Vortices alicubi harmonice alibi non harmonice moveri pro lubitu finxit. Vide Acta Li [illeg] ps.
Ann. 17   pag Harmonicæ circulatit |o|n[is] obstant Vortices P satellitum Saturni Iovis ac Terræ.
Motum Cometarum \Leibnitius/ non attingit, Comet[a] Planetæ et Cometæ ijsdem legibus [illeg]va[hi] Newtonus
|det[illeg]it[illeg] | revolvuntur apud Newtonum. Vortices alicubi harmonice alibi non harmonice moveri \Leibnitius/ I[illeg] pro
lubitu finxit: [illeg] harmon[illeg] proh[illeg]it harmonicæ circulationi obstant vortices Satellitum Saturni
Iovis [ac] Terræ \ Harmonice [illeg] Motibus Cometarum Vortices non favent./ . [sic] Motum harmonicum Planetarum \Leibnitius non probavit sed in Tentaminis Artic 6/ [ex] [Princi] assumpsit|.| a on probavit: Newtonus
motum harmonicum corporum omnium in centrum immotum attractorum demonstravit. Motum circu-
lationis & motum paracentricum Leibnitius nunc a diversis causis deducit nunc ab eadem deducit
Newtonum |s| utrum ab eadem causa \(pro simplicitate naturæ/ semper deducit. Vim centrifugam . . . .

^a A relatione Differentiarum ad Tangentes Leibnitius se methodum differentia
lem habuisse hic fatetur, \id est a methodo determinandi tangents per differentias/ [illeg] [illeg] /Archimedes\ Fermatius Gregorius, [illeg] Barrowus \ & Newto [illeg] nus / methodū
differentialem |rum| ad Tangentes applicuera |e| [nt] Newtonus hanc methodum \ducendi tangentes aux er |it| at & præterea/ [illeg] ad Quadraturas
Curvarum & alia multa problematū \genera/ applicando, \applicuit &/ valde generalem reddider |it| at, & idem signi
ficaver |it| at in Epistolis suis ad Collinium A. C 1672 & Oldenburgum \A.C. 167 [sic] / 1676. Scripser |it| at \ [mox] mox/ Leibnitius
methodum inversam tangentium in potestate esse ab æquationibus et quadraturis non pendere
|&| responder |it| at L Newtonus hanc methodum \hanc [inversam] / ex potestate esse \hanc/ inversam \ tangentium etiam/ in potestate esse. Quibus
omnibus [int] [illeg] se collatis \admonitas/. Leibnitius in eandem methodum incidit, ut ex verbis ejus hic positis cum
[illeg] epistola ejus ad Oldenburgum anno 1677 scripta collatis man[illeg] p[e]tit \manifestum est/. Vide supra pag.

^b Nulla est hujusmodi analogia \Differentiæ non sunt differentiæ summarum/ Leibnitium |s| primam lucem a consideratione, tangentium
habuit per Newtonum auct[æ] ab hac \methodi/ aliunde habuit.

$16\times 438⁤;\frac{1}{2}+46$.

$\begin{array}{rrr}\phantom{15)}& 1754& \phantom{15)}\\ \phantom{15)}& 7016& \phantom{15)}\\ \phantom{15)}& 46& \phantom{15)}\\ 15)& \overline{7062}& (470⁤;\frac{4}{5}\\ \phantom{15)}& 106\phantom{0}& \phantom{15)}\\ \phantom{15)}& 105\phantom{0}& \phantom{15)}\\ \phantom{15)}& 12& \phantom{15)}\end{array}$

$\begin{array}{r}15\left)7068\right(471⁤;\frac{1}{5}\\ \phantom{15)}106\phantom{8(471⁤;\frac{1}{5}}\\ \phantom{15)}105\phantom{8(471⁤;\frac{1}{5}}\\ \phantom{15)}18\phantom{(471⁤;\frac{1}{5}}\end{array}$

$\overline{)438\times 16+52}$

$\begin{array}{r}\phantom{15)}1752\phantom{(470⁤;\frac{2}{3}}\\ \phantom{15)}7008\phantom{(470⁤;\frac{2}{3}}\\ \phantom{15)}52\phantom{(470⁤;\frac{2}{3}}\\ 15\left)\overline{7060}\right(470⁤;\frac{2}{3}\\ \phantom{15)}1060\phantom{(470⁤;\frac{2}{3}}\\ \phantom{15)}105\phantom{0(470⁤;\frac{2}{3}}\\ \phantom{15)}10\phantom{(470⁤;\frac{2}{3}}\end{array}$

$\mathrm{e}+\frac{\mathrm{a}\mathrm{o}}{\mathrm{e}}-\frac{\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{o}}{2\mathrm{e}3})\mathrm{a}\mathrm{o}-\mathrm{o}\mathrm{o}(\frac{\mathrm{a}\mathrm{o}}{\mathrm{e}}-\frac{\mathrm{a}\mathrm{a}\mathrm{o}\mathrm{o}}{\mathrm{e}3}-\mathrm{a}\mathrm{a}-\frac{\mathrm{a}\mathrm{a}\mathrm{o}\mathrm{o}}{\mathrm{e}\mathrm{e}}+\frac{\mathrm{n}\mathrm{n}\mathrm{a}{\mathrm{o}}^3}{2{\mathrm{e}}^4}+\frac{\mathrm{a}\mathrm{a}\mathrm{o}\mathrm{o}}{{\mathrm{e}}^2}+\frac{{\mathrm{a}}^3{\mathrm{o}}^3}{{\mathrm{e}}^4}$

$\frac{\mathrm{a}\mathrm{o}}{\mathrm{e}}-\frac{\mathrm{a}\mathrm{a}\mathrm{o}\mathrm{o}}{\mathrm{e}3}+\frac{\mathrm{a}{\mathrm{o}}^3}{2{\mathrm{e}}^3}+\frac{3{\mathrm{a}}^3{\mathrm{o}}^3}{2{\mathrm{e}}^5}$

$\frac{{\mathrm{a}}^3{\mathrm{o}}^3}{2\mathrm{e}4}+\frac{\mathrm{e}\mathrm{e}\mathrm{a}{\mathrm{o}}^3}{2\mathrm{e}4}+\frac{2{\mathrm{a}}^3{\mathrm{o}}^3}{2\mathrm{e}4}$

$\mathrm{e}+\frac{\mathrm{a}\mathrm{o}}{\mathrm{e}}-\frac{\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{o}}{2\mathrm{e}3})\mathrm{a}\mathrm{o}-\mathrm{o}\mathrm{o}+✱(\frac{\mathrm{a}\mathrm{o}}{\mathrm{e}}-\frac{\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{o}}{\mathrm{e}3}+\frac{3\mathrm{a}\mathrm{n}\mathrm{n}{\mathrm{o}}^3}{2\mathrm{e}5}-\mathrm{a}\mathrm{o}-\frac{\mathrm{a}\mathrm{a}\mathrm{o}\mathrm{o}}{\mathrm{e}\mathrm{e}}+\frac{\mathrm{a}\mathrm{n}\mathrm{n}{\mathrm{o}}^3}{2\mathrm{e}4}+\frac{\mathrm{a}\mathrm{n}\mathrm{n}{\mathrm{o}}^3}{{\mathrm{e}}^4}+3\mathrm{a}\mathrm{n}\mathrm{n}{\mathrm{o}}^3$

$\frac{\mathrm{a}\mathrm{o}}{\mathrm{e}}-\frac{\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{o}}{2{\mathrm{e}}^3}+\frac{\mathrm{a}\mathrm{n}\mathrm{n}{\mathrm{o}}^3}{2{\mathrm{e}}^5}+\frac{\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{o}}{2{\mathrm{e}}^3}-\frac{\mathrm{a}\mathrm{n}\mathrm{n}{\mathrm{o}}^3}{2{\mathrm{e}}^5}$

$\frac{\mathrm{a}{\mathrm{n}}^3{\mathrm{o}}^4}{{\mathrm{e}}^6}\times \frac{{\mathrm{e}}^6}{\mathrm{n}4\mathrm{o}4}=\frac{\mathrm{a}}{\mathrm{n}}$

$-\frac{\mathrm{a}}{\mathrm{n}}$

$\frac{\mathrm{a}\mathrm{o}}{\mathrm{e}}\times \frac{\mathrm{e}}{\mathrm{n}\mathrm{o}}$

$+\frac{\mathrm{a}}{\mathrm{n}}$