214. There is a kind of geometry which Herr Jung of Hamburg, one of the most admirable men of his time, called 'empiric'. It makes use of conclusive experiments and proves various propositions of Euclid, but especially those which concern the equality of two figures, by cutting the one in pieces, and putting the pieces together again to make the other. In this manner, by cutting carefully in parts the squares on the two sides of the right-angled triangle, and arranging these parts carefully, one makes from them the square on the hypotenuse; that is demonstrating 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.