In the preceding chapters I have enumerated most of the eminent mathematicians educated at Cambridge, and have indicated the lines on which the study of mathematics developed. I propose now to consider very briefly the kind of instruction provided by the university, and the means adopted for testing the proficiency of students.

Until 1858 the chief statutable exercises for a degree were the public maintenance of a thesis or proposition in the schools against certain opponents, and the opposition of a proposition laid down by some other student. Every candidate for a degree had to take part in a certain number of these discussions.

The subject-matter of these “acts” varied at different times. In the course of the eighteenth century it became the custom at Cambridge to “keep” some or all of them on mathematical questions, and I had at first intended to confine myself to reproducing one of the disputations kept in that century. But as the whole mediæval system of education—teaching and examining—rested on the performance of similar exercises, and as our existing system is derived from that without any break of continuity, I thought it might be interesting to some of my readers if I gave in this chapter a sketch of the course of studies, the means of instruction, and the tests imposed on students in earlier times; leaving the special details of a mathematical act to another chapter.