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“This bounded terminal speed will be called the maximum that such a heavy body can naturally attain through the air”

Salviati, Day Four, 278-279 Stillman Drake translation (1974)
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)
Context: The speed of the ball—thanks to opposition from the air—will not go on increasing forever. Rather, what will happen is seen in bodies of very little weight falling through no great distance; I mean, a reduction to equable motion, which will occur also in a lead or iron ball after the descent of some thousands of braccia. This bounded terminal speed will be called the maximum that such a heavy body can naturally attain through the air...

“My dear Kepler, what would you say of the learned here, who, replete with the pertinacity of the asp, have steadfastly refused to cast a glance through the telescope? What shall we make of this? Shall we laugh, or shall we cry?”

Galileo Galilei

Letter to Johannes Kepler (1610), as quoted in The Crime of Galileo (1955) by Giorgio De Santillana
Other quotes

“I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use.”

Galileo Galilei Letter to the Grand Duchess Christina

Variant: I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use.
Source: Letter to the Grand Duchess Christina (1615)
Context: I do not feel obliged to believe that the same God who has endowed us with senses, reason, and intellect has intended us to forgo their use and by some other means to give us knowledge which we can attain by them.
Context: I do not feel obliged to believe that the same God who has endowed us with senses, reason, and intellect has intended us to forgo their use and by some other means to give us knowledge which we can attain by them.<!-- ¶22

“I have never met a man so ignorant that I could not learn something from him.”

Galileo Galilei

As quoted in The Story of Civilization : The Age of Reason Begins, 1558-1648 (1935) by Will Durant, p. 605
Attributed

“I have succeeded in proving; and what I consider more important, there have been opened up to this vast and most excellent science, of which my work is merely the beginning, ways and means by which other minds more acute than mine will explore its remote corners.”

Galileo Galilei

Author, Third Day. Change of Position
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)
Context: It has been observed that missiles and projectiles describe a curved path of some sort; however no one has pointed out the fact that this path is a parabola. But this and other facts, not few in number or less worth knowing, I have succeeded in proving; and what I consider more important, there have been opened up to this vast and most excellent science, of which my work is merely the beginning, ways and means by which other minds more acute than mine will explore its remote corners.

“The sun, with all those planets revolving around it and dependent on it, can still ripen a bunch of grapes as if it had nothing else in the universe to do.”

Galileo Galilei book Dialogue Concerning the Two Chief World Systems

Loose paraphrase of Salviati on Day 3 http://law2.umkc.edu/faculty/projects/ftrials/galileo/dialogue3.html: "For when the sun draws up some vapors here, or warms a plant there, it draws these and warms this as if it had nothing else to do. Even in ripening a bunch of grapes, or perhaps just a single grape, it applies itself so effectively that it could not do more even if the goal of all its affairs were just the ripening of this one grape." Dialogue Concerning the Two Chief World Systems (1632)

“They do not reflect that if men were immortal, they themselves would never have come into the world.”

Galileo Galilei book Dialogue Concerning the Two Chief World Systems

Sagredo Variant translation: I cannot without great wonder, nay more, disbelief, hear it being attributed to natural bodies as a great honor and perfection that they are impassable, immutable, inalterable, etc.: as conversely, I hear it esteemed a great imperfection to be alterable, generable, and mutable. It is my opinion that the earth is very noble and admirable by reason of the many and different alterations, mutations, and generations which incessantly occur in it. And if, without being subject to any alteration, it had been one great heap of sand, or a mass of jade, or if, since the time of the deluge, the waters freezing which covered it, it had continued an immense globe of crystal, wherein nothing had ever grown, altered, or changed, I should have esteemed it a wretched lump of no benefit to the Universe, a mass of idleness, and in a word superfluous, exactly as if it had never been in Nature. The difference for me would be the same as between a living and a dead creature. I say the same concerning the Moon, Jupiter, and all the other globes of the Universe. The more I delve into the consideration of the vanity of popular discourses, the more empty and simple I find them. What greater folly can be imagined than to call gems, silver, and gold noble, and earth and dirt base? For do not these persons consider that if there were as great a scarcity of earth as there is of jewels and precious metals, there would be no king who would not gladly give a heap of diamonds and rubies and many ingots of gold to purchase only so much earth as would suffice to plant a jessamine in a little pot or to set a tangerine in it, that he might see it sprout, grow up, and bring forth such goodly leaves, fragrant flowers, and delicate fruit? It is scarcity and plenty that makes things esteemed and despised by the vulgar, who will say that there is a most beautiful diamond, for it resembles a clear water, and yet would not part from it for ten tons of water. 'These men who so extol incorruptibility, inalterability, and so on, speak thus, I believe, out of the great desire they have to live long and for fear of death, not considering that, if men had been immortal, they would not have come into the world. These people deserve to meet with a Medusa's head that would transform them into statues of diamond and jade, that so they might become more perfect than they are. Part of this passage, in Italian, I detrattori della corruptibilitá meriterebber d'esser cangiati in statue., has also ben translated into English as "Detractors of corruptibility deserve being turned into statues." Dialogo sopra i due massimi sistemi del mondo. (PDF) http://www.liberliber.it/biblioteca/g/galilei/le_opere_di_galileo_galilei_edizione_nazionale_sotto_gli_etc/pdf/le_ope_p.pdf, Le Opere di Galileo Galilei vol. VII, pg. 58. Compare Maimonides "If man were never subject to change there could be no generation; there would be one single being..." Guide for the Perplexed (c. 1190) Dialogue Concerning the Two Chief World Systems (1632) Context: I cannot without great astonishment — I might say without great insult to my intelligence — hear it attributed as a prime perfection and nobility of the natural and integral bodies of the universe that they are invariant, immutable, inalterable, etc., while on the other hand it is called a great imperfection to be alterable, generable, mutable, etc. For my part I consider the earth very noble and admirable precisely because of the diverse alterations, changes, generations, etc. that occur in it incessantly. If, not being subject to any changes, it were a vast desert of sand or a mountain of jasper, or if at the time of the flood the waters which covered it had frozen, and it had remained an enormous globe of ice where nothing was ever born or ever altered or changed, I should deem it a useless lump in the universe, devoid of activity and, in a word, superfluous and essentially non-existent. This is exactly the difference between a living animal and a dead one; and I say the same of the moon, of Jupiter, and of all other world globes. The deeper I go in considering the vanities of popular reasoning, the lighter and more foolish I find them. What greater stupidity can be imagined than that of calling jewels, silver, and gold "precious," and earth and soil "base"? People who do this ought to remember that if there were as great a scarcity of soil as of jewels or precious metals, there would not be a prince who would not spend a bushel of diamonds and rubies and a cartload of gold just to have enough earth to plant a jasmine in a little pot, or to sow an orange seed and watch it sprout, grow, and produce its handsome leaves, its fragrant flowers, and fine fruit. It is scarcity and plenty that make the vulgar take things to be precious or worthless; they call a diamond very beautiful because it is like pure water, and then would not exchange one for ten barrels of water. Those who so greatly exalt incorruptibility, inalterability, etc. are reduced to talking this way, I believe, by their great desire to go on living, and by the terror they have of death. They do not reflect that if men were immortal, they themselves would never have come into the world. Such men really deserve to encounter a Medusa's head which would transmute them into statues of jasper or of diamond, and thus make them more perfect than they are.

“I do not feel obliged to believe that the same God who has endowed us with senses, reason, and intellect has intended us to forgo their use and by some other means to give us knowledge which we can attain by them.”

Galileo Galilei Letter to the Grand Duchess Christina

Letter to the Grand Duchess Christina (1615)

“Salvio. A book which, indeed, is not to be placed second to any produced by the most eminent geometers either of the present or of the past; a book which, as soon as it fell into the hands of our Academician, led him to abandon his own researches along these lines; for he saw how happily everything had been treated and demonstrated by Valerio.”

Galileo Galilei

Source: Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638), P. 148

“It seems to me that it was well said by Madama Serenissima, and insisted on by your reverence, that the Holy Scripture cannot err, and that the decrees therein contained are absolutely true and inviolable. But I should have in your place added that, though Scripture cannot err, its expounders and interpreters are liable to err in many ways; and one error in particular would be most grave and most frequent, if we always stopped short at the literal signification of the words.”

Galileo Galilei book Sidereus Nuncius

Sidereus Nuncius (Venice, 1609), Letter to Benedetto Castelli http://www.heritage-history.com/www/heritage.php?Dirbooks&MenuItemdisplay&authorgibson&bookscientists&storyletter (1613)

“What has philosophy got to do with measuring anything? It's the mathematicians you have to trust, and they measure the skies like we measure a field.”

Galileo Galilei

"Matteo" in Concerning the New Star (1606)
Other quotes

“Surely, God could have caused birds to fly with their bones made of solid gold, with their veins full of quicksilver, with their flesh heavier than lead, and with their wings exceedingly small. He did not, and that ought to show something. It is only in order to shield your ignorance that you put the Lord at every turn to the refuge of a miracle.”

Galileo Galilei

Notes in a copy of Jean-Baptiste Morin's "Famous and ancient problems of the earth's motion or rest, yet to be solved" (published 1631), as quoted in The Crime of Galileo (1976) by Giorgio De Santillana, p. 167
Other quotes

“Alas! Your dear friend and servant Galileo has been for the last month hopelessly blind; so that this heaven, this earth, this universe, which I by my marvelous discoveries and clear demonstrations had enlarged a hundred thousand times beyond the belief of the wise men of bygone ages, henceforward for me is shrunk into such a small space as is filled by my own bodily sensations.”

Galileo Galilei

Letter to Élie Diodati (2 January 1638), as translated in The Private Life of Galileo : Compiled primarily from his correspondence and that of his eldest daughter, Sister Maria Celeste (1870) by Mary Allan-Olney, p. 279
Other quotes

“Of such are the mathematical sciences alone; that is, geometry and arithmetic, in which the Divine intellect indeed knows infinitely more propositions, since it knows all. But with regard to those few which the human intellect does understand, I believe its knowledge equals the Divine in objective certainty, for here it succeeds in understanding necessity, beyond which there can be no greater sureness.”

Galileo Galilei book Dialogue Concerning the Two Chief World Systems

In the 1661 translation by Thomas Salusbury: … such are the pure Mathematical sciences, to wit, Geometry and Arithmetick: in which Divine Wisdom knows infinite more propositions, because it knows them all; but I believe that the knowledge of those few comprehended by humane understanding, equalleth the divine, as to the certainty objectivè, for that it arriveth to comprehend the necessity thereof, than which there can be no greater certainty." p. 92 (from the Archimedes Project http://archimedes.mpiwg-berlin.mpg.de/cgi-bin/toc/toc.cgi?page=92;dir=galil_syste_065_en_1661;step=textonly) In the original Italian: … tali sono le scienze matematiche pure, cioè la geometria e l’aritmetica, delle quali l’intelletto divino ne sa bene infinite proposizioni di piú, perché le sa tutte, ma di quelle poche intese dall’intelletto umano credo che la cognizione agguagli la divina nella certezza obiettiva, poiché arriva a comprenderne la necessità, sopra la quale non par che possa esser sicurezza maggiore." (from the copy at the Italian Wikisource). Dialogue Concerning the Two Chief World Systems (1632)

“If you could see the earth illuminated when you were in a place as dark as night, it would look to you more splendid than the moon.”

Galileo Galilei book Dialogue Concerning the Two Chief World Systems

Salviati, p. 88
Dialogue Concerning the Two Chief World Systems (1632)

“To this end they make a shield of their hypocritical zeal for religion. They go about invoking the Bible, which they would have minister to their deceitful purposes. Contrary to the sense of the Bible and the intention of the holy Fathers, if I am not mistaken, they would extend such authorities until even in purely physical matters — where faith is not involved — they would have us altogether abandon reason and the evidence of our senses in favor of some biblical passage, though under the surface meaning of its words this passage may contain a different sense.”

Galileo Galilei Letter to the Grand Duchess Christina

Letter to the Grand Duchess Christina (1615)

“Copernicus never discusses matters of religion or faith, nor does he use argument that depend in any way upon the authority of sacred writings which he might have interpreted erroneously. … He did not ignore the Bible, but he knew very well that if his doctrine were proved, then it could not contradict the Scriptures when they were rightly understood.”

Galileo Galilei Letter to the Grand Duchess Christina

Letter to the Grand Duchess Christina (1615)

“If what we are discussing were a point of law or of the humanities, in which neither true nor false exists, one might trust in subtlety of mind and readiness of tongue and in the greater experience of the writers, and expect him who excelled in those things to make his reasoning most plausible, and one might judge it to be the best. But in the natural sciences, whose conclusions are true and necessary and have nothing to do with human will, one must take care not to place oneself in the defense of error; for here a thousand Demostheneses and a thousand Aristotles would be left in the lurch by every mediocre wit who happened to hit upon the truth for himself. Therefore, Simplicio, give up this idea and this hope of yours that there may be men so much more learned, erudite, and well-read than the rest of us as to be able to make that which is false become true in defiance of nature.”

Galileo Galilei book Dialogue Concerning the Two Chief World Systems

Salviati, p. 61
Dialogue Concerning the Two Chief World Systems (1632)