behaved very unfairly: he represents Cluvier as placing the essence of his
method in the solution of the problem _construere mundum divinae menti
analogum_, to construct a world corresponding to the divine mind. Nothing
to begin with: no way of proceeding. Now, it ought to have been _ex data
linea construere_,[618] etc.: there is a given line, which is something to
go on. Further, there is a way of proceeding: it is to find the product of
1, 2, 3, 4, etc. for ever. Moreover, Montucla charges Cluvier with
_unsquaring_ the parabola, which Archimedes had squared as tight as a
glove. But he never mentions how very nearly Cluvier agrees with the Greek:
they only differ by 1 divided by 3n^2, where n is the infinite number of
parts of which a parabola is composed. This must have been the conceit that
tickled Leibnitz, and made him wish that Cluvier and Nieuwentiit should
fight it out. Cluvier, was admitted, on terms of irony, into the Leipzig
Acts: he appeared on a more serious footing in London. It is very rare for
one cyclometer to refute another: _les corsaires ne se battent pas_.[619]
The only instance I recall is that of M. Cluvier, who (_Phil. Trans._,
1686, No. 185) refuted M. Mallemont de Messange,[620] who {334} published
at Paris in 1686. He does it in a very serious style, and shows himself a
mathematician. And yet in the year in which, in the _Phil. Trans._, he was
a geometer, and one who rebukes his squarer for quoting Matthew xi. 25, in
that very year he was the visionary who, in the Leipzig Acts, professed to
build a world resembling the divine mind by multiplying together 1, 2, 3,
4, etc. up to infinity.

THE RAINBOW PARADOX.

There is a very pretty opening for a paradox which has never found its
paradoxer in print. The philosophers teach that the rainbow is not
material: it comes from rain-drops, but those rain-drops do not _take_
color. They only _give_ it, as lenses and mirrors; and each one drop gives
_all_ the colors, but throws them in different directions. Accordingly, the
same drop which furnishes red light to one spectator will furnish violet to
another, properly placed. Enter the paradoxer whom I have to invent. The
philosopher has gulled you nicely. Look into the water, and you will see
the reflected rainbow: take a looking-glass held sideways, and you see
another reflection. How could this be, if there were nothing colored to
reflect? The paradoxer's facts are true: and what are called the refl