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part of the history of mathematical science, anti illus-trate the powers of great minds, such as that of thesubject of this memoir, these problems have now lostall their interest. The powerful instruments of in-vestigation supplied by the differential and integralcalculus, have reduced their solution to the mere ele-ments of transcendental mathematics. At the epochwhen they engaged the attention of Pascal, before theinvention of the modern methods, they were questionspresenting the most formidable difficulties. To Pascal,however, they were mere matters of mental relaxation,resorted to with a view to divert his attention from hisacute bodily sufferings. He entertained, himself, nointention of making them public. It - was, however,the wish of several of his companions in religiousretirement that they should be made public, were itonly to afford a proof that the highest mathematicalgenius is not incompatible with the deepest and mostsincere Christian faith. Pascal yielded, and, accordingto a custom which was then usual, however puerile itmay now appear, he, in the first instance, proposed the 1658.several questions which he solved as subjects for a^* atprize to the scientific world. Many competitors pre-sented themselves ; and others, who, though not com-peting for the prize, offered partial solutions. Amongthese were several who have since attained great cele-brity, such as Wallis, Huygens, Fermat, and sir Chris-topher Wren .

The prize, however, was not gained, nor the problemssolved. In the beginning of the year 1659, Pascalpublished his complete solutions of the problems of thecycloid, with some other mathematical tracts. Theseadmirable investigations cannot fail to excite in everymind a deep regret, that a morbid state of moral andreligious feeling should ever have diverted Pascal frommathematical and physical research.

Meanwhile his debility and sufferings increased ; buthe did not on that account, yield, but held fast by hissystem of self-denial, practising himself in turning his