Leibniz to Newton

Hanover, 7 March 1692/3

How great I think the debt owed to you, by our knowledge of mathematics and of all nature, I have acknowledged in public also when occasion offered. You had given an astonishing development to geometry by your series; but when you published your work, the Principia, you showed that even what is not subject to the received analysis is an open book to you. I too have tried by the application of convenient symbols, which exhibit differences and sums, to submit that geometry which I call ‘transcendent’ in some sense to analysis, and the attempt did not go badly. But to put the last touches I am still looking for something big from you, first how best problems which seek lines from a given property of their tangents, may be reduced to squarings, and next how the squarings themselves – and this is what I would like very much to see – may be reduced to the rectifications of curves, simpler in all cases than the measurings of surfaces or volumes.

But above all I would wish that, perfected in geometrical problems, you would continue, as you have begun, to handle nature in mathematical terms; and in this field you have by yourself with very few companions gained an immense return for your labour. You have made the astonishing discovery that Kepler’s ellipses result simply from the conception of attraction or gravitation and passage in a planet. And yet I would incline to believe that all these are caused or regulated by the motion of a fluid medium, on the analogy of gravity and magnetism as we know it here. Yet this solution would not at all detract from the value and truth of your discovery. …