Page 127 - Textos de Matemática Vol. 34

MATHEMATICS IN COIMBRA IN THE 19TH CENTURY 117
(1) In order that the Lessons of the Mathematics Course be done in good order, and with profit from the Students: the Professor of Geometry, to whom belong the Disciplines of the First Year, before entering the Lessons proper to his Discipline, will read the General Prolegomena of the Mathematical Sciences.
(2) In them he will make a brief Introduction, and concentrated to the Study of these Sciences: Showing the object, division, and its general prospect: Explaining the Method, that they use; the usefulness, and excellence of it: And making a Summary of the main accomplishments of its History through its most remarkable Times. They are: Since the origin of Mathematics, till Thales Century, and Pythagoras. From this till the foun- dation of the Alexandrian School. From this till the Christian Era. From this till the destruction of the Greek Empire. From this till Cartesio. And from Cartesio till the present time.
(3) This Summary shall be proportionate to the capacity of the Students: So that, it predisposes them, and encourages them to enter the study with pleasure. Because of it the Reader will not enter in the detailed description of the discoveries, that were made in the said Sciences in different times, and places; because it cannot be understood, unless the same Sciences have been studied; and then they will not need the voice of the Master, to be instructed in History. He will recommend nevertheless very much to his Disciples, that according to the their progression in the Mathematics Course that they should be instructed particularly in it: Showing them, that the first thing, that must be done by somebody that wants to study in the progress of Mathematics, is to instruct himself in the discoveries made before him; in order not to loose time in discovering for the second time the same things; nor in working in the tasks, and undertakings already carried out.
Some pages later, the Statutes (today we know this part was written by Jos´e Monteiro da Rocha), when speaking about the second year discipline, Algebra, points out this aspect again:
(1) To facilitate better his entrance in it, and assure the fruit of the Lessons: The Professor will begin with the respective Prolegomena: Giving a detailed idea of its purpose, and means, it applies to obtain its goal, that it proposes itself: Showing its origin, and progresses: And making a Summary of the history of the said Algebra through its most notable Times.