In 1592, Galileo constructed a thermometer, using expansion and contraction of air, in a bulb, to move water in an attached tube. 
This device, in the words of his associate Francesco Sagredo (1613), who used the device for measuring the difference in temperature between air, snow, and ice, was "an instrument for measuring heat." 
In 1596, Galileo, age 32, received a copy of an age 25 Johannes Kepler's The Cosmic Mystery, the first book to use a Copernican system model of the universe; Galileo replied as follows: 
“Many years ago, I accepted Copernicus’ theory, and from that point of view I discovered the reasons for numerous natural phenomena which unquestionably cannot be explained by the conventional cosmology. I have written down many arguments as well as refutations of objections. These, however, I have not dared to publish up to now. For I am thoroughly frightened by what happened to our master, Copernicus. Although he won immortal fame among some persons, nevertheless among countless – for so large is the number of fools – he became a target of ridicule and derision. I would of course have the courage to make my thoughts public, if there were more people like you. But since there aren’t, I shall avoid this kind of activity.”
In 1610, Galileo built a telescope, in Holland, and began doing research with this new instrument, therein discovering things such as that Jupiter has four moons, which revolve about it (not earth); this was the final nail in the coffin of Ptolemaic cosmology. 
In 1613, Galileo, in his Letters on Sunspots, published his first formal endorsement of Copernican cosmology.
In 1616, the church banned him from teaching Copernican theory.
In 1632, Galileo penned, but did not formerly publish, his Dialogue Concerning the Two Chief World Systems, comparing the then controversial Copernican system with the inconsistencies of the older earth-centric Ptolemaic system.
In 1633, he was famously brought to trial (see: religion vs science legal cases) and convicted.
In 1638, Galileo, freed to some extent from the restrictions his trial situation, formally published his Dialogue Concerning the Two Chief World Systems
, the ideas of which thereafter began to reach the world.The invention of dynamics
, as a mathematical science
, according to Irish mathematician William Hamilton
, was said to have been initiated by this publication. 
In 1623, Galileo published The Assayer (Il Saggiatore), which used so much atomic theory that it was called an Epicurean book; the church attacked the work per reason that it left no reason for the doctrine of transubstantiation. 
On 27 Jul 1630, Giovanni Baliani, a physicist and experimenter, wrote to Galileo asking him why a siphon, designed by Galliano, made to carry water over a hill of 21 meters, failed to work? If the tube of the siphon was filled with water by means of a pump, and then the pump was stopped, the water separated high in the tube and flowed out both ends.  Galileo responded as follows, namely stated his view that water was like a rope that broke:
“If hemp or steel cords break under excessive weight, what doubt could we have that a cord of water will likewise break? In fact, it will break more easily, insofar as the parts of water, becoming separated from one another, do not have to overcome resistances other than that of the vacuum that is created at the moment of division. This is because in the case of iron and other solids, there is a very strong and tenacious attachment of the parts that is absent in water.”
— Galileo (1630), “Letter to Giovani Baliani” (Ѻ), Aug 6
On 22 Feb 1632, Galileo, having thought a good deal about the pump problem, published his opinions on the matter in Discourses Concerning the Two New Sciences, wherein he takes up the issue of why water cannot be raised more than a certain height via a thought experiment as illustrated adjacent, wherein CABD represents the cross section of a cylinder of the pump, made of metal or glass, and EGHF is cylinder of wood, fitted into the cylinder, capable of up and down motion, through which a hole is bored through the cylinder to receive an iron wire carrying a hook at the bottom, which has a conical head I at the top of the wire, which makes a perfect fit with the countersunk wooden cylinder.
The cylinder, in the area above the wooden piston, is then filled completely with water, and weights are added gradually, into the bucket (supposedly), until the water separates, i.e. “breaks” (like a rope) as Galileo envisioned things, and the bucket falls, according to which the weight of the stopper, wire, bucket, and contents, thus measures the “force of the vacuum”, according to Galileo; he summarized his view as follows:
“Up to this time, I had been so thoughtless that, although I knew a rope... if sufficiently long would break by its own weight when held at the upper end, it never occurred to me that the same thing would happen only much more easily to a column of water. And really is not that thing which is attracted in the pump [raising water from the well] a column of water attached at the upper end and stretched more and more until finally a point is reached where it breaks, like a rope, on account of its excessive weight.”
— Galileo (1638), Two New Sciences (character: Segredo, a challenger of Galileo’s views)
“That is precisely the way it works; this fixed elevation of 18 cubits (about 10 m) is true for any quantity of water whatever, be the pump large or small.”
— Galileo (1638), Two New Sciences (character: Salviati, spokesman for Galileo)
Galileo, in sum, argued that the reason that the siphon failed to work over hills greater than twenty-one meters in height was that it was the power of the vacuum that held the water up, but that past a certain height the amount of water simply became too much and the force could not hold any more, like a cord that can only withstand so much weight hanging from it.
Galileo’s friend and student Italian physicist Evangelista Torricelli made the first mercury barometer in 1643 in his investigations of the vacuum.
It would seem that Galileo, in his independent manner of thinking, was influenced greatly by his father Italian musician Vincenzo Galilei who had the anti-appeal to authority mentality that:
“Those who rely simply on the weight of authority to prove any assertion, without searching out the arguments to support it, act absurdly. I wish to question freely and to answer freely without any sort of adulation. That well becomes any who are sincere in the search for truth.”
It would well seem that Galileo adopted this motto to the fullest degree.
Quotes | On
The following are notes of praise and or tribute:
“Galileo does not say that he admits the operations of heavy air, but persists in asserting that nature also concurs in resisting a vacuum.”
— Evangelista Torricelli (1644), “Letter to Michelangelo Ricci”, Jun 11 
“Dynamics is the science of accelerating or retarding forces, and of the varied motions which they must produce. This science is wholly due to the moderns, and Galileo is the one who threw or made the first foundations.”
— Joseph Lagrange (1788), Analytical Mechanics (Volume One, pg. 221) 
“What the founders of modern science, among them Galileo, had to do, was not to criticize and to combat faulty theories, and to correct or replace them by better ones. They had to do something different. They had to destroy one world [view] and to replace it by another. They had to reshape the framework of our intellect itself, to restate and reform its concepts, to evolve a new approach to ‘being’, an new concept of knowledge, a new concept of science—and even to replace a pretty natural approach, that of common sense, by another.”
— Alexandre Koyre (1943), “Galileo and Plato” 
Quotes | By
The following are noted quotes:
“Like you, I accepted the Copernican position several years ago and discovered from thence the causes of many natural effects which are doubtless inexplicable by the current theories. I have written up many of my reasons and refutations on the subject, but I have not dared until now to bring them into the open, being warned by the fortunes of Copernicus himself, our master, who procured immortal fame among a few but stepped down among the great crowd (for the foolish are numerous), only to be derided and dishonored. I would dare publish my thoughts if there were many like you; but, since there are not, I shall forebear.”
— Galileo Galilei (1597), “Letter to Johannes Kepler” (Ѻ)
“I think, my Kepler, we will laugh at the extraordinary stupidity of the multitude [common herd]. What do you say to the leading philosophers of the faculty [academy] here, who are filled with the stubbornness of an asp and do not want to look at either the planets, the moon or the telescope, even though I have freely and deliberately offered them the opportunity a thousand times. Truly, just as the asp stops its ears, so do these philosophers shut their eyes to the light of truth.”
— Galileo Galilei (1610), “Letter to Johannes Kepler”, Aug 
“If the vacuum cannot be recognized either by the senses or by the intellect, how have you managed to find out that it does not exist?”
— Galileo (c.1620), annotations, in his copy of Julius Galla’s On the Appearance of the Orbit of the Moon (De phaenomenis in orbe lunare), after the phrase ‘concerning the vacuum’; cited by William Middleton (1964) in The History of the Barometer (pg. 5)
“Philosophy is written in that great book that lies before our gaze—I mean the universe—but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written.”
— Galileo Galilei (1623), The Assayer 
“The book of nature is written in the language of mathematics and without it one wanders about in a dark labyrinth.”
— Galileo Galilei (c.1620) 
“I do not think it is necessary to believe that the same god who has given us our senses, reason, and intelligence wished us to abandon their use, giving us by some other means the information that we could gain through them.”
— Galileo Galilei (c.1630), in FSM app
“Nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called into question, much less condemned, upon the testimony of biblical passages.”
— Galileo Galilei (c.1630) in FSM app
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● Galileo Galilei – Wikipedia.