530 PHILOSOPHICAL TRANSACTIONS. [aNNO l68l-2. 



thematician, not averse to labour, may acquire so much skill, that without the 

 aid of books or instruments he may accomplish the solution of any mathemati- 

 cal problem, and that as easily as another by only turning over books. 



This then is that idea of the mathematics which, in my manner, I have long 

 since figured to myself; being always firmly persuaded, that then only we can 

 hope for success in great undertakings, when we have conceived an exact idea 

 of them in our minds, and of the fittest means of putting them in execution. 

 And if we cannot express this idea completely, yet it is something to come as 

 near as may be. I conceive this is so far from being above the human powers, 

 that I think it may be accomplished by the industry of one man alone, who is 

 not prevented by the multitude of other concerns. For it is manifest that the 

 Library and Catalogue may easily be procured, if money be not wanting. And 

 as to the Pandects, if the task of composing them were committed to me, I 

 should impose on myself much severer conditions than those above mentioned. 

 For first I would delineate the infallible process of human reason in the investi- 

 gation of whatever it proposes to itself ; showing how it proceeds from the first 

 rudiments or principles, by an uninterrupted chain, to the highest as well as 

 the lowest application of them. An art which men would not perhaps be long 

 without, if they were but carefully to examine, by what means such ideas have 

 arisen in the minds of certain men whom they admire, and how such apt means 

 have been discovered for attaining that end. How these pandects may be abridged 

 into a manual, such as may be fit for common use, cannot be difficult to under- 

 stand. But so to fix them in mind, that there shall be no further need of books, 

 which is the thing aimed at in our self-sufficient mathematician, may be thought 

 by most to exceed the power of the human mind. Yet I think men will abate 

 of their doubts on this head, when they carefully consider what arts have been 

 devised for strengthening the imagination, for assisting the memory, and for 

 directing the reasoning faculty, as well as what wonderful effects may be pro- 

 duced by the united and constant exercise of these faculties. 



The foregoing Idea considered and objected to, Oct. 1639. By P. Mersenne.* 



Philos. Collect. N°5, p. 135. 



Instead of all that apparatus which the author of the idea proposes, about 



• Marin Mersenne, a celebrated philosopher and mathematician of the I7th century, was bom 

 1588, at Oysc in Maine. He Was fellow student with Descartes at la Fleche, where they contracted 

 a friendship that lasted through life. Going afterwards to Paris, he studied theology in the Sorbonne, 

 and entered in the order of the Minims. He was teacher of theology in the convent of Nevers, 

 from 1615 to 1619, and became afterwards superior of that convent. Wishing hovv^ever to be more 

 at liberty for philosophical studies, he resigned all the offices of his order, and travelled into Italy, 



