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HISTORICAL VIEW OF THE

mathematicians, yet even at the present day the sub-ject is invested with difficulties which have not beenovercome.

Progress of the Fluxional Methods.

Newton and the English geometers did very littletowards perfecting this branch of analysis. The conti-nental mathematicians, on the other hand, were zealouslyengaged in improving its methods an,d pushing forwardits applications. Leibnitz published in the “Acta Eru-ditorum,” and other journals, a number of papers full oforiginal views and important hints, thrown out very brief-ly, and requiring the elucidations which his illustrious-friends the Bernoullis and others were always so willingand able to supply. Their tracts, like his, were scat-tered in the different periodical works of that time ; andseveral years elapsed before any complete treatise ex-plained the general methods, and illustrated them byexamples. The first book in which this was done, sofar, at least, as concerned the differential or direct cal-culus, was the “ Analyse des infiniment Petits” of themarquis de l’Hopital , published in 1696 , a work ofgreat merit, and which did much to diffuse a knowledgeof the calculus. The author was a man of considerablegenius and indefatigable industry, and enjoyed theadvantages of instructive intercourse with John Ber-noulli . In the collection of the works of the latter(not published till 1724) is inserted a tract of somelength on the integral calculus, written in 1691 , as isexpressly mentioned, for the use of M. de l’Hopital, towhose work it would seem intended as a sequel.

Newton, besides his letters, inserted in the “ Com-mercium Epistolicum,” had written at an early period,as we before observed, the “ Analysis per aquationes,”&e. But this, together with another tract, was notpublished till 1711- The treatise on the quadratureof curves, though written in 1 666 , did not appear till1704, when, together with the “ Enumeratio linearum