Barozzi helped in the general reappraisal of the geometry of Euclid, and corresponded with numerous mathematicians, including the German Jesuit Christopher Clavius.

Barozzi also discussed 13 ways of drawing a parallel line in his Admirandum illud geometricum problema tredecim modis demonstratum quod docet duas lineas in eodem plano designare, quae nunquam invicem coincidant, etiam si in infinitum protrahantur: et quanto longius producuntur, tanto sibiinuicem propiores euadant (1586).

He studies Epistemology, discusses the mathematical proofs and the degree of certainty of each one, applying the principles of Aristotelian theory of demonstrative science.

[3] The Greek Nikolaos Panagiotakis, writes that he was the only one of the Venetian nobles who contributed to the Cretan Renaissance, bringing Crete on the spiritual currents of Europe.

[4] Barozzi was accused of being a sorcerer, a charge that he did not help refute by publishing his Pronostico Universale di tutto il mondo (Bologna, 1566), a collection of the prophecies of Nostradamus for the years 1565–1570.

He also published a special edition of Oracula Leonis in 1577, a collection of cryptic prophecies attributed to the Byzantine Emperor Leo VI the Wise and dedicated to the Cretan governor, Giacomo Foscarini.