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By a parcel of Letters which passed between me & Mr Cotes while he was writing the second Edition of the Principles, I find that the first 28 sheets of that Edition ending with page 224, were printed off before April 15 1710 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 . In order to a third Edition I have 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, ideoque Linea quæsita PQ recte exhibetur Q.E.F. [When Mr N. Bernoulli was in London (which was in Autumn 1712) & told me that there was a fault in the resolution of Prob: III Lib. II, & that he look it be in {rule} a mistake in second differences; I answered that I would examin & told him the next time I saw him (which was within a day or two) that I had examined it & there was a mistake, but it lay in drawing the tangent of the Arch lC 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 . 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 Manuscript was sent to the Royal Society in Spring 1686; & the shortness of the time in which I wrote it, makes me not ashamed of having committed some faults These things I meant] But I can strike them out if you think it may be better to omit them.

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.

Inspiciendo Epistolas quas a D. Cotes olim accepi, animadverto quod in editione secunda libri Principiorum schedæ primæ 24. (id est usque ad Pag. 224 inclusive) impressæ sunt ante 15 Aprilis 1710 stylo veteri id est antequam hæ lites cœperunt. Et quod sub autumno anni 1712 cum D. Nicolaus Bernoulli mihi significaverat emendari esse aliquam in resolutione Prop X Prob. III Lib. II Princip. et Propositionem examinaveram; [respondi mendam in positione tangentis arcus Cl, et quod Propositionem illam iterum imprimi curarem Arcum utique lC, CG tangentes Ck, CF exhibere debuissent momenta prima curvæ Lk a corpore descriptæ et propterea in eandem plagam cum motum corporis duci.] eandem emendatam ipsi dedi dicendo quod imprimari Propositionem impressam antequam ederetur , perinde emendari curarem.

Inspiciendo literas quas olim a Domino Cotes, interea dum Editionem secundam libri Principiorum curaret, accepi, animadverto quod Schedæ prima triginta septem (id est usque ad paginam 296 inclusive) impressæ fuerunt ante 30 June 1710, stylo veteri id est, antequam hæ lites cœperunt. Sed momente tandem D. Nicolao Bernoulli quod error aliquis admissus fuisset in Prop. X, Lib. II. Constructionem Propositionis correxi, et correctam imprimi curavi non furtim sed eo cognoscente. Cætera in lucem prodierunt uti fuerant impressa.

Per experimenta et mea et ea Domini Mariotti (pag 245 Traite du Movement des Eaux) & alia a D. Cotes mecum communicata, constat ex quantitaate aquæ per datum foramen in fundo vasis dato tempori effluve{illeg} quod velocitas ejus in foramen, ea {sit} quam 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 ad Prop. LXIX Lib I, quabus abunde constat me gravitatem corporibus essentialem minime fecisse.

Deinde Idem D. Cotes in Epistola 21 Sept 1710 ad me data deduxit ex quantitat{e} aquæ dato tempore per datum foramen in fundo vasis factum effluente, juxta experimentum D. Mariotti (pag 245 Traite du Movement des Eaux) sæpe & accurate repetitam, quod velocitas aquæ in ipso foramine ea sit quam corpus cadendo a dimidio altitudine aquæ in vasis stagnantis acquirere potest. Et in alia Epistola 5 Octob 1710 scripsit se quoque Experimentum idem bis cepisse eodem successo. Ego vero experimentum idem ceperam ante editionem primam his Libri. Et ex his omnibus certissima redditur conclusio prædicta. Sed aqua post exitum acceleratur uti constat per alia experimenta a me sub initio anni sequentis ac deinceps ab alijs capta. Tandem mense Octobri anni 1712 ubi Liber totus usque ad pag. 456 inclusive impressus esset, D. Nicholaus Bernoulli me monuit quod error aliquis admissus fuisset in resolutione Prop X Lib. II Edit. I ( 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 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, usque 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 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 auctorem esse Epistolæ ad ipsum 7 Junij 1713 datæ et mox in Germania impressæ, et per orbem literarium sparsæ. Sed cum ex literis D. Bernoulli jam acceptis intelligam ipsum non fuisse autorem, amicitiam ejus lubenter amplector et colo. Et eo nomine Literas inclusas ad ipsum scripsi quas oro ut ubi occasionem nactus fueris ad ipsum mittas. Oro etiam ut Academiæ vestræ gratias meas reddas ob munera Historiæ suæ annuatim ad me missæ, te curante. Sed et gratiæ meæ tibi ipsi debentur ob Ephemerides ad me missas. Antequam literis tuis responderem cupiebam colloqui cum Domino Keil qui aberat in agro Northamptoniensi. Sed is jam in Urbem hanc redijt [& cum eo collocutus sum,] et quantum sentio ab his a litibus in posterum abstinebit.

Inspiciendo literas quas Dominus Cotes interea dum curaret Editionem secundam Libri mei Principiorum ad me scripsit observo quod Schedae primae triginta septem (id est usque ad paginam 296 inclusive) impressæ fuerunt ante 30 Junij 1710 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 subdole sed eo cognoscente. Cætera in lucem prodierunt uti fuerant ante has lites impressa.

Per experimenta et mea, et ea Domini Mariotti (pag 245 Traite du Mouvement des eaux,) 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.

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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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