But the ordinate: the sub-tangent; hence
,
giving 2x for the value of the sub-tangent. This method differs from that of the differential calculus only in notation.[31]
NEWTON TO EULER.
It has been seen that in France prodigious scientific progress was made during the beginning and middle of the seventeenth century. The toleration which marked the reign of Henry IV. and Louis XIII. was accompanied by intense intellectual activity. Extraordinary confidence came to be placed in the power of the human mind. The bold intellectual conquests of Descartes, Fermat, and Pascal enriched mathematics with imperishable treasures. During the early part of the reign of Louis XIV. we behold the sunset splendour of this glorious period. Then followed a night of mental effeminacy. This lack of great scientific thinkers during the reign of Louis XIV. may be due to the simple fact that no great minds were born; but, according to Buckle, it was due to the paternalism, to the spirit of dependence and subordination, and to the lack of toleration, which marked the policy of Louis XIV.
In the absence of great French thinkers, Louis XIV. surrounded himself by eminent foreigners. Römer from Denmark, Huygens from Holland, Dominic Cassini from Italy, were the mathematicians and astronomers adorning his court. They were in possession of a brilliant reputation before going to Paris. Simply because they performed scientific work in Paris, that work belongs no more to France than the discoveries of Descartes belong to Holland, or those of Lagrange to Germany, or those of Euler and Poncelet to Russia. We
