Cosmo, Grand Duke of Tuscany, invites Galileo to Pisa--Galileo visits Venice in 1609, where he first hears of the Telescope--He invents and constructs one, which excites a great sensation--Discovers Mountains in the Moon, and Forty Stars in the Pleiades--Discovers Jupiter's Satellites in 1610--Effect of this discovery on Kepler--Manner in which these discoveries were received--Galileo appointed Mathematician to Cosmo--Mayer claims the discovery of the Satellites of Jupiter--Harriot observes them in England in October 1610, CHAPTER III. 42 Galileo announces his discoveries in Enigmas--Discovers the Crescent of Venus--the Ring of Saturn--the Spots on the Sun--Similar Observations made in England by Harriot--Claims of Fabricius and Scheiner to the discovery of the Solar Spots--Galileo's Letters to Velser on the claims of Scheiner--His residence at the Villa of Salviati--Composes his work on Floating Bodies, which involves him in new controversies, CHAPTER IV. 56 Galileo treats his Opponents with severity and sarcasm--He is aided by the Sceptics of the day--The Church Party the most powerful--Galileo commences the attack, and is answered by Caccini, a Dominican--Galileo's Letter to the Grand Duchess of Tuscany, in support of the motion of the Earth and the stability of the Sun--Galileo visits Rome--Is summoned before the Inquisition--And renounces his opinions as Heretical--The Inquisition denounces the Copernican system--Galileo has an audience of the Pope, but still maintains his opinions in private society--Proposes to find out the Longitude at Sea by means of Jupiter's Satellites--His negotiation on this subject with the Court of Spain--Its failure--He is unable to observe the three Comets of 1618, but is involved in the controversy to which they gave rise, CHAPTER V. 72 Urban VIII., Galileo's friend, raised to the Pontificate--Galileo goes to Rome to offer his congratulations--The Pope loads Galileo with presents, and promises a Pension to his Son--Galileo in pecuniary difficulties, owing to the death of his patron, Cosmo--Galileo again rashly attacks the Church, notwithstanding the Pope's kindness--He composes his System of the World, to demonstrate the Copernican System--Artfully obtains a license to print it--Nature of the work--Its influence on the public mind--The Pope resolves on suppressing it--Galileo summoned before the Inquisition--His Trial--His Defence--His formal Abjuration of his Opinions--Observations on his conduct--The Pope shews great indulgence to Galileo, who is allowed to return to his own house at Arcetri as the place of his confinement, CHAPTER VI. 102