[1] Federico was the first of eleven legitimate male children and was born in Palazzo Cesi, in via della Maschera d'Oro, Rome, on 26 February 1585.

In 1603, at the age of eighteen, Cesi invited three slightly older friends, the Dutch physician Johannes van Heeck (in Italy Giovanni Ecchio), and two fellow Umbrians, mathematician Francesco Stelluti of Fabriano and polymath Anastasio de Filiis of Terni to join with him in the founding of the Accademia dei Lincei ("Academy of the Lynxes"), aimed at the understanding of all natural sciences through a method of research based upon observation, experiment, and the inductive method.

The four men chose the name "Lincei" (lynx) from Giambattista della Porta's book "Magia Naturalis", which had an illustration of the fabled cat on the cover and the words "...with lynx-like eyes, examining those things which manifest themselves, so that having observed them, he may zealously use them".

The academy's motto, chosen by Cesi, was: "take care of small things if you want to obtain the greatest results" (minima cura si maxima vis).

Since it was an uncertain time to conduct scientific research — in 1578 the Inquisition had closed Giambattista della Porta's Academia Secretorum Naturae in Naples under suspicion of sorcery[5] — the Accademia dei Lincei had rough beginnings.

[4] The four "Lynxes" soon returned to their native cities and continued to communicate only by letter, adopting astronomical pen names: Cesi, perpetual president, was Celívago.

[7] The Academy's chancellor and secretary Johaness Faber donated his entire scientific collection to Cesi and he acquired a number of other texts from other compatriots.

[4] The academy survived due to Cesi's personal wealth and his diplomatic skills in navigating the politics of Counter-Reformation Rome.

[7] His interest in the cosmos led him to the invention of the telescope, and him meeting two well-known astronomers, Giovanbattista della Porta and Galileo Galilei.

[9] The letter was sent by Giovanbattista della Porta, an Italian natural philosopher, and it depicted an illustration of the early telescope along with instructions on how to manufacture one.

[15] They trusted that replacing these ideologies could be countered by enforcing Plato's philosophy outlined in the Timaeus, describing the connections between man and the universe.