In the 16th century, Tycho Brahe and Michael Maestlin demonstrated that comets must exist outside of Earth's atmosphere by measuring the parallax of the Great Comet of 1577. Within the precision of the measurements, this implied the comet must be at least four times more distant than from Earth to the Moon. Based on observations in 1664, Giovanni Borelli recorded the longitudes and latitudes of comets that he observed, and suggested that cometary orbits may be parabolic. Despite being a skilled astronomer, in his 1623 book The Assayer, Galileo Galilei rejected Brahe's theories on the parallax of comets and claimed that they may be a mere optical illusion, despite little personal observation. In 1625, Maestlin's student Johannes Kepler upheld that Brahe's view of cometary parallax was correct. Additionally, mathematician Jacob Bernoulli published a treatise on comets in 1682.