Had Leibnitz at the time of receiving this letter been entirely ignorant of his own differential method, the information thus conveyed to him by Newton could not fail to stimulate his curiosity, and excite his mightiest efforts to obtain possession of so great a secret. That this new method was intimately connected with the subject of series was clearly indicated by Newton; and as Leibnitz was deeply versed in this branch of analysis, it is far from improbable that a mind of such strength and acuteness might attain his object by direct investigation. That this was the case may be inferred from his letter to Oldenburg (to be communicated to Newton) of the 21st June, 1677, where he mentions that he had for some time been in possession of a method of drawing tangents more general than that of Slusius, namely, by the differences of ordinates. He then proceeds with the utmost frankness to explain this method, which was no other than the differential calculus. He describes the algorithm which he had adopted, the formation of differential equations, and the application of the calculus to various geometrical and analytical questions. No answer seems to have been returned to this letter either by Newton or Oldenburg, and, with the exception of a short letter from Leibnitz to Oldenburg, dated 12th July, 1677, no further correspondence seems to have taken place. This, no doubt, arose from the death of Oldenburg in the month of August, 1677,[62] when the two rival geometers pursued their researches with all the ardour which the greatness of the subject was so well calculated to inspire. In the hands of Leibnitz the differential calculus made rapid progress. In the _Acta Eruditorum_, which was published at Leipsic in November, 1684, he gave the first account of it, describing its algorithm in the same manner as he had done in his letter to Oldenburg, and pointing out its application to the drawing of tangents, and the determination of maxima and minima. He makes a remote reference to the _similar_ calculus of Newton, but lays no claim to the sole invention of the differential method. In the same work for June, 1686, he resumes the subject; and when Newton had not published a single word upon fluxions, and had not even made known his notation, the differential calculus was making rapid advances on the Continent, and in the hands of James and John Bernouilli had proved the means of solving some of the most important and difficult problems.