"All these lectures to consist in extemporary explications of books in such an easy, short, and clear manner as may be most profitable to the auditors. And if any Lecturer or other person shall compose any treatise which shall be preferred and used by the major part of the Mathematic or Philosophic Lecturers, the University shall give the author either £20, or if those Lecturers request it, £30, £40 or £50, out of their Common Chest. "Commissioners to be appointed for some years to set on foot, inspect, and amend the institution. "No oaths of office to be imposed on the Lecturers. I do not know a greater abuse of religion than that sort of oaths: they being harder to be kept than the Jewish Law, so that yearly absolutions have been instituted. The papists, who believe such absolutions, might be excused for instituting such oaths, but we have no such doctrine, and yet continue their practices. Admonitions and pecuniary mulcts for neglect of duty are less cruel punishments than the consequence of perjury, and may be as effectual." [Footnote 33: Camb. Univ. Library, Newton MSS. section viii, No. 5. Add. 4005/6, A.] CHAPTER XV. THE HISTORY OF THE MATHEMATICAL TRIPOS. The Mathematical Tripos has played so prominent a part in the history of education at Cambridge and of mathematics in England, that a sketch of its development[34] may be interesting to general readers. So far as mathematics is concerned the history of the University before Newton may be summed up very briefly. The University was founded towards the end of the twelfth century. Throughout the middle ages, the instruction given to students was organized on lines similar to those current at Paris and Oxford, and to qualify for a degree it was necessary to perform various exercises, and especially to keep a number of _acts_ or to oppose acts kept by other students. An act consisted in effect of a debate in Latin, thrown, at any rate in later times, into syllogistic form. It was commenced by one student, the _respondent_, stating some proposition, often propounded in the form of a thesis, which was attacked by an _opponent_ or _opponents_, the discussion being controlled by a senior graduate. The teaching was largely in the hands of young graduates--every master of arts being compelled to reside and teach for at least one year--though no doubt colleges and private hostels supplemented this instruction in the case of their own students.