a very unfit method argument to decide who was the best Mathematician or invented any thng 45 years ago when thing above 40 years ago before Mr Leibnitz understood Algebra. And as to Philosophy & still more unfit to prove me a plagiary. And as to Philosophy it is as little to the purpose. He colludes in the signification of words he takes words in new significations peculiar to himselfself, preferrs Hypotheses to Arguments of Induction taken from Phenomena accuses me of opinions that are not mine & wou instead of proposing Questions to be examined by experiments before they are admitted into Philosophy, he would have his Hypotheses admitted & beleived before they are examined. But all this is nothing to the Commercium Epistolicum.
He complains of the Committee
And this is as much as to say that the acknowledge that I had the method before it was published in Germany & that the Principia Philos were a proof that I had it & the first specimen made publick by wchwhich of applying it to the difficulter Problems.
– There you will see that in my Letter of 10 Decem 1672 I described the extent of the method & some of its Characters & that in th my Analysis communicated by Dr Barrow to Mr Collins in the year 1669 I couched both the Diff Differential method & the summatory.
108562
after 1715.
SrSir
You know that the Commercium Epistolicum conteins the ancient Letters & Papers preserved in the Archives & Letter Books of the Royal Society & Library of Mr Collins relating to the dispute between Mr Leibnitz & Dr Keill & that they were collected & published by a numerous Committee of Gentlemen of several nations appointed by the Royal Society for that purpose. Mr Leibnitz hath hitherto avoided returning an Answer to the same: for the book is matter of fact & uncapable of an Answer. To avoid answering it he pretended the first year that he had not seen this book nor had leasure to examin it, but had desired an eminent Mathematician to examin it. And the Answer of the Mathematician (or pretended Mathematician) dated 7 Iun Iune 16713 was inserted into a defamatory Letter dated 29 Iuly following & published in Germany without the name of the Author or Printer or city where it was printed. And the whole has been since translated into French & inserted into another abusive Letter (of the same Author as I suspect) & answered by Dr Keill in Iuly 1714 & no answer its yet given to the Doctor.
Hitherto Mr Leibnitz avoided returning an Answer to the Commercium Epistolicum by pretending that he had not seen it: And now he avoids it by telling you that the English shall not have the pleasure to answer to see him return an answer to their slender reasonings (as he calls them) & by endeavouring to engage my me in disputes about Philosophy & about solving of Problems both which are nothing to the Question.
As to Philosophy, he colludes in the signifationssignifications of words, preferrs Hypotheses to arguments of Induction from experiments, accuses me of opinions wchwhich are not mine, & instead of proposing Questions to be examined by experiments before they are admitted into Philosophy he proposes Hypotheses to be admitted & beleived before they are examined. But all this is nothing to the Commercium Epistolicum.
He complains of the Committee of the Royall Society as if they had acted partially in omitting what made against me. But he fails in proving the accusation. For he instances in a Paragraph concerning my ignorance pretending that they omitted it, & yet you will find it in the Commercium Epistolicum pag. 74 lin. 10, 11, & I am not ashamed of it. He saith that he saw this Paragraph in the hands of Mr Collins when he was in London the second time, that is, in October 1676. It is in my Letter of 24 Octob. 1676, & therefore he then saw that Letter. And in that & some other Letters writ before that time I described my method of fluxions. And in the same Letter I described also two general methods of series, one of wchwhich is now claimed from me by MrLeibnitz.
I beleive you will think it reasonable that Mr Leibnitz be constant to himself, & still acknowledge what he acknowledged above 15 years ago, & still forbear to contradict what he forbore to contradict in those days.
In his Letter of 20 May 1675 he acknowledged the Receipt of a Letter from Mr Oldenburge dated 15 Apr. 1675 wthwith several converging series conteined therein. And I expect from him that he still acknowledge the Receipt thereof. Many Gentlemen of Italy France & Germany (you your self being one of them) have seen the original Letters & the entrys thereof in the old Letter books of the Royal Society., & the series of Gregory is in the former of these two Letter of 15 Apr. 1675 & in Gregories original Letter dated 15 Feb. 1671.
In a Letter dated 12 May 1676 he acknowledged that he wanted the method for finding a series for the Arc whose sine was given, & by consequence that that he wanted it when he wrote his Letter of 24 Octob. 1674. And I expect that he still acknowledge it.
In the Acta Eruditorum for May 1700, he acknowledged that no man so far as he in answer to Mr Fatio who had said that I was the oldest inventor by many years, he acknowledged that no body, so far as he knew, had the method of fluxions or differences before me & him & that no body before me had proved by a specimen made publick that he had it. Here he allowed that I had the method before it was published or communicated by him to any body in Germany, & that the Principia Philosophiæ were a proof that I had it & the first specimen made publick of applying it to the difficulter Problemes. And I expect that he still continue to make the same acknowledgement. At that time he did not deny what Mr Fatio affirmed & nothing but want of candor can make him unconstant to himself.
In a Letter to me dated 7 March 1693 & now in the custody of the R. Society, he wrote, Mirifice ampliaveras Geometriam tuis seriebus, sed edito Principiorum opere ostendisti patere tibi etiam quæ Analysi receptæ non subsunt. Conatus sum Ego quoque notis commodis adhibitis quæ differentias et summas exhibent, Geometriam illam quam transcendentem appello, Analysi quodammodo subjicere, nec res male processit &c. And what he then acknowledged he ought still to acknowledge
564
To abbe Conti, Ka p. 100
Leicester Fields, London. 26 Feb. 171.
SrSir
You know that the Commercium Epistolicum conteins the ancient Letters & Papers preserved in the Archives & Letter Books of the Royal Society & Library of Mr Collins relating to the dispute between Mr Leibnitz & Dr Keill & that they were collected & published by a numerous Committee of Gentlemen of severall nations appointed by the R. Society for that purpose. Mr Leibnitz has hitherto avoided returning an Answer to the same; for the Book is matter of fact & uncaplable of an Answer. To avoid answering it he pretended the first year that he had not seen theis Book nor had leasure to examin it, but had desired an eminent MathematianMathematician to examin it. And the Answer of the Mathematician (or pretended Mathematician) dated 7 Iune 1713, & was inserted into a defamatory Libettelr dated 29 Iuly following, & published in Germany without the name of the Author or Printer or City where it was printed. And the whole has been since translated into French & inserted into another abusive Letter (&of the same kind Author as I suspect) & answered by Dr Keill in I Iuly 1714., & no answer is yet given to the Doctor.
Hitherto he Mr Leibnitz avoided returning an Answer to the Commercium Epistolicum by pretending that he had not seen it. And now he avoids it by telling you that the English shall not have the pleasure to see him return an Answer to their slender reasonings (as he calls them) & by endeavouring to engage me in disputes about Philosophy & about solving of Problems, both which are nothing to the Question.
I have left off Mathematicks 20 years ago & look upon solving of Problemes as a very unfit argument to decide who was the best Mathematician or invented any thing above 450 years ago. And aAs to Philosophy it is as little to the purpose. He colludes in the significations of words ✝ ✝ calling those things miracles wchwhich create no wonder & those things occult qualities wchhos causes are occult tho the qualities themselves be manifest, & those things the souls of men wchwhich do not animate their bodies. His Harmonia præstabilita is miraculous & contradicts the daily experience of all mankind, every man finding in himsefhimself a power of seeing with his eyes & moving his body by his will. He preferrs Hypotheses, Preferrs Hypotheses to Arguments of Induction drawn from experiments, accuses me of opinions wchwhich are not mine, & instead of proposing Questions to be examined by Experiments before they are admitted into Philosophy he proposes Hypotheses to be admitted & beleived & examined before they are examined. But all this is nothing to the Commercium Epistolicum.
He complains of the Committee of the Royall Society as if they had acted partially in omitting what made against me But he fails in proving the accusation. For he instances in a Paragraph concerning my ignorance, pretending that they omitted it, & yet you will find it in the Commercium Epistolicum pag 74 lin. 10, 11, & I am not ashamed of it. He saith that he saw this Paragraph in the hands of Mr Collins when he was in London the second time, that is, in October 1676. It is in my Letter of 24 Octob. 1676, & therefore he then saw that Letter. And in that & some other Letters writ before that time I described my method of fluxions. And in the same Letter I described also two generall methods of series, one of wchwhich is now claimed from me by MrLeibnitz.
I beleive you will think it reasonable that Mr Leibnitz be constant to himself & still acknowledge what he acknowledged above 15 years ago, & y& still forbear to contradict what he forbore to contradict in those days.
In his Letter of 20 May 1675 he acknowledged the Receipt of a Letter from Mr Oldenburg dated 15 Apr. 1675 with several converging series conteined therein. And I expect from him that he still acknowledge the receipt thereof. ‖‖ Many Gentlemen of Italy France & Germany (you your self being one of them) have seen the original Letters & the entries thereof in the old Letter books of the Royal Society, & the Series of Gregory is in the Letter of the 15 Apr. 1675, & in Gregories original Letter dated 15 Feb. 1671.
In a Letter dated 12 May 1676 (seen by the same Gentlemen) he acknowledged that he then wanted &c In a Letter dated 12 May 1676 seen by the same Gentlemen he acknowledged that he then wanted the method for finding a series for the Arc whose sine was given, & by consequence that he wanted it when he wrote his Letter of 24 Octob 1674 And I expect that he still acknowledge it. ‖ Many Gentlemen
In the Acta Eruditorum for May 1700, he in answer to Mr Fatio who had said that I was the oldest inventor by many years, Mr Leibnitz acknowledged that no body so far as he knew, had the method of fluxions or differences before me & him, & that no body before me had proved by a specimen made publick that he had it. Here he allowed that I had the method before the two Bernoullis & it was published or communicated by him to any Body in Germany that the Principia Philosophiæ were a proof that I had it, & the first specimen made publick of applying it to the difficulter Problemes, And I expect that he still continue to make the same acknowledgement. At that time he did not deny what Mr Fatio affirmed, & nothing but want of candor can make him unconstant to himself.
In a Letter to me dated 7 March 1693 & now in the custody of the R. S. he wrote, Mirifice ampliaveras Geometriam tuis seriebus, sed edito Principiorum opere ostendisti patere tibi etiam quæ Analysi receptæ non subsunt. Conatus sum Ego quoque notis commodis adhibitis quæ differentias & summas exhibent, Geometriam illam quam transcendentem appello, Analysi quodammodo subjicere nec res male processit. And what he then acknowledged he ought still to acknowledge.
In his Letter of 21 Iune 1677 writ in Answer to mine of 24 Octob 1676 wherein I had described my method partly in plain words & partly in cyphers, he said that he agreed with me me that the method of tangents of Slusius was not yet made perfect, & then set down a differential method of Tangents published by Dr Barrow in the year 1670, & disguised it by a new notation, pretending that it was his own & shewed how it might be improved tso as to perform those things wchwhich I had ascribed to my method, & concluded from thence that mine differed not much from his, especially since it faciliated Quadratures. And in the Acta Eruditorum for October 184, in publishing the Elements of this method he added that it extended to the difficulter Problemes which without this Method or another like it, could not be managed so easily. He understood therefore in those days that in the eyar 1676 when I wrote my said Letter I had a method which did the same things with the method wchwhich he calls differentiall, & he ought still to acknowledge it, ‖, especially ‖ especially now the sentences in cyphers are decyphered & other things in that Letter relating to the method are fully explained, & the Compendium mentioned therein is made publick.
In his Letter of 27 Aug. 1676 he represented that he did not beleive that my Methods were so generall as I had described them in my Letter of 13 Iune predceding, & affirmed that my methods there were many Problemes so difficult that they did not depend upon Equations nor Quadratures, such as (amongst many others) were the inverse Problemes of tangents. And by these words it appears he acknowledged that he had not yet found the reduction of Problems to Differential Equations. And what he then acknowledged, he acknowledged again in the Acta Eruditorum for April 1691 pag. 178, & ought in candor to acknowledge still.
Dr Wallis in the Preface to the two first Volumes of his works published in April 1695, wrote that I in my two Letters written in the year 1676 had explained to Mr Leibnitz the Method (called by me the differe method of fluxions & by him the differential method) invented by me ten years before or above (that is, in the year 1666 or before) & in the Letters which followed between them, Mr Leibnitz had notice of this Paragraph & did not then condradictcontradict it nor found any fault with it. And I expect that he still forbeare to contradict it.
But as he has lately attaqued me with an accusation wchwhich amounts to plagiary: if he goes on to accuse me, it lies upon him by the laws of all nations to prove his accusation on pain of being accounted guilty of calumny. He hath hitherto written Letters to his correspondents full of affirmations complaints565 complaints & reflexions without proving any thing. But he is the aggressor & it lies upon him to prove his charge.
I forbear to descend further into particulars. You have them in the Commercium Epistolicum & the Abstract thereof, to both which I refer you. I am
SrSir
YorYour most humble and most obedient Servant
Is. Newton
114)566
To Conti 21
SrSir
I thank your for shewing me the Postscript to the Letter of Mr Leibnitz. And for setting those matters in a true light, I beg the favour that I may will lay them before you in an historical manner in as few words as I can in an historical manner.
Mr Newton I gave an Example of thise method of fluxions in his my Analysis communicated by Dr Barrow to Mr Collins in the year 1669, & described the universality of it in his my Letter to Mr Collins dated 10 Decem 1672 with an example thereof in drawing of TangensTangents, a copy of wchwhich Letter was sent to Mr Leibnitz at Paris in the year 1676 by Mr Old. in the same Packet with Mry Newtons Letter of 13 Iune 1676 & therefore was received by him. In this Letter I said.
Mr Leibnitz was in London in February 1673 & after a few days went thence to Paris, & at that time & some time after (as he tells you) in the said Postscript he knew nothing of the higher Geometry, but some time after (suppose in the year 1674) was instructed in it at Paris by Mr Huygens as he represents in his Letter to you Postscript above mentioned. In those days Mr Collins communicated to his friends at home & abroad several Series invented by Mr Newton me & Mr Iames Gregory. And Mr Leibnitz that same A.C. 1674 met with a series one of these series namely that for for finding any Arc whose sine was is given & by consequence the whole circumference by the proportion th to that Arc when its proportion to that arc is given, Mr Leibnitz in the year 1674 signified that he had invented such a series. And thereupon Mr Oldenburg to Mr Oldenburg having notice of the series, sent eight series invented by Mr Newton & Mr Iames Gregory, to Mr Leibnitz in a letter dated 15 Apr. 1675, & Mr Leibnitz in a Letter dated 20 May 1715 acknowledged the receipt thereof, & said he would compare those series with his own but the same year communicated to his friends at Paris one of those series as his own w. And the next year Mr Leibnitz, upon receiving two others of those series a second time from London, desired Mr Oldenburgh (by a letter dated 12 May 1676) to procure from Mr Collins the Demonstration of those two series, meaning the method of finding them; & promised to recompence him with something of his own very different. One of the two series of which he wanted the Demonstration was that for finding the Arc whose sine was given. He pretended two yeares before to have found this series himself & now he wanted the method of finding it. The series wchwhich he sent back as a recompence was one of those which he had received from Mr Oldenburg the year before & did not then know to be his own .but the same year communicated it to his friends at Paris as his own & afterwards published in the Acta Eruditorum as his own without letting the world know that he had received it from London. Vpon this request of Mr Leibnitz Mr Newton Hereupon Mr Newton at the request of Mr Oldenburg & Mr Collins wrote his Letter of 13 Iune 1676 conteining his method of Seires illustrated with divers examples of Series. And Mr Leibnitz laid his hands upon in his Answer dated claimed four of the series, pretending that he had found them before he received the Letter, that is, before he had the method of finding them. And when at his request Mr Newton further explained the inverse method of series, he so soon as he understood it, he replied that he had found it before as he perceived by his old papers, but had forgot it.
Mr Newton neare the end of his said Letter of 13 Iune 1676, represented that Analysis by the help of these series, extended to allmost all problems but yet became not universall without the help some further methods. And in his next Letter dated Octob. 24, he said that [one of those Methods consisted in the extraction of a fluent out of an Equation involving its fluxion: & the other the Probleme]. The first method shews that when Mr Newton wrote these two Letters Letters he had differential fluxional equations & had then carried Analysis in such equations to a very great height & by this Analysis had improved the Method of Series & made it general. The second method is that wchwhich Mr Leibnitz in his letter to you claims to himself, saying that altho Mr Newton indeed preceded him in the method of series, but at length he (Mr Leibnitz) found a general method for series & after this he had no more need of Mr Newton's extractions. Mr Leibnitz has been intruding himself into the methods of series all his life tmn above these 40 years, but really has nothing to do with them & ought to forbear But this Method being Mr Newtons Mr Leibnitz has no right to any part of the method of Series
Mr Newton in his said Letter of 24 Octob. 1676 mentioned his Analysis communicated by Dr Barrow to Mr Collins & another Tract composed in the year 1671 about Series & the a method of Tangents which readily gave the method of Slusius, & stuck not at surds & extended to questions de maximis & minimis & quadratures & others & was obvious or easy to be found out & was founded in the slution of this Probleme [Data Æquatione quotcunque fluentes quantitates involvente, Fluxiones invenire & vice versa.] This is therefore the method of Fluxions whereof Mr Leibnitz now pretends to have been the first inventor calling it the differential method. This is that method wchwhich Mr Newton d in his Letter of 10 Decem 1672 called his general method & said that it not only determined Tangents, but extended also to abstruser Problems concerning the Curvities, Areas Lengths Centers of gravity of Curves &c & proceeded even in Eq Mechanical Curves & in Equations involving surds. And the things wchwhich Mr Newton in his Letter of 24 Octob 1676 cited out of his book of Quadratures shew that he had in those days carried the fluxional Analysis to a higher pitch then Mr Leibnitz & his followers have been able to carry the differential Analysis to this day.
Mr Newton's Letter of 10 Decem 1672 was sent toby Mr Oldenburg to Mr Leibnitz in the same packet wthwith his Letter of 13 Iune 1672, & therefore he Mr Leibnitz received it. In October following he came from Paris to London & there Mr Collins shewed him a part of his correspondence wthwith Mr Gregory & Mr Newton as he acknowledges in his Letter to you, & particularly he shewed him Mr Newton's Letter of 24 October just then come received by Mr Oldenburg & given to Mr Collins to be copied. For the sentence concerning Mr Newton's ignorance of the dimensions of the vulgar figures except the Cissoid, is in this Letter. You may see it in the Commercium pag. 74. And therefore Mr Leibnitz has injured the Committee of the R. Society in complaining that they omitted suppressed it. And if you please to read consult the place, you will see that the construction wchwhich he puts upon it, is as injurious to Mr Newton. His, whose words are: Sed in simplicioribus vulgoque celebratis figuris, vix aliquid relatu dignum reperi quod evasit aliorum conatus, nisi forte Longitudo Cissoidis ejusmodi sit censeatur.
Mr Leibnitz in his Letter to you represents that if the Differential method had been hinted to Mr Newton it would have been easy for him to have found it out. And certainly it was as easy for Mr Leibnitz by the hints which he had of the fluxional method in Mr Newtons Letters above mentioned to find out that method, notwithstanding that the sentences above set down within the brackets were in ciphers. In his journey therefore from London through Holland to Hannover, he was meditating how to make extend the method of Tangents & particularly that of Slusius become to all sorts of Problems, & first proposed to do it by a Table of tangents as appears by his Letter to Mr Oldenburg dated from Amsterdam 18 Novem. 1676, but after his arrival at Hannover he fell into the true method of doing it; as he himself has acknowledged in the Acta Eruditorum for April 1691 pag. 178, where he saith that by new matter & other affairs coming on he was hindred from fitting his arithmetical Quadrature for the Press, & after he found his new Analysis he did not think that Quadrature worth publishing in the vulgar manner. In his Letter of 27 Aug. 1676 he aff wondred that Mr Newton should pretend to such general methods, & affirmed that Inverse Problemes & many others could not be reduced to equations or quadratures567 quadratures: but after he returned to Hannover & fell into publick business he found out how to reduce such Problems to equations & quadratures & in his Letter of 21 Iune 1677 sent back a specimen of his new method, pretending (according to his usual candor) that he had found it long before. Clarissimi Slusij Methodum Tangentium, saith he, nondum esse absolutam Newtono assentior. Et jam a multo tempore rem Tangentium generalius tractavi, scilicet per tdifferentias Ordinatarum. Then he sets down his new method of Tangents & how it gives the method of Slusius, & adds that it is of larger extent then his former method of Tangents & shews how it proceeds (like Mr Newton's method) without taking away surds, & then adds Arbitror quæ celare voluit Newtonus de Tangentibus ducendits ab his non abludere. Quod addit, ex hoc eodem fundamento quadraturas quoque reddi faciliores me in sententia hac confirmat, nimirum semper figuræ illæ sunt quadrabiles quæ sunt ad æquationem differentialem. Mr Newton in his Letter of 24 Octob 1676 represented that he had a general method on upon which he had written a Treatis five years before, & that this was a certain method of Tangents wchwhich extended to all sorts of Problems & readily gave the method of Slusius & stuck not at surds & rea faciliated Quadratures. Mr Leibnitz at length finds a method of Tangents which did the same things & thence concludes it like the method wchwhich Mr Newton had described in his Letters & concealed in this sentence exprest enigmatically, Data æquatione quotcunque fluentes quantitates involvente, fluxiones invenire, & vice versa. But now he contends either that Mr Newton when he wrote those Letters had no such method, .or that the Differential method was found [jam tum a multo tempore] long before yethe year 1677.
When the Differential Method began to be celebrated in Holland Dr Wallis in the Introduction to his Works printed in the year 1695, wrote that this method was the same wthwith the Method of fluxions wchwhich Mr Newton had explained to Mr Leibnitz in his Letters written in the year 1676, & had invented then years before that time or above. Mr Leibnitz in the correspondence which followed between him & Dr Wallis did not deny this nor contend for any thing more then that he had added some things to Mr Newton's method, & that what he had added was his own.
Afterwards in the year 1699 Mr Fatio published that Mr Newton was the oldest inventor of this Calculus by many years & Mr Leibnitz the second Inventor And Mr Leibnitz in his Answer published in the Acta Eruditorum for May 1710, did not dispute it, but granted that commended Mr Newton for his candor in representing in his Principia Philosophiæ (pag. 258, 259) that up in the year where he represented that upon signifying to Mr Leibnitz that in the year 1676 that he had a method of determining Maxima & minima, drawing Tangents, & solving such like Problems wchwhich proceeded without taking away surds & concealing the method in this sentence exprest enigmatically [Data æquatione quotcunque fluentes quantitates involvente, fluxiones invenire, & vice versa:] Mr Leibnitz wrote back [the next year] that he had also fallen into such a method & th communicated his method scarce differing from Mr Newton's except in forms of words & chcaraters: & that the foundation of both Lemmas w methods was continued in the second Lemma of the second book of his Principles p 250. By commending Mr Newton for his candor in making this Representation, he acknowledged the truth of the Representation: & its now too late to dispute it. All that he can now pretend to is that he found the differential method [a multo tempore] long before the year 1677 or at least that he has added some things to Mr Newton's method & that what he has added is his own. In either case he is to prove what he pretends to.
In the same Answer to Mr Fatio, Mr Leibnitz wrote: Quam [methodum] ante Dominum Newtonum et me nullus quod sciam Geometra habuit; uti ante hunc maximi nominis Geometriam Nemo Specimine publice dato se habere probavit: ante Dominos Bernoullios et me nullus communicavit. Bernoulli is here made a party a party & therefore can be no judge, & Mr Newton is here acknowledged to have been the first who by giving a publick specimen proved that he had this method. When Mr Leibnitz first published his method (vizt A.C. 1684) he extended it no further then to Tangents & maxima & minima, but added that it was might be extended to the difficulter problems, wchwhich could not be solved without this calculus or another like it, meaning Mr Newton's years before. But neither of them proved the extent of their method to the difficulter Problems by a publick specimen before the edition of the Principia Philosophiæ, wchwhich the Marquess de l'Hospital acknowledged to be full of this cal consist almost wholy of this calculus. And Mr Leibnitz himself in his Letter from Hanover to Mr Newton 17 Mach 1693 now in the custody of the R. Society, said wrote thus concerning it: Mirifice ampliaveras Geometriam tuis seriebus, sed edito Principiorum opere ostendisti patere tibi etiam quæ Analysi receptæ non subsunt. Conatus sum ego quoque notis commodis adhibitis quæ differentias & summas exhibeant, Geometriam illam quam transcendentem appello Analysi quodammodo subjicere: nec res male processit. His first endeavour to do this was in his there papers published in the year 1689 de lineis Opticis, de resistentia Medij & de motuum cœlestium causis. In the end of the second of these Papers he said: Nobis nunc fundamenta Geometriæca jecisse suffecerit in quibus maxima consistebat difficultas. Et fortasse attente consideranti vias quasdem novas vel certe satis antea impeditas aperuisse videbimur. Omnia autem respondent nostræ Analysi Infinitorum &c. This was the first specimen wchwhich he published of the extent of his method to the difficulter Problems. It was writ in plain words & answered to the Analysis infinitorum in imitation of Mr Newton's Principia Philosophiæ writ in the same manner. For these three Papers were nothing else then a part of the Principia Philosophiæ put into a new dress. As Mr Leibnitz by imitating Mr Newton invented the differential calculus, so he imitated him in the first specimen which he gave of the extent of this calculus.
In October 1703 Dr Wallis died, the last of the old men who corresponded with Mr Oldenburgh & Mr Collins in these matters. And hitherto Mr Leibnitz forbore to claim the precedency of invention, & contented himself with pretending that he had invented the method apart & augmented it. But heh has since begun (according to his usual candor) to contradict Dr Wallis & Mr Fatio & represent Mr Newton a Plagiary, & now refuses to make good his accusation, pretending that he will not oblige the English so far & that the Committee of the Royall Society are not legal judges. That he might not seem to have received any light into the differential method from Mr Newtons Letter of 24 Octob. 1676 he said in his Answer, A multo tempore rem tangentium generalius tractavi, scilicet per differentias Ordinatarum, I have long ago made the method of Tangents by the differences of the Ordinates become a general methods. And now he goes a step further & pretends that he made the method general not only without receiving light from Mr Newton, but even before him. He confesses that he knew nothing of the higher Geometry in the year 1673 when he went from London to Paris, & that in the year 1675 he composed his Quadratura Arithmetica in a vulgar manner before he found out his new Analysis, & that in the year 1676 he knew not how to reduce inverse Problemes of Tangents to equations or quadratures: & yet he pretends that he found out the new Analysis not only without receiving light from Mr Newton but even before him. But it lies upon him to prove his pretenses. And finding himself unable to do this, he seeks excuses & makes a clamour. But he is to know that by the laws of all nations he that accuses another publickly & doth not prove his accusation as publickly, is to be accounted guilty of calumny. And thus much in answer to the first part of his Postscript.
115)2568
To Conti?
SrSir
I thank you for shewing me the Postscript to the Letter of Mr Leibnitz. For setting those matters in a true light, I will lay describe them to you in an historical manner in as few words as I can.
In my Analysis communicated by Dr Barrow to Mr Collins in the year 1669 I gave an a plain example of the Method of fluxions & described the uni in my Letter to Mr Collins dated 10 Decem 1672 I described the universality of it saying that it extended to Problems about Tangents, Curvities, Areas, Lengths, Centrers of gravity of Curves &c geometrical or mechanical &c & proceeded without taking away surds. And I there gave an example of it in drawing of Tangents. And a copy of this Letter was sent to Mr Leibnitz at Paris by Mr Oldenburg in the same Packet wthwith the Extracts of Mr Iames Gregories Letters & with my Letter of Iune 13 1676, & therefore it came to his hands.
Mr Collins in the years 1669, 1670, 1671 & 1672 Mr Collins communicated very freely to his friends at home & abroad several series which he had received from me & Mr Gregory. And in February 1673 Mr Leibnitz was in London & after a few days went thence to Paris, & at that time he knew nothing of the higher Geometry, but some time after (suppose in the year 1674) was instructed in it at Paris by Mr Hugens, as he represents in his Postscript above mentioned, & then he wrote to Mr Oldenburg that he had found a method which gave him a series for any Arc whose sine was known. If the proportion of the arc to the whole circumference was known it gave him the whole circumference: if theat proportion was not known yet method gave him a series for the Arc. And yet he had only met with Mr one of Mr Newtons my series & wanted the method of finding it. For in his Letter of 122 May 1676 he desired Mr Oldenburg to procure & send to him the Demonstration of this very series, that is, the method of finding it.
In a Letter dated Apr 15th 1675 Mr Oldenburg sent to Mr Leibnitz eight series invented by Mr me & Mr Gregory; & Mr Leibnitz in a letter dated 20 May following, acknowledged the receipt thereof, & said he would compare these series with his own. At that time he did not know any of those series to be his own, & yet the same year communicated one of thesem series to his friends at Paris & afterwards published it in Germany as his own without ever acknowledging that he had received it from London.
Vpon the aforesaid request of Mr Leibnitz backt by the request of Mr Oldenburge Mr Newton & Mr Collings I wrote his my Letter of 13 Iune 1676 explaining my method of Series & illustrated the same with several series set down by way of examples. And Mr Leibnitz in his Answer dated 27 August.569 August 1676, pretended that he had found four of those series before he received my Letter, that is, before he had the method of finding them. And at the same time he desired me to explain my method further & therefore did not yet understand it. And when I had explained it further & he understood it, he replied that he had found it before, as he perceived by his old papers, & but had forgot it.
In his aforesaid Postscript he allows that I preceded him in the method of Series Mr Newton preceded him, but he adds that at length he found a general method for series & after that had no further need of Mr Newtons extractions. But his general method is mine.
The method of converging Series & the Method of Fluxions have great affinity with one another, so as both together to compose one universal Analysis & separately to be imperfect. I found them both in the years 1665 & 1666 by degrees. And in Iuly 1699 Dr Barrow communicated to a Mr Collins a little Tract of Analysis written by me in which I founded the method of Series upon three Rules & dēemmonstrated the first Rule by the method of fluxions. And in the year 1671 I wrote a larger Tract upon these two methods, with a designe to have published it together with another Tract concerning Light & Colours. But finding that these matters began to entangle me in disputes I laid my designe aside being in love with a quiet life, & let these matters rest till the year 1676. as I represented in my Letter of 24 October 1676
In the year 16969, 1670, 1671 & 1672 Mr Collins communicated to his friends at home & abroad several series partly taken out of the said Tract of Analysis & partly sent to him by Mr Iames Gregory of Scotland. For Mr. Gregory by the help of one of my Series fell into the same Method of converging Series. And in La Letter to Mr Collins dated 10 Decem 1672 I described the universality of the Method of fluxions saying that it extended to Problemes about the Tangents, Curvities, Areas, Lengths, Centers of gravity of Curves &c Geometrical or Mechanical &c & proceeded without taking away surds. And I there gave an example of this method in drawing of Tangents by a Rule which proved to be the Method of Slusius. And a copy of this Letter was sent to Mr Leibnitz at Paris by Mr Oldenburg in the same Packet with Mr the Extracts of Mr Gregories Letters & with my Letter of Iune 13th 1676, & therefore it came to h is hands. And thiese two Letters (if I mistake not) gave him the first light into the differential meth put him first upon searching after a general method wchwhich would do the same things gave him the first notice of such a general method of Analysis
He was in London in Feb 1673 & there pretended to have the method of Mouton, & after a few days went thence to Paris & staid there some time before he knew any thing of the higher Geometry, but at length (suppose I think in the year 1674) he was instructed in it at Paris by Mr Hugens, as he represents in his Postscripst above mentioned. And one of my series being fallen into his hands For (that for finding the either Arc whose sine was given) or separately invented by himself And then he wrote that year to Mr Oldenburg For he began that year to write to Mr Oldenburg about the higher Geometry pretending that that he could find a series for any Arch whose sine was known. If the proportion of the Arc to the whole circumference was known it gave him the whole circumference, if the proportion was not known yet the series gave him the Arc. And this he pretended to be his own invention, tho he but did not yet to know the Method of finding this series inventing it inventing it. For in his Letter of 12 May 1676 he desired Mr Oldenburg to procure from Mr Collins the method of finding this very series & tos end it to him. He is desired to let us know how to came by that series two years before he had the method of finding it
In a Letter dated April 15th 1675 Mr Oldenburg sent to Mr Collins Leibnits from Mr Collins eight series invented, some of them by me, & others by Mr Gregory. And Mr Leibnitz in a Letter dated 20 May following, & still extant acknowledged the receipt thereof, & said he would compare those series with his own. At that time he did not know any of those series to be his own; & yet the same yeare he communicated one of them to his friends at Paris as his oneown & afterwards published it in Germany as his own without ever acknowledging that he had received it from London. This series was sent by Mr Gregory to Mr Collins the year 1671 ., & a copy of Mr Gregories Letter was sent to Mr Leibnitz in the year same packet with my Letter of 13 Iune 1676 & therefore came to his hands.
Vpon the aforesaid request of Mr Leibnitz bk by Mr Oldenburg & Mr Collins wrote to me to communicate my method of Series to Mr Leibnitz, & I did so in my Letter of 13 Iune 1676, & therin I added that I Analysis by the means of this method was much enlarged so as to extend to almost all Problems except except perhaps some numeral ones like those of Diophantus, but became not universal without the help of some further methods of reducing Problems to converging series which I forbore to describe, having tired my self wthwith these studies long ago so ha to have absteined from them the last five years, meaning since the year 1671. And Mr Leibnitz in his Answer dated 27 Aug. 1676 replied that he did not beleive that Mr Newton's Method was so general: for (said he) there are were many Problems so difficuntdifficult as not to depend upon Equations or Quadratures, such as are (among many others) the inverse Problemes of Tangents. And by these words its most certain that Mr Leibnitz had not yet found out the Differential method. In the same Letter Answer he claimed some of the s pretended to have found some of these series before he received them from me, that is before he had the method of finding them.
In my Answer dated 24 Octob. 1676, at the request of Mr Leibnitz I described how I found out the Method of Series a little before the Plague wchwhich happened in the year 1665. And after I had mentioned the aforesaid Tract wchwhich communicated by Dr Barrow to Mr Collins, (wchwhich has been since printed from a copy found in the hand writing of Mr Collins by Mr Iones who purcheased th his Library) & the other Tract written in the year 1671) 1671 upon both the methods in the year 1671: I added that the Method of fluxions readily gave the method of Tangents of Slusius & determined Maxima & Minima & Quadratures & other hard Problemes, & stuck not at Equations involving surds. & was easy to be found. And because I was not then at leasure to describe it at large I couched it in the following Probleme exprest Enig Enigmatically An Equation involving any number of fluent quantities being given, to find their fluxions; & on the contrary. This is the first Proposition of my book of Quadratures. And in this Letter I cited so many things out of thisat Book as abundantly shews that that Book was then written & what was the method of fluxions which I wrote of in that Letter. And in the end of the Letter I added that my methods extended to Inverse Problemes of Tangents & others more difficult for solving of which by by Series I used two methods, & were in my power by the help of two methods, wchwhich methods I couched in the following words exprest enigmatically. One method consists in the extraction of a fluent quantity out of an equation involving its fluxion: the other in assuming a Series for any unknown quantity from wchwhich the other quantities might conveniently rest desired may conveniently be deduced & in collating the homologous terms of the resulting æquation [with the condition of the Problem] for d determining the terms of the assumed series. By these two methods I had made the inverse method of Series universal al become general five years before the writing of theseat two letter or above. The first method shews not only that I had fluxional equations in those days, but also that I had then carried the inverse method of fluxions to a great degree of perfection. The second method is now claimed from me by Mr Leibnitz For in h is aforesaid Postscript he s allows that I preceded him in the method of series, but he adds that at length he found a general method for series & after that he had no further need of my extractions. This General method he described in the Acta Eruditorum for April 1693 pag. 178. And it is the same with mine wthwith mine. [I do not know that he hath any pretence to any part of the method of Series. & therefore he ought to He invented indeed a transmutation of figures All that he can pretend to is He found indeed a transmutation of figures for doing that by division wchwhich might may be better done without it: But this transmutatationtransmutation is no But the division is not his.]
He came to London the second time in NOctober 1676 but & before he went from thence into t into Holland he Mr Collins shewed him a part of his correspondence wthwith Mr Gregory & me & as he tells you in his Postscript. And amongst there he saw mey aforesaid Reply or Letter of 24 October 1676 just then received by Mr Oldenburg & put into the hands of Mr Collins, I suppose to be copied. For he tells you that he observed in the corresponden papers which Mr Collins shewed him he observed that I acknowledged my ignorance in many things & said among other things that I had found nothing about the dimension of the celebrated Curves besides the dimension of the celebrated Curves Cissoid. And this passage is in the said Letter of I 24 Octob 1676. Whether Mr Collins did not at the same time shew him my Analysis may be doubted. For that Analysis was the fountain of all thaet correspondence about Series. He complains that all this passage about my pretended ignorance was omitted by the Committee of the R. Society, & gives this as an instance of the corruption partiality of the Committee in not printing things the Letters entire. But he accuses them unjustly injuriously for the passage is printed entire in the Commercium Epistolicum pag. 74. My Letter of 10 Decem. 1672 is printed entire And The Letters of Mr Leibnitz dated 15 Iuly 1674, 26 Octob 1674, 12 Iuly 1675 28 Decem 1675, 27 Aug. 1676, 18 Novem 1676, 21 Iune 1677 & 12 Iuly 1677 & those of Mr Newton dated 123 Iuly Iune 1676 & 24 Octob 1676 have been printed entire by Dr Wallis withou by the without any dispitute arising upon them & they that please to compare them with the excerpta taken out of them by the Committee will find that nothing of the R. Society will find that nothing of moment has been the Questi to the controversy has been omitted by them. And thoseat of Mr Oldenburg dated 15 Apr. 1675 & those of Mr Leibnitz extant in his own hand writing & extant in his own hand writing & dated 20 May 1675 & 12 May 1676 have been examined by the Origin collated with the extracts in the presence of many Gentlemen of Germany Italy France & England you your self being present, & one of them. And these being all the Letters of Moment (for those of Mr Collins written in the years 1669, 1670, 1671 & 1672 were were only to show how free he was in communicating the Series wchwhich he had received from me & Mr Gregory) it is evident that the complaint of Mr Leibnitz against the Committee of the R. Society is very frivolous & injurious injurious. And what he saith against the interpretations put upon the Letters, being only in general terms deserves no answer.
Mr Leibnitz in his aforesaid PoscriptPostscript saith that it iswould have been easy for me to have found out the differential method if I had notis it had been hinted to me. And this is an acknowledgment that it was easy for him to find it out by the light wchwhich I gave him into it. For I in my Letter of 24 Octob. 1676 I hinted the method to him very plainly & said it was obvious. And I gave him so much light into it that Dr Wallis in the Preface to the two first Volumes of his works printed above 20 years ago said that in my two Letters written that year in the year 1676 I explained to Mr Leibnitz that Method found by me ten years before that year or above. And Mr Leibnitz in the Letters wchwhich followed thereupon between him & the Doctor Wallis did not deny what the DrDoctor had affirmed, nor blame him for it nor made the least dispute about it, but said only that he had added to my method as Des Cartes had added to yethe Analysis of Vieta.
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To Conti? about Desmaiaux
SrSir
The writing of Letters It requiring some time to write Letters receive answers & doing what else you & I were discousingdiscoursing about about this morning in order to before yethe plublishing of the Letters of Mr Leibnitz his Letters requiring some time: I beg the fauvour to signify to yoryour Bookseller that if he pleases to deferr publishing them till Lady next I will give him twelve Guineas for as a recompense for the loss of his time. I am
YorYour humble Servant
Is. Newton.
13571
SrSir
The more I consider the Postscript of Mr Leibnitz the less I think it deserves an answer. For it is nothing but a piece of railery from the beginning to the end. He saith that that the English would be the soulle Inventors & another man may say that they would migh be be so if Mr Leibnitz would let them keep their inventions. He saith that it doth not appear that I had the differenti infinitesimal Characteristique lef & Analysis before him, but he has accused me of plagiary it lies upon him to prove that he ha he is to prove against me that he had it before me. For he has accused me of plagiary before the R. S. & by the laws of all nations he is guilty of calumny if he doth not prove his accusation. He appeals to the judg from the judgment of the Committee of the R. S. to the judgment of Mr Bernoulli but Dr Keill hath shewed in but Bernoulli but Bernoulli a jud but he has corrupted Bernoulli but Dr Keill has proved that Bernoulli has acted very But N Bernoulli claims a share wthwith Mr Leibnitz in the Inve infinitesimal method, & Dr Keill hath shewed that Mr Bernoulli hath erred & Dr Wallis above 20 years ago gave a contrary judgment. & Dr Keill hath shewed that. He saith that it was easy for me to have found the Method before him if it had been notified to me: & Dr Wallis said above 20 years ago that I notified explained it to Mr Leibnitz in the year 1676.. He saith that the Committee of the R. Society have misinterpreted attacked his candor by misrepresentations, but & that he will not answer their little reasons: but thethey that read the Papers printed by them Committee wthwith their Observations upon them will find that the interpretati whole is matter of fact which admits of no answer. He complains that th in falling upon series they go from the fact, but the Question is whether Mr Leibnitz or I be guilty of Plagiary & what they say about series is very apposite to decide that Question He insists upon his own candor & gives his testimony for himself endeavours to make himself a witness in his own c & they speak to the credit of the witness. HO On the other hand he himself is guilty of what he complains of in others. For he goes from the fact both when he falls foul upon my Philosophy, & when he sends mathematical Problems to try who was the best Mathematician 45 or 450 years ago when he knew nothing of Geometry. He saith allows saith that I invented series before him but at length he found a general method after wchwhich he had no further need of my extractions. But I thatis general method is mine. It is mentioned in my Letters of 13 Iune & 24 Octob. 1676. He complains that the Comittee of the R. S. did not print the Letters entire as Dr Wallis did with his consent: but it would have been impertinent to print what did not relate to the matter in hand. He saith that when he came to London with his the second time (wchwhich was in Octob. 1676) he saw in the hands of Mr Collins a part of his Commerce d with me & Gregory, & there he observed that I acknowledged my ignorance in many thisngs & particularly that I had said that I had found nothing about the dimension of the celebrated Curvi-linesaars besides theat of the Cissoid: & that the Committee had supprest all this. This He alledges this as an proof instance that they had acted partially in omitting things which made against me. But he injures them. For you will find all this printed in the Commercium Epistolicum pag 74, & I am not ashamed of it. It is a part in my Letter of 24 Octob. 1676 & therefore he saw that Letter in the hands of Mr Collins before he left London. And he might at the same time see my Analysis wchwhich Dr Barrow in the year 16769 communicated to Mr Collins, & in wchwhich my method of moments & fluxions was described.
After this he falls foul upon my Philosophy, & opposes that is upon the Philosophy of the ancient Greeks & Phenicians & Greeks as if they had introduced miracles & occult qualities. And to make this out he & tells tells you that they introduced they introduced miracles & occult qualities that all the actions of God are miracles the he has proved to Mr Bayle that [all the actions of God are miracles or wonders even tho they happen constantly & by reason of their con happening constantly create no wonder, that is, he has proved that the word miracles signifies constant events wchwhich create no wonder] tells you that he has proved to Mr Bayle that the word Miracles signifies not only wonders but also constant events, such as wchwhich by reason of their constancy create no wonder. And He tells you also that God cannot be in the world without animating the world tho a mans soul according to his Philosophy doth not animate his body. He accuses me as if I said that the world was God had a sensorium in a literal sense. He pretends that all places not filled with tangible bodies may be filled with an intangible corporeal fluid, that its the fault of yethe workman & not of the Watch that it will at length cease, & that it would be the fault of Gods fault if the world should ever want an amendmente That He commends Experitall PhilophyExperimentall Philosophy & yet adheres to such Hypotheses as can never be proved by experiments nor have any place in & brings them his hypotheses as arguments against things proved by from experiments by means of the argumtargument of Induction & thereby endeavours to overthrow that Philosophy, & then to set up in its room a heap of precarious Hypotheses wchwhich are nothing better then a Romance.
But I beg leave to acquaint you that its almost 40 years since I left of writing Letters about Mathematicks & PhilophyPhilosophy & twenty years since I left of those studies. And therefore I cannot now suffer my self to be engaged in disputes of this kind; especially since they are nothing to the Question in hand,, about the infinitesimal method, [for understanding of which I have hereunto aed the history of the infinitesimal taken from the Commercium Epistolicum & other authentic Records] I am And For understanding this Question more flullyfully I must referr you to the Commercium Epistolicum it self & to the Account given of it in the Phil. Transactions & the Answer of Dr Keill to the Libel published in Germany & Holland against the Committee of the R. S.
After th
He falls foul upon
He accuses me & by consequence the ancient Phenicians & Greeks for intr as if they had introduced miracles & the occult qualities Ph of the Schoolmen into Philosophy. And to make this appear he tells us that he has proved to Mr Bayle that the word Miracles, that is wonders, includes the laws of God imprest by God upon nature tho by their constant acting they create no wonder, & that the words occult qualities do n signify qualities wchwhich are manifest to us if their not occult but whose causes be occult tho qualities be never S very manifest. He saith that God must be Intelligentia supramundana because if he were in the world he would be the soul of the world that is he would animate the world, & yet according to his Philosophy of an Harmonia præstabilita the soul of a man doth not animate his body He accuses me of as if I affirmed that God hath a Sensorium in a litteral sense. He saith that I have not demonstrated uni a vacuum nor universal gravity nor Atomes. But he never demonstrated any thing in Philosophy himself, & he denyes Conclusions without shewing the fault of the Premisses, & never demonstrated any thing in Philosophy himself, & & means that the Argument of Induction from Experiments upon wchwhich eperimentalexperimental Philosophy is grounded is not a good one. For I never attempted to demonstrate any thing universally in natural Philosophy by any stronger argument then that of Induction from Experiments, nor And as for Atomes I never attempted to to demonstrate Atomes them by this Argument, but put them amongst a set of Quæres. He saith that Space is the order of coexistences & time the order of successive existences: I suppose he meanes that space is the order of coexistences in space & time the order of sucscessive existences in time, or that space is space in space & time is time in time. He saith insinuates that its is the fault of the workman & not of the materials that a Watch will at length cease to go & in like matnner that it would be Gods fault if the world should ever decay & want an amendment. And by the same way of arguing a man may say that it would be Gods fault if matter doth not think or if humane bodies want a Soul. He applauds Experimental Philosophy but recommends Hypotheses to be admitted into Philosophy in order to be examined by experiments: whereas he should propose not HypothesHypotheses b to be admitted but Questions to be examined & decided & decided by experiments –572 experiments before they are admitted into Philosophy. ✝ And ✝ And whilst he comm applauds experimental Philosophy & cries out against miracles, he introduces an Ha Hypothesis of an Harmonia præstabilita wchwhich [is contrary to the daily experience of all Mankind &] would cannot be true without an incredible mairacle, & which is contrary to the daily experience of all mankind who find For all men find by experience that they can move their bodies by their will, & that they hear & see & hear & feel by means of their bodies. [He is of opinion that space void of all tangible body may be full of a corporeal intangible fluid whereas plato the Ancients beleived that all things intangible were incorporeal. By tangibility I understand tangibility not in a mathematical but in a physical sense, such a tangibility as by some resistance can affectsaffect the sense of touching.] He glories in the number of disciples, but should consider you know that he has spent his life of making them by a general correspondence whilst I leave truth to shift for it self. For its almost 40 years since I left of wr all correspondence about MathMathematicks & Philos.Philosophy & about 20 since I left of these studies. And for that reason I hope you will pardon me if I am averse from being engaged in disputes of this kind.
He sends you also Mathematical Problemes to be solved by the English Mathematicians. And all this is nothing else then an amusement for avoiding instead of to avoid proving his accusation against me & returning a fair answer to the matter of fact wchwhich has been published by order of the R. Society. If he pleases to return such answer, I desire that he will be sconstant to himself & continue to acknowledg whatever he acknowledged above 15 years ago & not contradict what he did not contradict in those days;, or else to forbeare telling us boasting of his candor, By his Letter of he acknowledged the recieptreceipt of Mr Oldenburgs Letter of & expect that he continue to acknowledge it still. By his Letter of he acknowledged that he had not then the method of finding a series for the arc whose sine was given, & I expect that he acknowledg it still.
He complains that in falling upon series they go from the fact: but & yet he himself goes from the fact both in falling foul upon my Philosophy & in sending a Probleme to try who was the best Mathematician 45 or 50 years ago before he when at which time he understood nothing of the Geometry The Question is whether about Mr Leibnitz's candor & mine & if he claimed one of my Series as invented by himseflf & after two years before he had the met & afterwards wrote to Mr Oldenburg for themy Method to procure & send to him the method of inventing it; if he received from London a series fr invented by Mr Gregory & afterwards published it as his own: the world by these things instances may judge of his candor in being silent 20 years ago when Dr Wallis told him that I had found it by my Letters in the year 1676 explained to him the metho method of fluxions found by me ten years before or above & now claiming it from me. pretending that he was the first inventor. He saith that I invented Series before him
Dr Wallis died in October 16703, the last of the old men who w knew what had passed between Mr Leibnitz & me by means of Mr Oldenburg. And soon afterwards I was accused in the Acta Eruditorum & before the R. Society as a plagiary who had taken the method from Mr Leibnitz. And when the R. Society caused the ancient Letters & papers extant in their Archives & Letter Books & in the Library of Mr Collins to be published, all wchwhich are unanswerable matters of fact; instead of a fair Answer answering the same in a fair manner, & proving his accusation of plagiary a defamatory Libel dated 29 Iuly 16713 was published in Germany against them the R. Society me in Germany without the name of the Author or publisher or City where it was published, & dispersed over Germany France & Italy, & the Libel it self represents that Mr Leibnitz set it on foot. And to avoid Ans A And henc instead of proving his accusation he goes on to write defamatory L wrangling Letters.
In the Latter part of his Postscript he falls foul upon my Philosophy as if I (& by consequence the ancient Phenicians & Greeks) introduced Miracles or Wonders into Philoso & occult qualities. And to make this appear he gives the name of miracles or wonders to the laws aimprest by God upon nature tho they by reason of their constant working they create no wonder, & that of occult qualities to qualities wchwhich are not occult but whose causes are occult tho the qualities themselves be very manifest.
110/573
SrSir
The more I consider the Postscript of Mr Leibnitz the less I think it deserves an answer. For it is nothing but a piece of railery from the beginning to the end. He saith that it doth not appear that I had the Infinitesimal Characteristique & Calculus before him; but he is to prove that he had it before me. For he has accused me of plagiary before the Royall Society, & by the Laws of all nations he is guilty of calumny if he doth not prove his accusation. He appeals from the judgment of the Royal Society to the judgment of his friend Mr Bernoulli: But Mr Bernoulli claims an interest in the Infinitesimal method Dr Wallis gave a contrary judgment above 20 years ago, & Mr Bernoulli is allowed an interest in the Differential Method by Mr Leibnitz & vales himself upon it without being contradicted till of late, & Dr Keill hath proved that Mr Bernoulli hath erred. Mr Leibnitz saith that it was easy for me tohave found the Method before him if I had been advised of it: And Dr Wallis published above 20 years ago that I explained it to Mr Leibnitz in the year 1676. He saith that the Committee of the Royal Society have attaqued his Candor by misrepresentations, & that he will not answer thiseir little reasons: but they that read the Papers printed by the Committee with their Observations upon them, will find that the whole is matter of fact which admits of no answer. He complains that in falling upon series they go from the fact, & yet he himself goes from the fact both in falling upon my Philosophy & in sending a Probleme to try who was the best Mathematician 45 or 50 years ago, at which time he understood nothing of Geometry. The Question is about the candor of Mr Leibnitz & me . And if he claimed one of my Series as invented by himself, & afterwards wrote to Mr Oldenburg to procure & send to him the Method of inventing it; if he received from London a Series invented by Mr Gregory, & afterwards published it as his own: the world by these instances may see judge of his candor in pretending now to be the first inventor of the D Infinitesimal method, which he did not pretend to till of late. For notwithstanding that 21 years ago when Dr Wallis had published that I by my Letters in the year 1676 had explained it to him Mr Leibnitz the infinitesimal method found by me ten years before or above & given noth him notisce hereof to Mr Leibnitz, he found no fault with what the DrDoctor had said nor pretended to any thing more then that he had added some things to my Method He saith that I invented Series before him, but at length he found a general method after wchwhich he had no further need of my extractions: But this general Method is mine. It is mentioned in my Letters of 13 Iune & 24 Octob. 1676. He complains that the Committee of the Royal Society did not print the Letters entire as Dr Wallis did with his consent;: whereas & yet it would have been impertinent to print what such parts of the Letters as did not relate to the matter in hand. He saith that when he came to London the second time (which was in October 1676) he saw in the hands of Mr Collins Mr Collins a part of his Commerce with me & Mr Gregory, & there he observed that I acknowledged my ignorance in many things & particularly that I said that I had found nothing about the dimension of the Curvilinear figures besides that of the Cissoid, & that the Committee had supprest all this. He alledges this as an instance that I they had acted partially in omitting things which made against me. But he injures them. For you will fintd all this printed in the Commercium Epistolicum pag. 74, & I am not ashamed of it. It is in my Letter of 24 Octob. 1676, & therefore he saw that Letter in the hands of Mr Collins before he left London. And he might at the same time see my Analysis wchwhich Dr Barrow in the year 1669 communicated to Mr Collins, & in wchwhich my method of moments & fluxions was described before Mr Leibnitz knew any thing of Geometry.