e most regular is always opportune for all creatures
simultaneously; and I judge _a posteriori_, for the plan chosen by God is
not so. I have, however, also shown this _a priori_ in examples taken from
mathematics, and I will presently give another here. An Origenist who
maintains that all rational creatures become happy in the end will be still
easier to satisfy. He will say, in imitation of St. Paul's saying about the
sufferings of this life, that those which are finite are not worthy to be
compared with eternal bliss.

212. What is deceptive in this subject, as I have already observed, is that
one feels an inclination to believe that what is the best in the whole is
also the best possible in each part. One reasons thus in geometry, when it
is a question _de maximis et minimis_. If the road from A to B that one
proposes to take is the shortest possible, and if this road passes by C,
then the road from A to C, part of the first, must also be the shortest
possible. But the inference from _quantity_ to _quality_ is not always[261]
right, any more than that which is drawn from equals to similars. For
_equals_ are those whose quantity is the same, and _similars_ are those not
differing according to qualities. The late Herr Sturm, a famous
mathematician in Altorf, while in Holland in his youth published there a
small book under the title of _Euclides Catholicus_. Here he endeavoured to
give exact and general rules in subjects not mathematical, being encouraged
in the task by the late Herr Erhard Weigel, who had been his tutor. In this
book he transfers to similars what Euclid had said of equals, and he
formulates this axiom: _Si similibus addas similia, tota sunt similia_. But
so many limitations were necessary to justify this new rule, that it would
have been better, in my opinion, to enounce it at the outset with a
reservation, by saying, _Si similibus similia addas similiter, tota sunt
similia_. Moreover, geometricians often require _non tantum similia, sed et
similiter posita_.

213. This difference between quantity and quality appears also in our case.
The part of the shortest way between two extreme points is also the
shortest way between the extreme points of this part; but the part of the
best Whole is not of necessity the best that one could have made of this
part. For the part of a beautiful thing is not always beautiful, since it
can be extracted from the whole, or marked out within the whole, in an
irregular man