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By the \a parcel of/ Letters wch passed between me & |Mr| Cotes while he was writing the second Edition of the Principles, {illeg} I find that the first 28 sheets of th \of that Edition/ ending |w|a|i|t|h| page 224, were printed off before April 15 1710 st. vet. And this I note that you may know that the alterations made in those sheets had no relation to the disputes about the method{illeg} of fluxions {illeg} 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 \{illeg}/. 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, ideoq Linea quæsita PQ recte exhibetur Q.E.F. But I {illeg} [When Mr N. Bernoulli was in London (wch was in Autumn {illeg} 1712) {illeg} & told me that there was a falult in the resolution of Prob: III Lib. II, & \that/ he look it be in {t|r|ule} of finding \a mistak {sic} in/ second differences; I \answered that I would examin {illeg} &/ toold {sic} him the next time I saw him \(wch was wit{illeg}|h|in 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 {illeg} 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 {illeg}. And I added I that I would cause that sheet to be reprinted. & I gave him \also/ the scheme set right & the calculation suited th{illeg}|e|reunto, & 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 MS was sent to ye R. S. 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 ment {sic}] wch words But I can strike them out if you think it may be better to omit them.

Nam vi{illeg}|re|s centripet{illeg}|æ| {illeg} qu{illeg}|i|bus corpus \circa centrum S/ revolvi potest \per {ca.}/ in his Lineis inventis \revolvi potest/ eri|un|t 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 {illeg}|i|nventis revolvi potest, sit reciproce ut quadratum distantiæ \corporis/ a centro. {illeg}

In{illeg}|s|picienti|do| Literas Esp Epistolas quas a D. Cotes {illeg} olim accepi, animadverto \quod in editione secunda libri Principiorum/ quod {illeg} Liberi {sic} Principiorum mei{illeg} ejus Editione secunda \schedæ primæ 24./ (id est usq ad Pag. 224 inclusive) impressæ fuerunt \sunt/ ante 15 Aprilis 1710 st. vet. et propterea quæ alterationes in illis schdis {sic} addit{illeg}|æ| vel mutat{illeg}|æ| fuerunt id est antequam hæ lites cœperunt. Sed Et quod sub autumno anni 1712 cum intelligerem D. Nicolaus Bernoulli mihi significa\ve/re|a|t {illeg}{illeg}|e|mendari \esse/ aliquam Propositioni in resolutione \Prop X/ Prob. III Lib. II Princip. {illeg} Propositionem illam iterum imprimi curabam. \Propositionem illam iterum iprimi {sic} cura{illeg}/ et Propositionem examinaveram; [respondi mendam in positione tangentis arcu{illeg}|s| Cl, et quod Propositionem illam iterum imprimi curarem Arcum utiq lC, CG a corpore \projecto/ descriptorum tan\tan/gentes sunt \Ck, CF/ exhibere deb{illeg}\uissent/ momenta prima curvæ Lk a corpore descriptæ et propterea in eandem plagam cum motū corporis duci.] eandem emendatam ipsi dedi et {illeg} {illeg} dicendo quod {illeg} imprimari {illeg} {curavam} Editionem \Propositionem/ impressam {illeg}ndum \antequam/ ederetur {illeg}, perinde emendari curarem.

Inspiciendo literas quas olim a Dno Cotes, interea dum Edi\ti/onem secundam libri Principiorum curaret, ad me scripsit accepi, animadverto quod Schedæ prima viginti quatuor \octo/ \triginta septem/ (id est usq ad paginam 224 \296/ inclusive) impressæ fuerunt ante 15 Apr \30 June/ 1710, \st/ st. vet. id est{illeg}, a{illeg}|n|tequam hæ lites cœperunt. [Et {illeg} propterea Liber totus impressus fuit ante finem mensis Novembris 1712. Et {illeg} /sed\ Prop X Lib. II iterum imprimi curavi ad correxi {illeg} a Jacubo Bernoulli a \D./ Nicolao Bernoulli de menda admonitus, Propositionem X Lib. II correxi \ad incudem revcari {sic}/, & iterū imprimi curavi.] Sed momente tandem D. Nicolao Bernoulli quod Prop. X Lib. II error aliquis admissus fuisset in Lib. Prop{illeg}. X, Lib. II. {illeg} Constructionem Prop.sitionis correxi, et corre{illeg}|c|tam imprimi curav{illeg}|i| non furtim sed eo cognoscente. Cætera in lucem prodierunt absq uti fuerat|n|t impressa.

Per experimentis|a| et meis|a| et ijs|ea| Dni Mari\o/tti (pag 245 {illeg} Traite du Movem. des {illeg}|E|aus {sic}) & alijs|a| a D. Cotes mecum communicatis|a|, constat quod \ex/ quantita{illeg}|at|e aquæ per datum foramen in fundo vasis \dato tempori/ effluv{illeg}e{illeg} {illeg} ea sit quæ exire potest \quod velocitas ejus in/ {illeg} velocitate \foramen, ea {sit}/ qu{illeg}|ā| corpus, cadendo a dimidia altitudine aquæ in vasis stagnantis, acquirere potest. Sed aqua post exitum acceleratur uti constat per alia experimenta.

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Præter verba quæ ex Libro Principiorum citasti extant alia in ejusdem Libr{illeg}|i| \in {sic} ad Prop. LXIX Lib I/, quabus abunde constat me nunquam gravitatem corporibus essentialem {illeg} minime fecisse. Ea sunt hujusmodi Vocem Attractionis Utrum vis centripetæ qu{illeg}|ib| corpora cælestia retinentur in orbibus suis sint {illeg} eorum gravitates vel alijs nominibus vocentur, parum inter

In Epistola ejusdem Dni Cotes Aug 1710 data

\Deinde/ Idem D. Cotes in Epistola {illeg} 21 Sept 1710 ad me data deduc|x|it {illeg} ex [D. D. Mariotti experimento (pag. 245 Taite {sic} du Movement des Eaux sæpe repetita, et summa cum diligentia repetita, quod velocitas aquæ per {illeg}] quantitat{e} aquæ dato tempore per datum foramen in fundo vasis factum effluente, (juxta experimentum \et {illeg}/ D. Mariotti sæpe (pag 245 Traite du Movement de {sic} Eaux) sæpe{illeg} {illeg} summa cum diligentia \& accurate/ repetit{illeg}|a|m,) quod velolicas {sic} velocitas aquæ in ipso foramine ea sit quam corpus acquirere potest i{illeg} cadendo a dimiidio {sic} altitud{illeg}|e|ne {sic} aquæ in vase {sic} stagnantis \acquirere potest/. Et in alia Epistola {illeg} 5 Octob 1710 scripsit se \quoq/ Experimentum idem {illeg} quoq {illeg} \bis/ cepisse eodem success{illeg}|o|. Ego vero experimentum hujusmodi \idem/ ceperam ante editionem primam \his Libri/. Et ex his omnibus certissima {illeg} est \redditur/ aquam non {illeg} 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 usq 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 {illeg}|L|ibri \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 {illeg}|i|nterea dum Editionem curaret accepi, constat quod schedæ primæ triginta septem (id est, usq ad paginam 296 inclusive) impressæ fuerunt ante 30 Junij 1710. Postea D. Cotes in

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Literas tuas amicissimas accepi, \26 Julij datas,/ et gratias reddo tibi maximas quod exemplaria duo Optices ad D. Johannem Berno\u/lli meo nomine misisti et eo pacto nos reconciliare conatus fueris; quod et fecisti, ut ex literis ejus {illeg} intelligo. Nam D. Leibnitius Epistolis aliquot quas vidi, disertis verbis affirmaverat D. Bernoullium authorem {sic} esse Epistolæ ad ipsum 7 Junij 1713 scriptæ \datæ/ et mox in Germania {illeg}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 Iudic{illeg}|e| \me condemnant{illeg}|e|/ script{illeg}|a| fuisset. [Et cum author {sic} ille {illeg} 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/ intellxi {sic} 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 {illeg}|mea|s reddas ob munera Historiæ vestræ suæ annuatim ad me miss{illeg}|æ|, te curante. {illeg} Sed et gratiæ meæ tibi ipsi debentur ob scriptem Ephemerides ad me missas. Literis t Antequam literis tuis responderem vobis {mox{illeg}} injecere chartis nonnullis cupiebam colloqui cum Dno Keil qui aberat in agro Northamptoniensi. Sed is jam in Urbem hanc redijt [& cum eo collocutus sum,] et quantum sentio ab {ulteri{illeg}|o|ris} \ab his/ \a/ litibus in posterum abstinebit. Nonnulla Hiene præterita

Inspiciendo literas quas olim {illeg} Dn{illeg}|u|s Co{illeg}|t|es interea dum \curaret/ Editionem secundam Libri P mei Principiorum curar{illeg} accepi{illeg} \ad me scripsit/ a{illeg}as observo quod Schedae primae triginta septem (id est usq ad paginam 296 inclusiv{illeg}|e|) impressæ fuerunt ante 3{illeg} 30 Junij 1710 st. vet. id est antequam hæ lites cœperunt. Sed monente tandem D. Nicolao Bernoulli quod error aliquis admissus fuisset in Prop. X Lib. II{illeg}|I|: constructionem Propositionis correxi et correctam \ei ostendi &/ imprimi curavi non furtim \subdol{illeg}|e|/ sed eo cognoscente. Cætera in lucem prodierunt uti fuerant \ante has lites/ impressa. [Et in his omnibus nihil \a{illeg}i{illeg}o/ contra D. Bernoullium scrip{illeg}|s|i{illeg} fuit.]

Per experimenta et mea, et ea Dni Mariotti (pag 245 Traite du Mouvement des eaus {sic},) et alia a D. Cotes facta et mecum communicata, constat, ex quantitate aquæ per datum foramen in {illeg} fundo vasis dato tempore effluentis, quod velocitas ejus in foramine ea sit quam corpus cadendo a dimidia altitudine aquae in vase stagnantis {illeg}|a|cquirere 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 {illeg} quibus clarissime constat me gravitatem corporibus essentialem minime fecisse. Sed spero quod contentiones hæ omnes in posterum cessabunt.

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Professor Rob Iliffe
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Scott Mandelbrote,
Fellow & Perne librarian, Peterhouse, Cambridge

Faculty of History, George Street, Oxford, OX1 2RL - newtonproject@history.ox.ac.uk

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