pure mathematics, where everything
proceeds in order, and where it is possible to fathom them by a close
contemplation which grants us an enjoyment, so to speak, of the vision of
the ideas of God. One may propose a succession or series of numbers
perfectly irregular to all appearance, where the numbers increase and
diminish variably without the emergence of any order; and yet he who knows
the key to the formula, and who understands the origin and the structure of
this succession of numbers, will be able to give a rule which, being
properly understood, will show that the series is perfectly regular, and
that it even has excellent properties. One may make this still more evident
in lines. A line may have twists and turns, ups and downs, points of
reflexion and points of inflexion, interruptions and other variations, so
that one sees neither rhyme nor reason therein, especially when taking into
account only a portion of the line; and yet it may be that one can give its
equation and construction, wherein a geometrician would find the reason and
the fittingness of all these so-called irregularities. That is how we must
look upon the irregularities constituted by monstrosities and other
so-called defects in the universe.

243. In this sense one may apply that fine adage of St. Bernard (Ep. 276,
Ad Eugen., III): 'Ordinatissimum est, minus interdum ordinate fieri
aliquid.' It belongs to the great order that there should be some small
disorder. One may even say that this small disorder is apparent only in the
whole, and it is not even apparent when one considers the happiness of
those who walk in the ways of order.

244. When I mention monstrosities I include numerous other apparent defects
besides. We are acquainted with hardly anything but the surface of our
globe; we scarce penetrate into its interior beyond a few hundred fathoms.
That which we find in this crust of the globe appears to be the effect of
some great upheavals. It seems that this globe was once on fire, and that
the rocks forming the base of this crust of the earth are scoria remaining
from a great fusion. In their entrails are found metal and mineral [278]
products, which closely resemble those emanating from our furnaces: and the
entire sea may be a kind of _oleum per deliquium_, just as tartaric oil
forms in a damp place. For when the earth's surface cooled after the great
conflagration the moisture that the fire had driven into the air fell back
upon the