Monsieur:

Perhaps you will have seen in The News of the Republic of Letters for the month of September what I replied to M. l'Abbe C. It is a remarkable thing to see how many people reply, not to what has been said, but to what they have imagined. This is what M. l'Abbe has done up to the present. For this reason it was necessary to break off abruptly, and bring him back to the first objection. I have only taken the opportunity of this argumentation to put forward a very curious geometricomechanical problem which I have just solved. It is to find what I call an isochronous curve, in which a body shall descend uniformly and approach equal distances to the horizon in equal times, notwithstanding the acceleration it undergoes. This latter I offset by continually changing the inclination. I did this in order to bring out something useful and to show M. l'Abbe that the ordinary analysis of the Cartesians is too limited for difficult problems. I succeeded partly in this, for M. Hugens *005 gave a solution of the problem in the News for October. I knew well enough that M. Hugens could do it, and therefore I didn't expect that he would take the trouble, or, at least, that he would publish his solution and set M. l'Abbe free: since, however, M. Hugens' solution is in part enigmatical, apparently to see if I can do it also, I have sent him the rest of it. Now we will see what M. l'Abbe will say about it. It is true that if the nature of the line which M. Hugens has published is known, the rest can be obtained by ordinary analysis, but without that the thing is difficult, for the converse of the rule of tangents, to find the line, having given the property of the tangents, to which this proposed problem reduces itself, is a problem which M. Descartes himself has confessed in one of his letters not to have mastered. For, usually, what I call transcendentals result, which have no degree; and when the problem reduces itself to curves of a certain degree, as it happens in this case, an ordinary analyst will have difficulty in recognizing it.

I wish, with all my heart, that you might have leisure to think over for half an hour my objection to the Cartesians, which M. l'Abbe tries to meet. Your enlightenment and your sincerity assure me that we should come to the point and that you would recognize in good faith what was the real discussion. The discussion is not long, and the matter is of importance, not only for mechanics, but also in the realm of metaphysics, because movement in itself separated from force is something merely relative and its subject cannot be determined; force, however, being something real and absolute, and its calculations, as I clearly show, different from that of motion, we must not be surprised if nature preserves the same quantity of force but not the same quantity of motion. It follows that there is in nature something besides extension and motion, unless all force or energy be denied to things, which would be to change them from substances into modes, as Spinoza does, who holds that God alone is a substance and that all other things are modifications of him. Spinoza is full of confused reveries and his pretended demonstrations de Deo have only an apparent truth. However, I hold that one created substance, in metaphysical strictness, does not act upon another, that is to say, with a real influence; furthermore, it is impossible to explain distinctly in what this influence consists unless we refer it to God, whose operation is a continual creation, and the source of this influence is the essential dependence of created things. If we wish to speak as ordinary men do, who say that one substance acts upon another, we must give some other conception to what is called action. It would take too long to develop this point and I refer to my last letter, which is prolix enough.

I do not know whether the Rev. Father Malebranche has replied to my answer given in one of the summer months of last year, where I advanced another general principle useful in mechanics as in geometry, which clearly overthrew all the laws of motion that Descartes put forward as well as those of Malebranche himself, together with what he said in The News to defend them.

Some day, if I find leisure I hope to write out my meditations upon the general characteristic or method of universal calculus, which should be of service in the other sciences as well as in mathematics. I have already made some successful attempts. I have definitions, axioms, and very remarkable theorems and problems in regard to coincidence, determination (or de unico ), similitude, relation in general, power or cause, and substance, and everywhere I advance with symbols in a precise and strict manner as in algebra. I have made some applications of it in jurisprudence, and it can be truly said that there are no authors whose style approaches nearer that of the geometers than the style of the jurists in the Digests. But you will ask how is calculation to be applied to conjectural matters. I reply that it is in the way that Pascal, Hugens, and others, have given demonstrations of possible chances, Because the most probable and the most certain can always be determined in so far as it is possible to know anything ex datis.

I do not however wish to take more of your time, and perhaps I have already taken too much. I should not dare to do it so frequently, if the matters upon which I desire to have your criticisms were not important. I pray God to prolong your life a long time, so that we may always profit by your enlightenment. I am, with zeal, etc.

XXVI: Leibniz to Arnauld

Venice, March 23, 1690.

I am now on the point of returning home after a long journey, undertaken under the orders of my Prince for the purpose of historical investigations. And I have found diplomas, certificates and indubitable proofs sufficient to establish the common origin of the noble Houses of Brunswick and Este, which Justel, du Cange and others had strong grounds for calling in question, because there were contradictions and errors on the part of the historians of Este in this respect, together with a complete confusion in dates and personages.