590 Gesammtsitzung 



ton and Cotes, Lond. 1850) noch Brewster (Memoirs of the 

 life, writtings , and discoveries of Sir Isaac Newton, Edinb. 

 1855, 2 Voll.) haben weiteres Material beigebracht. 



Newton versichert, dass er die Methode der Reihen und 

 Fluxionen im Jahre 1665 gefunden und im folgenden Jahre weiter 

 ausgebildet habe. Aus einem Manuscript, welches vom 13. No- 

 vember 1665 datirt ist, führt er die Behandlung des Problems an, 

 zu einer gegebenen Gleichung die Fluxionsgleichung zu suchen, 

 worin die directe Methode der Fluxionen enthalten sei, und be- 

 merkt, dass er auf dieselbe Weise die Tangenten und Krümmungen 

 der Curven bestimmt habe. In einer kleinen Abhandlung, die im 

 November 1666 geschrieben ist, habe er die Methode so weit ver- 

 vollkommnet, dass sie auf Brüche und Transcendenten anwendbar 



that an Eighth Proposition is here added, containing the Inverse Method of 

 Fluxions so far as I had then attained it, namely, by Quadratures of Cur- 

 vilinear Figures, and particularly by the three Rules upon which the Analy- 

 sis per Aequationes numero terminorum infinitas, is founded, and by most of 

 the Theorems set down in the Scholium to the Tenth Proposition of the 

 Book of Quadratures. And that in this Tract, when the Area arising from 

 any of the Terms in the Valor the Ordinate cannot be expressed by vulgär 

 Analysis, I represent it by prefixing the Symbol □ to the Term. As if the 



Abscissa be x, and the Ordinate ax — 6 + , the Area will be -^ axx — 



a-\- X 



^ ^ + D • And that in the same Tract I sometimes used a Letter 



a -\- X 



with one Prick for Quantities involving first Fluxions, and the same Letter 

 with two Pricks for Quantities involving second Fluxions. And that a larger 

 Tract which I wrote in the Year 1671, and mentioned in my Letter of the 

 24th of Octob. 1676, was founded upon this smaller Tract, and began with 

 the Reduction of finite Quantities to converging Series, and with the Solu- 

 tion of these two Problems: 1. Reiatione Quantitatum fluentium inter se 

 data, Fluxionum relationem determinare. 2. Exposita aequatione Fluxiones 

 Quantitatum involvente, invenire relationem Quantitatum inter se. And that 

 when I wrote this Tract, I had made my Analysis composed of the Methods 

 of Series and Fluxions together, so universal, as to reach to almost all 

 Sorts of Problems, as I mentioned in my Letter of the 13th of June 1676, 

 and that this is the Method described in my Letter of the lOth of Decemb. 

 1672. 



