One of the most immediate consequences of the remarkable telescopic observations of Galileo in 1609-10, was the debate it generated among the mathematicians and astronomers of the Society of Jesus. As is well known, in Rome these men closely followed and reproduced Galileo’s observations and engaged in an intense debate on the correct cosmological order of the Universe that the new observations demanded. This debate culminated with the adoption of Tycho Brahe’s system, made "official" with the publication of Giuseppe Biancani’s Sphaera mundi seu cosmographia, in 1620.

Not so generally realized is that some of the participants in these controversies were in Lisbon in the years immediately after these remarkable events, either as teachers of mathematics in Portuguese colleges, or merely in transit to the Asian missions -- and hence that Portuguese Archives are worth inspecting more carefully.

In this communication I examine some documentation hitherto unexplored, left by these men. A particular attention will be devoted to the lecture notes of Giovanni Paolo Lembo, one of the four signatories of the famous reply of the Jesuit mathematicians to cardinal Bellarmino (24 April 1611), who taught mathematics in Lisbon in 1615-17. These notes are the earliest known documents testifying the teaching of Galileo´s discoveries in Portugal, the construction of telescopes, and the carrying out of telescopic observations in that country.

In addition to their interest for understanding the spreading of Galileo´s ideas in Portugal – which Portuguese historiography had traditionally placed in the late 1620´s and early 1630´s - these notes also contain important information on the debates that led to the adoption of the cosmological system of Tycho Brahe by the Jesuits. In fact, in Lembo’s and some other Jesuits' lecture notes, one can find careful explanations of Galileo’s new findings, their cosmological significance and consequences discussed, and the defence of Tychonic or semi-Tychonic world systems.