Paul Gordan's theses were published in De linea geodetica and digitised by Google, from which I reproduce the relevant page:
Translation:
- I. The method of functional division, proposed by the respectable Cournot as an analytical and empirical method, appears unsuitable, since one does not have fully empirical functions.
- II. The method of the infinitely-small is, I claim, no less precise than the method of limits.
- III. It is of greater interest to investigate the implicit properties of a function defined by a differential equation than to investigate in terms of which known functions it can be expressed.
- IV. The principles of Democritus remain to the present day as the foundation of the theory of atoms.