344 ACADEMY OP SCIENCES OF PARIS. 



if in sufficiently large number, strike the mind in so vivid a manner with their 

 relations and mutual dependence, that it would , seem, that after having been 

 detached by a species of violence from one another, they naturally seek to re- 

 unite themselves again." — Preface of 1699. 



§ 3. Of the metaphysics of the sciences. 



Each science has its metaphysics, or, as we more commonly say nowadays, 

 its philosophy. 



Descartes praises, in his cotemporary Dcsargues, certain new views on the 

 metaphysics of geometry. " The mode," he says, "in which he commences his 

 reasoning is so much the more commendable as it is more general, and seems to 

 be derived from what I am in t,he habit of calling the metaphysics of geometry." 

 ''The geometrical spirit," says Fonteuelle, "is not so identified with geometry 

 that it cannot be transferred to other subjects of knowledge."* And it was 

 in this connexion that he gave us his striking allusion to Descartes : " Sometimes 

 a great man gives the tone to his whole age, and he to whom we might most 

 justly ascribe the glory of having established a new art of reasoning was an 

 excellent geometer." 



What he admires in the sciences, and would especially challenge admiration 

 for, is not so much discovery as the art of discovering: "Perhaps," he says, 

 "the excellence of the geometric methods which from day to day are invented 

 or improved, will bring us at last to see the import of geometry — that is to say, 

 of the art of making discoveries in geometry, which is everything;" it is les^ 

 the material truth than the abstract truth. "Although lines and numbers," he 

 says, " should conduct absolutely to nothing, they would still teach us how to 

 operate upon truths;" it is less the fact than the idea. lie seeks everywhere 

 "that genius of metaphysics which," as he says, "hides itself, and can only be 

 perceived by eyes sufficiently penetrating." t 



Above physical science he sees an intellectual science : in physical science 

 the cases arc particular, the experiments bounded; it is intellectual scienco 

 which gives them a general force, and, to borrow one of his striking expressions, 

 a universal spirit.^ 



§ 4. Cf common language applied to the sciences. 



"When the Academy of Sciences," says Fontenelle, addressing the Academic 

 francaise, "assumed a new form at the hands of one of your most illustrious 

 colleagues, § he conceived the design of diffusing, as far as was in his power, the 

 taste of the abstract and elevated sciences which formed his sole occupation. 

 These employed, for the most part, as in ancient Egypt, only a species of sacred 

 language understood by none but priests and a few of the initiated. Their new 

 lawgiver desired that they should speak, as far as possible, the common language, 



* Elsewhere lie says, "f^eometiy, and what is still better worth, the geometric spirit." — 

 Eloge of Giiglulmini. "The art of discovery in mathematics is more valuable than the 

 greater part ot what is discovered." — Elogc of Liehnitz. 



i Discours a V Academic frmicaise, 1741. He says of Leibnitz: "He was a metaphysician 

 and it was next to impossible that he should not be so; ho had too universal a spirit. I mean 

 universal not only because he essayed everything-, but still more because in everything he 

 seized upon the highest and most general principles, which is the character of metaphysics."— 

 Eloge de Leibnitz. 



I He employs this expression in speaking of the necessary union of geometry and physics: 

 "It is requisite that the subtle speculations of the one should become embodied, so to say, 

 by connecting themselves with the experiments of the others; and that experiments naturally 

 liiinited to paiticular cases should assume, by means of speculation, a universal spirit, and bo 

 changed into principles." — I'reface o/16()6. 



^ The Abbe Bignon, member of the Academic francaise and honorary of the Academy of 

 Sciences. 



