g exactly a thing whose existence cannot be conceived.

And, indeed, would you not imagine that a man laughed at you who should
declare that there are lines infinitely great which form an angle
infinitely little?

That a right line, which is a right line so long as it is finite, by
changing infinitely little its direction, becomes an infinite curve; and
that a curve may become infinitely less than another curve?

That there are infinite squares, infinite cubes, and infinites of
infinites, all greater than one another, and the last but one of which is
nothing in comparison of the last?

All these things, which at first appear to be the utmost excess of
frenzy, are in reality an effort of the subtlety and extent of the human
mind, and the art of finding truths which till then had been unknown.

This so bold edifice is even founded on simple ideas. The business is to
measure the diagonal of a square, to give the area of a curve, to find
the square root of a number, which has none in common arithmetic. After
all, the imagination ought not to be startled any more at so many orders
of infinites than at the so well-known proposition, viz., that curve
lines may always be made to pass between a circle and a tangent; or at
that other, namely, that matter is divisible in _infinitum_. These two
truths have been demonstrated many years, and are no less
incomprehensible than the things we have been speaking of.

For many years the invention of this famous calculation was denied to Sir
Isaac Newton. In Germany Mr. Leibnitz was considered as the inventor of
the differences or moments, called fluxions, and Mr. Bernouilli claimed
the integral calculus. However, Sir Isaac is now thought to have first
made the discovery, and the other two have the glory of having once made
the world doubt whether it was to be ascribed to him or them. Thus some
contested with Dr. Harvey the invention of the circulation of the blood,
as others disputed with Mr. Perrault that of the circulation of the sap.

Hartsocher and Leuwenhoek disputed with each other the honour of having
first seen the _vermiculi_ of which mankind are formed. This Hartsocher
also contested with Huygens the invention of a new method of calculating
the distance of a fixed star. It is not yet known to what philosopher we
owe the invention of the cycloid.

Be this as it will, it is by the help of this geometry of infinites that
Sir Isaac Newton attained to the most sublime d