Notes on the Newton/Cotes correspondence of 1710 Isaac Newton c. 1,656 words The Newton Project Falmer 2012 Newton Project, University of Sussex

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 c 1713, c. 1,703 words, 2 ff. 2 ff. MS Add. 9597/2/18/79-80, Cambridge University Library, Cambridge, UK UKCambridgeCambridge University Library Macclesfield Collection MS Add. 9597/2/18/79-80 c 1713 England English Latin French Holograph Unknown Cataloguer MathematicsCorrespondence Daniele Cassisa started tagged transcription Catalogue information compiled from CUL Janus Catalogue by Michael Hawkins Proofed by Robert Iliffe Code audit by Michael Hawkins
79

By the a parcel of Letters wchwhich passed between me & Mr Cotes while he was writing the second Edition of the Principles, I find that the first 28 sheets of th of that Edition ending waith page 224, were printed off before April 15 1710 st. vet.stylo veteri And this I note that you may know that the alterations made in those sheets had no relation to the disputes about the method of fluxions but preceded them all ,. except that I caused the sheet In order to a third Edition I had have made an addit added to the XVIIth Proposition Lib. 1 the following words . Nam si corpus in his casibus revolvatur in Conica Sectione sic inventa, demonstratum est in Prop. XI, XII, & XIII quod vis centripeta erit reciproce ut quadratum distantiæ corporis a centro virium S, ideoqꝫue Linea quæsita PQ recte exhibetur Q.E.F. But I [When Mr N. Bernoulli was in London (wchwhich was in Autumn 1712) & told me that there was a falult in the resolution of Prob: III Lib. II, & that he look it be in trule of finding a mistakmistake in second differences; I answered that I would examin & tooldtold him the next time I saw him (wchwhich was within a day or two) that I had examined it the Resolution & found there was a mistake, but it lay in drawing the tangent of the Arch lC the wrong way from the wrong end of the arch. For the tangents of both arches lC & CG should have been drawn the same way with the motion of the body because they represent the moments of the motion . And I added I that I would cause that sheet to be reprinted. & I gave him also the scheme set right & the calculation suited thereunto, & added that I would cause that sheet to be reprinted. The Book of Principles was writ in about 17 or 18 months, whereof about two months were taken up with journeys, & the MSManuscript was sent to yethe R. S.Royal Society in Spring 1686; & the shortness of the time in which I wrote it, makes me not ashamed of having committed some faults & omitting some things These things I mentmeant] wchwhich words But I can strike them out if you think it may be better to omit them.

Nam vires centripetæ quibus corpus circa centrum S revolvi potest per ca.circa in his Lineis inventis revolvi potest eriunt reciproce ut quadratum distantiæ corporis a centro virium S, per Prop XI, XII, & XIII. Nam demonstratum est in Prop. XI, XII et XIII quod vis centripeta qua corpus in Lineis inventis revolvi potest, sit reciproce ut quadratum distantiæ corporis a centro. Inspicientido Literas Esp Epistolas quas a D. Cotes olim accepi, animadverto quod in editione secunda libri Principiorum quod LiberiLibri Principiorum mei ejus Editione secunda schedæ primæ 24. (id est usqꝫue ad Pag. 224 inclusive) impressæ fuerunt sunt ante 15 Aprilis 1710 st. vet.stylo veteri et propterea quæ alterationes in illis schdisschedis additæ vel mutatæ fuerunt id est antequam hæ lites cœperunt. Sed Et quod sub autumno anni 1712 cum intelligerem D. Nicolaus Bernoulli mihi significavereat emendari esse aliquam Propositioni in resolutione Prop X Prob. III Lib. II Princip. Propositionem illam iterum imprimi curabam. Propositionem illam iterum iprimiimprimi cura et Propositionem examinaveram; [respondi mendam in positione tangentis arcus Cl, et quod Propositionem illam iterum imprimi curarem Arcum utiqꝫue lC, CG a corpore projecto descriptorum tantangentes sunt Ck, CF exhibere debuissent momenta prima curvæ Lk a corpore descriptæ et propterea in eandem plagam cum motūum corporis duci.] eandem emendatam ipsi dedi et dicendo quod imprimari curavam Editionem Propositionem impressam ndum antequam ederetur , perinde emendari curarem. Inspiciendo literas quas olim a DnoDomino Cotes, interea dum Editionem secundam libri Principiorum curaret, ad me scripsit accepi, animadverto quod Schedæ prima viginti quatuor octo triginta septem (id est usqꝫue ad paginam 224 296 inclusive) impressæ fuerunt ante 15 Apr 30 June 1710, st st. vet.stylo veteri id est, antequam hæ lites cœperunt. [Et propterea Liber totus impressus fuit ante finem mensis Novembris 1712. Et sed Prop X Lib. II iterum imprimi curavi ad correxi a Jacubo Bernoulli a D. Nicolao Bernoulli de menda admonitus, Propositionem X Lib. II correxi ad incudem revcarirevocari, & iterūum imprimi curavi.] Sed momente tandem D. Nicolao Bernoulli quod Prop. X Lib. II error aliquis admissus fuisset in Lib. Prop. X, Lib. II. Constructionem Prop.sitionisPropositionis correxi, et correctam imprimi curavi non furtim sed eo cognoscente. Cætera in lucem prodierunt absqꝫue uti fueratnt impressa. Per experimentisa et meisa et ijsea DniDomini Mariotti (pag 245 Traite du Movem.Movement des EausEaux) & alijsa a D. Cotes mecum communicatisa, constat quod ex quantitaate aquæ per datum foramen in fundo vasis dato tempori effluve ea sit quæ exire potest quod velocitas ejus in velocitate foramen, ea sit quāam corpus, cadendo a dimidia altitudine aquæ in vasis stagnantis, acquirere potest. Sed aqua post exitum acceleratur uti constat per alia experimenta. Præter verba quæ ex Libro Principiorum citasti extant alia in ejusdem Libri in ad Prop. LXIX Lib I, quabus abunde constat me nunquam gravitatem corporibus essentialem minime fecisse. Ea sunt hujusmodi Vocem Attractionis Utrum vis centripetæ quibꝰus corpora cælestia retinentur in orbibus suis sint eorum gravitates vel alijs nominibus vocentur, parum inter In Epistola ejusdem DniDomini Cotes Aug 1710 data Deinde Idem D. Cotes in Epistola 21 Sept 1710 ad me data deducxit ex [D. D. Mariotti experimento (pag. 245 TaiteTraite du Movement des Eaux sæpe repetita, et summa cum diligentia repetita, quod velocitas aquæ per ] quantitate aquæ dato tempore per datum foramen in fundo vasis factum effluente, (juxta experimentum et D. Mariotti sæpe (pag 245 Traite du Movement dedes Eaux) sæpe summa cum diligentia & accurate repetitam,) quod velolicasvelocitas velocitas aquæ in ipso foramine ea sit quam corpus acquirere potest i cadendo a dimiidiodimidio altitudenealtitudine aquæ in vasevasis stagnantis acquirere potest. Et in alia Epistola 5 Octob 1710 scripsit se quoqꝫue Experimentum idem quoqꝫue bis cepisse eodem successo. Ego vero experimentum hujusmodi idem ceperam ante editionem primam his Libri. Et ex his omnibus certissima est redditur aquam non velocitatem aquaæ egredientis non majorem esse quam conclusio prædicta. Sed aqua post exitum acceleratur uti constat per alia experimenta a me tentata sub initio anni sequentis ac deinceps ab alijs capta. Tandem mense Octobri anni 1712 ubi Liber totus usqꝫue ad pag. 456 inclusive impressus esset, D. Nicholaus Bernoulli me monuit quod error aliquis admissus fuisset in resolutione Prop X Lib. II Edit. I (aut tractionem Resolutiones Propositiones subinde examinavi. et correxi et correctam ei ostende et imprimi curavi non subdole se eo cognoscente. Cætera in lucem prodierunt uti fuerant ante has lites impressa. In editione secunda Libri mei Principiorum D. Cotes qui Editionem curabat postulabat ut Corollarium 1 Prop XIII Lib. 1demonstratione aliqua munirem: & ut ei morem gererem addidi ver Corollarium aliquantulum auxi. Et hoc factum est antequam hæ lites cœperunt. Nam ex Literis quas a D. Cotes interea dum Editionem curaret accepi, constat quod schedæ primæ triginta septem (id est, usqꝫue ad paginam 296 inclusive) impressæ fuerunt ante 30 Junij 1710. Postea D. Cotes in
Literas tuas amicissimas accepi, 26 Julij datas, et gratias reddo tibi maximas quod exemplaria duo Optices ad D. Johannem Bernoulli meo nomine misisti et eo pacto nos reconciliare conatus fueris; quod et fecisti, ut ex literis ejus intelligo. Nam D. Leibnitius Epistolis aliquot quas vidi, disertis verbis affirmaverat D. Bernoullium authoremauctorem esse Epistolæ ad ipsum 7 Junij 1713 scriptæ datæ et mox in Germania issæ impressæ, et per orbem literarium sparsæ. Sed cum ex literis D. Bernoulli jam acceptis intelligam ipsum non fuisse autorem, & si quasi a magno quodam Iudice me condemnante scripta fuisset. [Et cum authorauctor ille falsis assertionibus et fallacibus argumentis me quasi plagiarij reum accuset, et ejus auctoritas quasi Judicis alsolatissimi jactaretur abstinui ab ejus amicitia D. Bernoullij donec per literas vestras novissimas ejus copia cum tuis novissimis ad me missas intellxiintellexi ipsum non fuisse autorem illius Epistolæ. Quod cum ipse affirmat ita sit] amicitiam ejus libere lubenter amplector et colo. Et eo nomine Literas inclusas ad ipsum scripsi quas oro ut ubi versus ad ipsum scribendi occasionem nactus fueris Literis tuis includas ad ipsum mittas. Oro etiam ut Academiæ tuæ vestræ gratias meas reddas ob munera Historiæ vestræ suæ annuatim ad me missæ, te curante. Sed et gratiæ meæ tibi ipsi debentur ob scriptem Ephemerides ad me missas. Literis t Antequam literis tuis responderem vobis mox injecere chartis nonnullis cupiebam colloqui cum DnoDomino Keil qui aberat in agro Northamptoniensi. Sed is jam in Urbem hanc redijt [& cum eo collocutus sum,] et quantum sentio ab ulterioris ab his a litibus in posterum abstinebit. Nonnulla Hiene præterita Inspiciendo literas quas olim DnusDominus Cotes interea dum curaret Editionem secundam Libri P mei Principiorum curar accepi ad me scripsit aas observo quod Schedae primae triginta septem (id est usqꝫue ad paginam 296 inclusive) impressæ fuerunt ante 3 30 Junij 1710 st. vet.stylo veteri id est antequam hæ lites cœperunt. Sed monente tandem D. Nicolao Bernoulli quod error aliquis admissus fuisset in Prop. X Lib. III: constructionem Propositionis correxi et correctam ei ostendi & imprimi curavi non furtim subdole sed eo cognoscente. Cætera in lucem prodierunt uti fuerant ante has lites impressa. [Et in his omnibus nihil aio contra D. Bernoullium scripsi fuit.] Per experimenta et mea, et ea DniDomini Mariotti (pag 245 Traite du Mouvement des eauseaux,) et alia a D. Cotes facta et mecum communicata, constat, ex quantitate aquæ per datum foramen in fundo vasis dato tempore effluentis, quod velocitas ejus in foramine ea sit quam corpus cadendo a dimidia altitudine aquae in vase stagnantis acquirere potest. Sed aqua post exitum acceleratur, uti constat per alia experimenta. Præter verba quæ ex libro Principiorum citasti, extant alia in Scholio ad Prop. LXIX Lib. I quibus clarissime constat me gravitatem corporibus essentialem minime fecisse. Sed spero quod contentiones hæ omnes in posterum cessabunt.