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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.

One can also learn from this publication that the opponents of Gordan at the March 1, 1862 Disputatio were Dr. Kretschmer, Mr. Geiser, and Mr. Rathke, presumably E.E. Kretschmer and C.F. Geiser. Gordan acknowledges as his teachers in mathematics the professors Kummer, Joachimstal, Richelot, Rosenhain, Schroeter, and Galle --- but it is unclear whether any of these were present at the defense ceremony.

Concerning the question "what was actually said at the defense"; at least in my University (Leiden) the practice through the centuries has been that the examination itself is not recorded, the secretary records only the outcome (pass/fail/cum laude etc.).

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.

One can also learn from this publication that the opponents of Gordan at the March 1, 1862 Disputatio were Dr. Kretschmer, Mr. Geiser, and Mr. Rathke, presumably E.E. Kretschmer and C.F. Geiser. Gordan acknowledges as his teachers in mathematics the professors Kummer, Joachimstal, Richelot, Rosenhain, Schroeter, and Galle --- but it is unclear whether any of these were present at the defense ceremony.

Concerning the question "what was actually said at the defense"; at least in my University (Leiden) the practice through the centuries has been that the examination itself is not recorded, the secretary records only the outcome (pass/fail/cum laude etc.).

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.

One can also learn from this publication that the opponents of Gordan at the March 1, 1862 Disputatio were Dr. Kretschmer, Mr. Geiser, and Mr. Rathke, presumably E.E. Kretschmer and C.F. Geiser. Gordan acknowledges as his teachers in mathematics the professors Kummer, Joachimstal, Richelot, Rosenhain, Schroeter, and Galle --- but it is unclear whether any of these were present at the defence ceremony.

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.

One can also learn from this publication that the opponents of Gordan at the March 1, 1862 Disputatio were Dr. Kretschmer, Mr. Geiser, and Mr. Rathke, presumably E.E. Kretschmer and C.F. Geiser. Gordan acknowledges as his teachers in mathematics the professors Kummer, Joachimstal, Richelot, Rosenhain, Schroeter, and Galle --- but it is unclear whether any of these were present at the defense ceremony.

Concerning the question "what was actually said at the defense"; at least in my University (Leiden) the practice through the centuries has been that the examination itself is not recorded, the secretary records only the outcome (pass/fail/cum laude etc.).

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.

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.

One can also learn from this publication that the opponents of Gordan at the March 1, 1862 Disputatio were Dr. Kretschmer, Mr. Geiser, and Mr. Rathke, presumably E.E. Kretschmer and C.F. Geiser. Gordan acknowledges as his teachers in mathematics the professors Kummer, Joachimstal, Richelot, Rosenhain, Schroeter, and Galle --- but it is unclear whether any of these were present at the defence ceremony.