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The programme was put forth in the name of Amos Dettonville, the anagram of Pascal’s assumed name as the writer of the ‘Provincial Letters.’ Huyghens, Sluzsius, a canon of the Cathedral of Liège, and Wren, the architect of St Paul’s, sent in partial solutions of the problems—those of Wren especially attracting the interest of both Fermat and Roberval.
A clear conception of this fact led almost immediately to the Method of Tangents of Fermat and Barrow; and this again is the stepping-stone to the Differential Calculus, itself a particular application of that instrument. Dr. Barrow regarded the tangent as merely the prolongation of any one of these infinitely small sides, and demonstrated the relations of these sides to the curve and its ordinates. His work, entitled "Lectiones Geometricae," appeared in 1669. To his high abilities was united a simplicity of character almost sublime. "Tu, autem, Domine, quantus es geometra!" was written on the title-page of his Apollonius; and in the last hour he expressed his joy, that now, in the bosom of God, he should arrive at the solution of many problems of the highest interest, without pain or weariness. The comment of the French historian conveys a sly sarcasm on the Encyclopedists: "On voit au reste, par-l
Mr. Fermat was the first to propound this property of refraction, holding with us, and directly counter to the opinion of Mr. Des Cartes, that light passes more slowly through glass and water than through air.
The calculus of probabilities, when confined within just limits, ought to interest, in an equal degree, the mathematician, the experimentalist, and the statesman. From the time when Pascal and Fermat established its first principles, it has rendered and continues daily to render services of the most eminent kind.
But, as we have already said, it is well to complete our view of his scientific labours in a single chapter. During an access of severe toothache which, in 1658, deprived him of sleep, his thoughts fastened on certain problems connected with the cycloid. Fermat, Roberval, and Torricelli had all been occupied with the subject, and made some definite progress in ascertaining its properties.
Its continuity is broken on the N. by a gap occupied by a depression, and there is a conspicuous crater below the crest on the S.W. The central mountain is connected with the N. wall by a ridge, recalling the same arrangement within Madler. A range of lofty hills, an offshoot of the Altai range, extends from Tacitus towards Fermat.
Thus, taking them from south-east to north-west, they appear on the French charts in the following order: 1, Cap Buffon; 2, Cap Lannes; 3, Baie de Rivoli; 4, Cap de Jaffa; 5, Cap Rabelais; 6, Cap Dombey; 7, Baie de Guichen; 8, Cap Bernoulli; 9, Baie Lacepede; 10, Cap Morard de Galles; 11, Cap Fermat; 12, Cap Monge 13, Cap Caffarelli; 14, Cap Villars; 15, Baie Mollien; 16, Cap Mollien 17, Baie Cretet; 18, Cap Cretet; 19, Iles Decaen; 20, Cap Decaen; 21, Cap Montelivet.
In the previous summer, when at Clermont, he had written to Fermat that he was so weak as to be “unable to walk without a stick, or to hold himself on horseback.” His weakness had grown apace, and in June 1662 he was seized with his last illness.
On the N. its contour is, if possible, rendered still more irregular by the intrusion of a smaller ring-plain. On the N.E. side of the floor stands a very bright little crater and two others on the S. of the centre, each with central mountains. FERMAT. An irregular ring-plain 25 miles in diameter on the W. of Sacrobosco.
The Altai Mountains form a magnificent chain, 275 miles in length, commencing on the outer eastern slope of Piccolomini, and following a tolerably direct north-east course, with a few minor bendings, to the west side of Fermat, where they turn more towards the north, ultimately terminating about midway between Tacitus and Catherina.
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