Notes on the Correspondence in Wallis's Works, Vol. 3
p. 258 lin, {illeg}5|4|. Facuit Newtonus pacis gratia, et seriem Gregorij Leibnitio \quæ \Coll{ini}us &/ Oldenburgus cum Leibnitio {illeg}/ tunc communicabat igno\ra/vit. Supra (impressa sunt Newtoni Consulat Lector Epistolas Newtoni {illeg}ss{illeg} p{illeg}am fuisset tunc ignoravat. /supra impressas.\
ib. lin 11. \Meditationes illæ/ A methodo fluxionum et æque nascebantur et prius nascebantur:
ib. lin 19. \Lineæ illæ/ Newtoniana primum methodo primum med|t|hodum æquationibus æquationibus finitis sunt expressæ {illeg}|&| sub leges Analyseos redactæ. Vide supra, pag.
p. 258 lin. 4. Facuit Newtonus pacis gratia, et quæ Collinius & Oldenburgus \eo tempore/ cum Leibnitio communica{illeg}|ba|nt\verant/ ignoravit. Tantum abest ut Leibnitius Postulabat Leibnitius methodum perveniendi ad series \quas acceperat{illeg} ab Oldenburgo acce quus a/, et quamprimum methodum illam acceperat cœpit a Newtono, cœpit series per methodum illam \illam/ inventas sibi arrogare.
p. 258. lin 4 Facuit Newtonus verbi pacis gratia. & sed i|I|n epistolis illis \suis/ Leibnitium primum esse methodi \vel/ methodi quam differentialem vocat inventorem esse primum minim{illeg} nam vel methodi serierum primum esse inventorem nullibi agnovit, Et series suas \Certe Leibnitius series Newtonianas/ et Gregorianas Anno 1675 & forte {an}{illeg} ad ipsum missas \ab Oldenburgo accepit/ fuisse ignorab|v|{illeg} tunc ignoravit \{illeg}ivit/. Certe Leibnitius \& unam earum earum {sic} pro sua ventavit, et/ anno proximo methodum \primum ind. ad/ series {illeg} \illas/ ad se mitti postub|l|a{illeg}|bi|t{illeg}, & seriem Gregorianam ad se missam pro sua venditavit. \Quæ omnia Newtonum lutebant./
ib. l. 11. Quasi methodo fluxionum nihil debeatur.
ib. l 19. Non primum Quasi Leibnitius ignoraret Newtonum methodum fluxionum prius invend|t|um fuisse. \Newtonum hæc omnia/ hæc omnia præstare per methodum fluxionū ib. l. 29. præstari & Newtonum prius præstare potuisse. Vide ejus Epistolas p & , et Analysin p.
ib. l. 19 Hæc Leinbitius, \quo est candore,/ sub nomine Editorum Actorum.
p. 259. l. 3. Quadraturam aut per seriem infinitam a D. Brunkero inventam Mercator per divisionem Wallisianam tantum demonstravit & ut supra nihil præterea.
Pag. 645|54| lin. 4. Ignoravit Wallisisus {sic} Gregorium hanc seriem cum anno 1671 cum Collinio Oldenburgum Anno 1675 cum Leibnitio communicasse, & Leibnitium in Anglia fuisse anno 1673 ubi methodus veterum \Collinius \de methodo serierū \lib{e} loqui &// series \aliquas/ cum amicis \libere/ communicare c{illeg}p{illeg}t/ ubi {sic} Collinius de methodo serierum libere loqui {illeg}|c|œperat et series aliquas cum amicis communicare.
Pag 673. lin. 15, 16, 19. Annon Newtonus hujusmodi æquationes prius invenit qui docuit fl{illeg}|u|entem ex æquationi|e|bus fluxionem simul involvente extrahere? /Annon tota fluxionum methodus inversa, ubi de Curvis agitur, pendeat ab hujusmodi series æquationibus ad Curvas applicata|i|s. Annon Newtonus Curvas omnes mechanicas ad æquationes reducere docuit pergendo ad ab hujusmodi æquationibus finita|i|s ad series infinitas.\ vide pag 86. Interea Nicolaus Mercator . . . . . non possunt.
Pag 674. Literas tuas . . . . . . . nam secus est. — Vbi dicitur Nicolaum Mercatorem . . . . . . . . sed res eadem est. — Et ni faller (sic \saltem/ mihi nunciatum est) . . . . . . . . . præjudicio esse debet.
Ad p 675 l. 4{4} 38. \Ipsa/ Series \ipsa/ quæ N. Mercatori passim {illeg} toties tribuitur a |D.| Brunkero primum inventa fuit – ut supra dictum est.
Pag 679 Methodum fluxionum . . . . . differunt in nonnullis.
Ad pag 679 lin 20. Hoc advertit & agnovit Leibnitius \Quasi Leibnitit|u|s hoc non advertisset/ Anno 1677 ubi primum {illeg}dit \incidit/ in methodum Newtoni|?| ut \Vide/ literas ejus supra impressas pag leguit patebit pag. 17, 18, \Vide etiam pag 18, 19, 52./ Sed nunquam adduci pot{illeg} \pag 90, 91. Cæterum/ Newtonum primum esse inventorem nunquam agnovit. Et quamvis D. Wallisius sæpius incul{illeg}t caret methodos \utrius/ rem eandem esse vel quam simillimam, adduci tamen non potuit Leibnitius ut differentiam aliquam \realem/ assign\ar/et. Si Newtonus est primus inventor, med|t|hodus ipsi deb\eb/itur. Si Leibnitius aliquid addiderit hoc erit Leibnitianum. Doceat igitur tandem Leibnitius quid addiderit huic methodo ac desinat tandem methodum {illeg} sibi arrogare, {illeg} nisi nomen m{ethodum} fluxionum New{illeg}
Pag. 681. Optaverim item ut . . . . . . intelligamus
Ad pag. 681 lin. 17. Vt Leibnitius quid suum sit exponat Wallisius iterum postulat sed frustra.
Newtono relinquere. Methodum differentialem Moutoni \olim/ sibi \olim/ arrogavit.. {A} {illeg} D. Pellio ob id reprehensus. In {illeg} Reductionibus æquationum ad radices non affectas Gregorius & Tschurnhausius. olim s{illeg}d Cum Gregorius et Tschunhausius in reductionibus æquationum ad s{illeg} radices non affectas occupati esset; ipse eos prævenire conatus est ob id reprehensus a Collinio. Cum Newtonus methodum serierum invenisset \& Leibnitius/ ipso sero ab \Collinio/ Oldenburgo et Mohro series aliquas accepisset \& spatio/ omni|e| toto \unius/ methodum perveniendi ad series illas invenire non potuisset; postulavit ab Oldenburgo meth {illeg}|od|um d|a|d se mitti, et interea serierum \acceptarū/ unam (quam forte per methodum trans{illeg} divisionem invenire didicere transmutationem figurarum invenire didicerat) pro sua {vulgo} cum amicis in Gallia communicare cœpit. Deinde accepta methodo generali Newtoni series alias per methodum illam inventas, mutatis s{illeg}{illeg}|(|levi facta mutatione) sibi rapere conatus est, et in Actis Leipsicis se inter inventores serierum passim numerat {illeg}, ob id merito reprehendus. Ex litteris Newtoni ad Collinium et Newtonum \Oldenburgū/ missis, noverat Newtonum in methodum incidisse ante annum {illeg} 16 Anno 16711 librum de methodo serierum & me{t} alia methodo alia {illeg} huic affini solvendi problemata difficillima & \cum/ ex characteribus & exemplis methodi illius per Newto ipse tand anno 1677 in eandem methodum incidit, Newtonum prævenit & anno 1684 pro et methodum ob id merito reprehen et methodum pro sua venditat.
ib lin 27 Litera Newtoni primam lucem affuderant.
Ib lin 27 Hæc et quæ sequuntur Leibnitius ante annum 1677 minime advertit. Et Literæ Newtoni primam lucem afuderant. Anno 1676 credidit inversa tangentium problemata ad æquat et similia ad æquationes reduci non posse.
And the Letters & Papers wch follow shew it appears that in the year 1671 at the desire of his friends he composed a larger Treatise on ye {illeg} this method (p ) ) that it was very general & easy without sticking at surds (p ) & extended to problemes of Tangents direct & inverse (p ) & to the finding the lengths areas lengths ce{illeg}|n|ters of gravity & curvatures of curves & solving other more difficult problems (p )② that it extended to the extracting of fluents out of equations involving their fluxions (p )③ & proceeded in difficulter cases by assuming the terms of a series gradually & determining them by the conditions of the Probleme (p )① that in Problemes reducible to Quadratures it proceeded by the Propositions since printed in the bok|o|k of Quadratures (p ) that it \extended to mechanical curves & (p ) & was/ was {sic} so general as to extend to almost all Problemes except the numeral ones of Diophantus & such like (p ) [& that it proceeded in \extended to/ mechanical curves as well as others (p ) {illeg} & by consequence proeeded by the consideration of the in\de/finitely {illeg} small particles of quantity called Indivisibles by Cavallerius & Leibnit Augmenta momentanea & momenta by Mr Newton, Infinitesimas & Differences by Leibnitz. For there is no other way of drawing Tangents to Mechanical curves or find of finding the areas lengths centers of gravity & curvatures of any Curves then that of \by/ considering the moments or infinitesimal particles of Quantities & their proportions to one another.] And all this was found out by Mr Newton before Mr Leibnits knew any thing of the method. For when Mr Oldenburgh had sent him some of the series found out by this method, the next year he desired Mr Oldenburg to procure him the method (p ) & in his Letter dated 27 Aug 1676 he wrote that he did not beleive that Mr Newtons method was so general. For, said he, there are many Problemes & particularly the inverse Problems of Tangents that cannot be reduced to {illeg}|æ|quations or quadratures (p ) & in the years 1675 & 1676 he wrote \communica/ a piece of this se \in a vulgar manner/ concerning a series which he had received of that year of Mr Oldenburg & continued to polish it the next year (p ) but after he found out the Differential method, thought it not worth publishing p. In all the Letters In all the Letters & papers there is not one word of his knowing the Differential method before his The first The first mention of his knowing the Differention is in his Letter of 21 Iune 1677. There he began to {illeg} In all these Letters & Papers there appears nothing of his knowing \finding/ \or knowing/ the Differential Method before ye year 1677. It is first mentioned by him in his Letter of 21 Iune 1677, & he began his description of it with these words. Hinc nominando IN PSTERVM dy differentiam duarum proximarum y &c. p 88.
If it be said that Mr Leibnitz notwithstanding \notwithstanding these things/ might find out the method apart & so far have a \some/ right to it as he was a second Inventor: it must be considered that \the/ first Inventor hath the sole right till another a second Inventor arises, & no mans right to any thing is to be taken from him without his consent \it would be is an act of injustice to take away any mans right to any thing/ & divide it between him & others \without his consent/, besides that to do it in this case|s| \of this nature/ would encourage P{er}|re|tenders & per perpetually imbroyl the first inventors in disputes with contentious people. But however it doth not appear that Mr Leibnitz invented the method \alone/ without receiving \some/ light from Mr Newton.
For he had se at his request Mr Newton communicated to him one half of the method in plain words in his Letter of 13 Iune 1676, \namely/ that half wch consists in the invention of ser inf reduction of Problems to infinite series so far as he could describe it without mentioning \discovering/ the other half. For he concealed \his Theorems for Quadratures derived from the other part of it &/ his he way of extracting fluents out of Equations involving their fluxions \(p. 56/. & Mr I. Gregory by having . . . . . . . . & how he derived reciprocal series from one another. About the
Abou Mr Newtons Letter of 10 Decemb 1672 was also sent him about the same time (p. 30, 47) in wch \Letter/ he had a general description of the method wth its large extent & an example of it in drawing of Tangents to mechanical \Geometrical/ curves & was told that this method of Tangents was but one particular or Corollary of the general method. And by this method he un Letter he understood \also/ that Mr Newtons method was agreed wth that of Slusius but was much in Geometrical Curves but was more general in extending to mechanical Curves & not sticking at radicals. And after th{is|e|} sight of this Letter, D his mind ran upon the improvement of Mr Slusius method; p 87, 88.
Mr Newton also in his two letters of 13 Iune & 24 Octob 1676 \mentioned some Propositions in his book of Quadratures &/ gave him a notable of example of his method in \a Rule found by it for/ the squaring of Curves & another notable example in the inverse method of Tangents & let him know that this method was so general that it extended to almost all Problemes except the numeral ones of Diophantus & such like. \✝/ {illeg} ✝ He told him also that his method extended to mechanical curves as well as others. (p. 5|3|0, 52, 54) whence it was obvious to conclude that it lay in proceeded by the consideration of . . . . . . proportions to one another. And And now \when/ he had discovered \communicated/ one half of his method in words at length & made so large a description of the other half as endangered the losing it; to secure it th to himself till he could have time to communicate it in open words at length he concealed |it| in ænigmas. And yet he discovered by circumstances what he thought to have concealed
pag 673. Intere Nicolaus Mercator . . . . . . . promittere non possum.
Ib. Ad lin. 15, 16, 19. Annon Newtonus hujusmodi æquationes prius invenit qui docuit fluentem ex æquatione fluxionem involvente extrahere, & Curvas ar{ea}s Mechanicas ad series inf æquationes reduxit pergen numero terminorum infinitas reduxit pergendo ab hujusmodi æquationibus finititis? Annon tota fluxionum methodus inversa ubi de Curvis agitur pendeat ab hujusmodi Curvis æquationibus ad Curvas applicatis?
Pag 674 & 675. Literas tuas . . . . . . . . . nam secus est. — Vbi dicitus {sic} Nicolaum Mercatorem . . . . . . . . . . . . . . . . Quod tamen neutri prejudicio esse debet.
Ad p 675 l. 38. Series ipsa quæ D. Brunkero tribuitur M Mercatori tribuitur, a D. Brunkero primum inventa fuit ut supra dictum est.
Pag 679, 670 Methodum fluxionum . . . . . . . . . . vellim non fraudari posteri \sed publice quo est professus./
Ad p 679 lin 20. Quasi Leibnitius hoc non advertisset anno 1677 ubi primum incidit in methodum Newtoni. Vide Literas ejus supra impressas pag. 90, 91. Cognationem methodorum & Newtono deberetur \et methodum fluxionum Newtoni ante quod ant|n|num 1671 inventam fuisse/ agnoscere debuit Anno 1684 ubi primum med|t|hodum differentialem in Actis Leipsicis exposuit, {illeg} {Et}.
Ib lin 24. Hic agnoscere videtur Leibnitius methodum utram esse unam et eandem paucis exceptis, sed inter ideo communi nomine Analyseos infinitesimalis a se designari, differre tamen in nonnullis. Quatenus inter s{e} una et eadem s non different, methodus erit primi tribui debet inventori primo, quatenus differunt, aliqua erunt addita ad Inventore secundo
Ad pag 679 lin 20. Quasi Leibnitius hoc non advertisset anno 1677 ubi primum incidit in methodum Newtoni. Vide Literas ejus supra impressas pag 90, 91. Certe methodum Newtoni ante annum 1671 inventam fuisse ex literis ejus \Leibnitius/ intellexit|erit| (pag ) sed in Actis Leipsicis hoc nunquam agnovit. Vide supra pag. 70, 71, 72.
Ib. lin 24. Quæritur, quis sit methodi hujus Analyseos hujus infinitesimalis addidit {illeg} Nam \Certe Newtonus tractatus hoc titulo insignitum Anno {illeg} supra impressum anno 1669 cum Collinio communicavit/ |Nam| At Leibnitius methodum totam \{illeg}/ subo nomine methodi differentialis sibi arrogatus assumit & nil nisi nomen nudum methodi Infinitesimalis \fluxionum/ Newtoni relinquit. Ad Et adduc non potest at differentiam det{illeg}bat |relinquere conatur.| Ib lin 26 Novimus quid Cartesius \addidit/ {illeg}|A|nalysi Vietææ, addidit dicat \tandem/ Leibnitius quæn{illeg} quid ipse Analysi addidit Analysi fluxionum.
Ib. lin 27. Literæ Newtoni primo Leibnitio Consideratio Literarum Newtoni incidit in methodum quam i{illeg} differentialem vocavit. Newtoni primam lucem \{Leibnitsio}/ affudera{n}t \Leibnitio/. His admonitus et exemplis quibusdam methodi fluxionum adjutus incidit in methodum differentialem Leibnit quam \nomine methodi/ differentiale|is|m vocavit a summatorio distinxit.
Ib. lin 35. {illeg} Anno 1676 Leibnitius /Leibnitius ante 1676|7| – – – – –\ hoc non vidit. Scripsit enim \anno 167/ {illeg} inversa tangentium problemata \& alia multa/ ab æquationibus non pendere. Rescripsit Newtonus hujusmodi problemata in potestate esse \nempe/ per æquationes sui|a|s. Et tum demum Leibnitius a Newtono admonitus hæc vidit. Vide pag. 65 lin 14.
Ib p 679 lin 49. Novit Leibnitius se primum Quando d Diu ante receptum ejus calculum Mirum est hæc a Leibnitio dici, qui novit legerat \ex/ literas Newtoni intellexerat methodum solvendi hujusmodi problemata {illeg} ante annum 1671 Newtono innotuisse, & Newto hunc primum a Vide supra pag. 71 lin 1 Certe \Sed et/ Newtonus etiam \ex Libro e Principijs ejus ipsum primum noverat ipsum primum/ per hanc methodum problemata pri{mu}s \felicitur/ tracta{illeg}it|sse| quæ ad transitum p{illeg}|er|tinet ad|a| Ge\o/metria ad Naturam.
Ib. lin {illeg}{5} 54. Hugenius Literas quæ Newtonum et Leibnitium mediante Oldenburgo intercesserant nunquam vidit.
Ib l. 24. Methodum fluxionum et Methodum differentialem esse \nonnullis quidem differre sed |licet in nonnullis differre possu|i|nt esse tamen|/ unam et eandam methodum hic agnoscit Leibnitius & ideo se communi, nomine designare solere Analyseos infinitesimalis, \licet in nonnullis differre possint ut Analysis Vietæ et Analysis Cartesij in nonnullis differunt/ Quæritur qu Quæritur quis sit methodi hujus \infinitesimal{illeg}/ inventor primus & quid alter alterius c|i|nventis addidebit. Novimus quid Cartesius addidit Analysi Vietæ, dicat tandem Leibnitius quid ipse addidit Analysi fluxionum.
<13r>Pag 673. Interea Nicolaus Mercator \Secuti sunt hos Iacobus Gregorius/ . . . . . . . . . . . promittere non possum \{illeg}/.
|1)| A{illeg}|d| lin. 10. Mercat{illeg}|o|r quadraturam D. Brunkeri per divisionem Wallisianam tantum demonstravit ut supra.
|2)| Ad lin 15, 16, 19 Leibnitius recitando inventa \nova/ Mathematica, prætermittit methodum fluxionum, quasi Analsis tota infinitesimalis sola sua opera accesserat.
|3)| Ad lin 19|7|, 18, 19. Annon Newtonus hujusmodi æquationes prius invenit qui docuit fluentem ex æquatione fluxionem involvente extrahere & Curvas Mechanicas ad æquationes numero terminorum infinitas reduxit pergendo ab hujusmodi æquationibus finitis? Annon tota fluxionum methodus inversa ubi de Curvis agitur, pendeat ab hujusmodi æquestionibus ad Curvas applicatis?
Pag. 674, 675 Literas tuas . . . . . . . . . . . nam secus est, — Vbi dicitur Nicolaum Mercatorem . . . . . . . . . . . Quod tamen neutro præjudicio est|s|e debe{illeg}t.
Ad p 675 l. 38 {illeg} Diximus Quadraturam per seriem infinitam quæ Mercatori tribuitur, non esse Mercatoris.
Pag. 679, 680. Methodum Fluxionum . . . . . . . . sed publice quo est professus \/
|4)| Ad pag. 679 lin. 20. Quasi Leibnitius hoc non advertisset anno 1677 ubi primum incidit in methodum Newtoni. Vide Literas ejus supra impressas p. 90, 91. Certe methodum Newtoni ante annum 1671 inventam fuisse Leibnitius ex Literis ejus intellexerat, sed in Actis Lipsiensibus hoc numquam agnovit. Vide supra p. 70, 71, 72.
|5)| Ad lin 24. Methodum fluxionum et Methodum differentialem esse unam & eandem methodum Leibnitius hic agnoscit, ideo communi nomine Analyseos infinitesimalis a se designari solere, licet in nonnullis differre possint ut Analysis Vietæ et Analysis Cartesij in nonnullis differunt. Quæritur quis sit Analyseos hujus infinitesimalis inventor primus & quid alter alaterius inventis addiderit. Novimus quid Cartesius, & alij addidit Analysi Victæ: dicat tandem Leibnitius quid ipse addidit Analysi fluxionum.
|6)| Ad lin 27. Consideratio Literarum Newtoni primam lucem affuderat Leibnitio. His admonitus & exemplis quibusdam methodi fluxionum adjutus, incidit in methodum quam nomine methodi differentialis a {illeg}|m|ethodo summatoria distinxit.
|7)| Ad lin 35. Leibnitius hoc non vidit ante annum 1677. Scripsit enim anno 1676 inversa tangentium problemata et alia multa ab æquationibus non pendere. Rescripsit Newtonus hujusmodi problemata in potestate esse nempe per æquationes suas. Et tum demum Leibnitius a Newtono admonitus hæc vidit. Vide pag 65. lin 14.
|8)| Ad lin. 49. Mirum est hæc a D. Leibnitio dici, qui ex Literis Newtoni & Principijs Newtoni intellexerat methodum solvendi hujusmodi problemata Newtono ante annum 1671 innotuisse, et ipsum primum per hanc methodum problemata tractasse quæ ad transitum pertinent a Geometria ad Naturam.
|10)| Ad p. 680. lin 9, {sic} 10. Imo anno 1677. Vide pag. 94. 95.
Pag. 681. Optaverim item . . . . . . . intelligamus.
|11| Ad lin. 17. Vt Leibnitius differentiam methodorum exponat, iterum rogat Wallisius sed frustra.
