empirically the 47th proposition of the first book of Euclid.  Now supposing that some of these pieces taken from the two smaller squares are lost, something[262] will be lacking in the large square that is to be formed from them; and this defective combination, far from pleasing, will be disagreeably ugly.  If then the pieces that remained, composing the faulty combination, were taken separately without any regard to the large square to whose formation they ought to contribute, one would group them together quite differently to make a tolerably good combination.  But as soon as the lost pieces are retrieved and the gap in the faulty combination is filled, there will ensue a beautiful and regular thing, the complete large square:  this perfect combination will be far more beautiful than the tolerably good combination which had been made from the pieces one had not mislaid alone.  The perfect combination corresponds to the universe in its entirety, and the faulty combination that is a part of the perfect one corresponds to some part of the universe, where we find defects which the Author of things has allowed, because otherwise, if he had wished to re-shape this faulty part and make thereof a tolerably good combination, the whole would not then have been so beautiful.  For the parts of the faulty combination, grouped better to make a tolerably good combination, could not have been used properly to form the whole and perfect combination.  Thomas Aquinas had an inkling of these things when he said:  ad prudentem gubernatorem pertinet, negligere aliquem defectum bonitatis in parte, ut faciat augmentum bonitatis in toto (Thom., Contra Gentiles, lib. 2, c. 71).  Thomas Gatacre, in his Notes on the book of Marcus Aurelius (lib. 5, cap. 8, with M. Bayle), cites also passages from authors who say that the evil of the parts is often the good of the whole.

215.  Let us return to M. Bayle’s illustrations.  He imagines a prince (p. 963) who is having a city built, and who, in bad taste, aims rather at airs of magnificence therein, and a bold and unusual style of architecture, than at the provision of conveniences of all kinds for the inhabitants.  But if this prince has true magnanimity he will prefer the convenient to the magnificent architecture.  That is M. Bayle’s judgement.  I consider, however, that there are cases where one will justifiably prefer beauty of construction in a palace to the convenience of a few domestics.  But I admit that the construction would be bad, however beautiful it might be, if it were a cause of diseases to the inhabitants; provided it was possible to make one that would be better, taking into account beauty, convenience and health all together.  It may be, indeed, that one cannot have all these[263] advantages at once.  Thus, supposing one wished to build on the northern and more bracing side of the mountain, if the castle were then bound to be of an unendurable construction, one would prefer to make it face southward.