Galileo Galilei Quotes (1564-1642)

“I therefore concluded, and decided unhesitatingly, that there are three stars in the heavens moving about Jupiter, as Venus and Mercury about the Sun; which at length was established as clear as daylight by numerous other observations. These observations also established that there are not only three, but four, erratic sidereal bodies performing their revolutions round Jupiter.”

“I therefore concluded, and decided unhesitatingly, that there are three stars in the heavens moving about Jupiter, as Venus and Mercury about the Sun; which at length was established as clear as daylight by numerous other observations. These observations also established that there are not only three, but four, erratic sidereal bodies performing their revolutions round Jupiter.”

“I mentally conceive of some moveable [sphere] projected on a horizontal plane, all impediments being put aside. Now it is evident... that equable motion on this plane would be perpetual if the plane were of infinite extent, but if we assume it to be ended, and [situated] on high, the movable, driven to the end of this plane and going on further, adds on to its previous equable and indelible motion, that downward tendency which it has from its heaviness. Thus, there emerges a certain motion, compounded...”

“I esteem myself happy to have as great an ally as you in my search for truth. I will read your work … all the more willingly because I have for many years been a partisan of the Copernican view because it reveals to me the causes of many natural phenomena that are entirely incomprehensible in the light of the generally accepted hypothesis. To refute the latter I have collected many proofs, but I do not publish them, because I am deterred by the fate of our teacher Copernicus who, although he had won immortal fame with a few, was ridiculed and condemned by countless people (for very great is the number of the stupid).”

“Do we not say that the judicious discovering of a most lovely Statua in a piece of Marble, hath sublimated the wit of Buonarruotti far above the vulgar wits of other men? And yet this work is onely the imitation of a meer aptitude and disposition of exteriour and superficial mem­bers of an immoveable man; but what is it in comparison of a man made by nature, composed of as many exteriour and inte­riour members, of so many muscles, tendons, nerves, bones, which serve to so many and sundry motions? but what shall we say of the senses, and of the powers of the soul, and lastly, of the understanding? May we not say, and that with reason, that the structure of a Statue falls far short of the formation of a living man, yea more of a contemptible worm?”

“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.”

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

“Names and attributes must be accommodated to the essence of things, and not the essence to the names, since things come first and names afterwards.”

“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.”

“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.”

“What was observed by us in the third place is the nature or matter of the Milky Way itself, which, with the aid of the spyglass, may be observed so well that all the disputes that for so many generations have vexed philosophers are destroyed by visible certainty, and we are liberated from wordy arguments.”

“Among all the great men who have philosophized about this remarkable effect, I am more astonished at Kepler than at any other. Despite his open and acute mind, and though he has at his fingertips the motions attributed to the earth, he nevertheless lent his ear and his assent to the moon's dominion over the waters, to occult properties, and to such puerilities.”

“I mentally conceive of some moveable [sphere] projected on a horizontal plane, all impediments being put aside. Now it is evident... that equable motion on this plane would be perpetual if the plane were of infinite extent, but if we assume it to be ended, and [situated] on high, the movable, driven to the end of this plane and going on further, adds on to its previous equable and indelible motion, that downward tendency which it has from its heaviness. Thus, there emerges a certain motion, compounded...”

“Persisting in their original resolve to destroy me and everything mine by any means they can think of, these men are aware of my views in astronomy and philosophy. They know that as to the arrangement of the parts of the universe, I hold the sun to be situated motionless in the center of the revolution of the celestial orbs while the earth revolves about the sun. They know also that I support this position not only by refuting the arguments of Ptolemy and Aristotle, but by producing many counter-arguments; in particular, some which relate to physical effects whose causes can perhaps be assigned in no other way. In addition there are astronomical arguments derived from many things in my new celestial discoveries that plainly confute the Ptolemaic system while admirably agreeing with and confirming the contrary hypothesis.”

“About ten months ago [1609] a report reached my ears that a certain Fleming [Hans Lippershey] had constructed a spyglass, by means of which visible objects, though very distant from the eye of the observer, were distinctly seen as if nearby... Of this truly remarkable effect several experiences were related, to which some persons gave credence while others denied them. A few days later the report was confirmed to me in a letter from a noble Frenchman at Paris, Jacques Badovere, which caused me to apply myself wholeheartedly to enquire into the means by which I might arrive at the invention of a similar instrument. This I did shortly afterwards, my basis being the theory of refraction. First I prepared a tube of lead, at the ends of which I fitted two glass lenses, both plane on one side while on the other side one was spherically convex and the other concave.”

“I will now say something which may perhaps astonish you; it refers to the possibility of dividing a line into its infinitely small elements by following the same order which one employs in dividing the same line into forty, sixty, or a hundred parts, that is, by dividing it into two, four, etc. He who thinks that, by following this method, he can reach an infinite number of points is greatly mistaken; for if this process were followed to eternity there would still remain finite parts which were undivided. ... Indeed by such a method one is very far from reaching the goal of indivisibility; on the contrary he recedes from it and while he thinks that, by continuing this division and by multiplying the multitude of parts, he will approach infinity, he is... getting farther and farther away from it. My reason is this. In the preceding discussion we concluded that, in an infinite number, it is necessary that the squares and cubes should be as numerous as the totality of the natural numbers [tutti i numeri], because both of these are as numerous as their roots which constitute the totality of the natural numbers. Next we saw that the larger the numbers taken the more sparsely distributed were the squares, and still more sparsely the cubes; therefore it is clear that the larger the numbers to which we pass the farther we recede from the infinite number; hence it follows that since this process carries us farther and farther from the end sought, if on turning back we shall find that any number can be said to be infinite, it must be unity. Here indeed are satisfied all those conditions which are requisite for an infinite number; I mean that unity contains in itself as many squares as there are cubes and natural numbers [tutti i numeri]. ... There is no difficulty in the matter because unity is at once a square, a cube, a square of a square, and all the other powers [dignitā]; nor is there any essential peculiarity in squares or cubes which does not belong to unity; as, for example, the property of two square numbers that they have between them a mean proportional; take any square number you please as the first term and unity for the other, then you will always find a number which is a mean proportional. Consider the two square numbers, 9 and 4; then 3 is the mean proportional between 9 and 1 [frac{1}{3} = frac{3}{9}]; while 2 is a mean proportional between 4 and 1 [frac{1}{2} = frac{2}{4}]; between 9 and 4 we have 6 as a mean proportional [frac{4}{6} = frac{6}{9}]. A property of cubes is that they must have between them two mean proportional numbers; take 8 and 27; between them lie 12 and 18 [frac{8}{12} = frac{18}{27}]; while between 1 and 8 we have 2 and 4 intervening [frac{1}{2} = frac{4}{8}]; and between 1 and 27 there lie 3 and 9 [frac{1}{3} = frac{9}{27}]. Therefore we conclude that unity is the only infinite number. These are some of the marvels which our imagination cannot grasp and which should warn us against the serious error of those who attempt to discuss the infinite by assigning to it the same properties which we employ for the finite, the natures of the two having nothing in common.”

“Neither one nor the other doth follow, for that both the assertions may be true. The Oracle adjudged Socrates the wi­sest of all men, whose knowledg is limited; Socrates acknowledgeth that he knew nothing in relation to absolute wisdome, which is infinite; and because of infinite, much is the same part as is little, and as is nothing (for to arrive... to the infinite number, it is all one to accumulate thousands, tens, or ciphers,) therefore Socrates well perceived his wisdom to be nothing, in comparison of the infinite knowledg which he wanted. But yet, because there is some knowledg found amongst men, and this not equally shared to all, Socrates might have a greater share thereof than others, and therefore verified the answer of the Oracle.”

“Do we not say that the judicious discovering of a most lovely Statua in a piece of Marble, hath sublimated the wit of Buonarruotti far above the vulgar wits of other men? And yet this work is onely the imitation of a meer aptitude and disposition of exteriour and superficial mem­bers of an immoveable man; but what is it in comparison of a man made by nature, composed of as many exteriour and inte­riour members, of so many muscles, tendons, nerves, bones, which serve to so many and sundry motions? but what shall we say of the senses, and of the powers of the soul, and lastly, of the understanding? May we not say, and that with reason, that the structure of a Statue falls far short of the formation of a living man, yea more of a contemptible worm?”

“Copernicus had taken one course in treating the earth as virtually a celestial body in the Aristotelian sense—a perfect sphere governed by the laws which operated in the higher reaches of the skies. Galileo complemented this by taking now the opposite course—rather treating the heavenly bodies as terrestrial ones, regarding the planets as subject to the very laws which applied to balls sliding down inclined planes. There was something in all this which tended to the reduction of the whole universe to uniform physical laws, and it is clear that the world was coming to be more ready to admit such a view.”

“In Santa Croce's holy precincts lie Ashes which make it holier, dust which is Even in itself an immortality, Though there were nothing save the past, and this, The particle of those sublimities Which have relapsed to chaos: here repose Angelo's, Alfieri's bones, and his, The starry Galileo, with his woes; Here Machiavelli's earth returned to whence it rose. These are four minds, which, like the elements, Might furnish forth creation:—Italy! Time, which hath wronged thee with ten thousand rents Of thine imperial garment, shall deny, And hath denied, to every other sky, Spirits which soar from ruin: thy decay Is still impregnate with divinity, Which gilds it with revivifying ray; Such as the great of yore Canova is to-day.”

“While Stevin investigated statics, Galileo pursued principally dynamics. Galileo was the first to abandon the Aristotelian idea that bodies descend more quickly in proportion as they are heavier; he established the first law of motion; determined the laws of falling bodies; and, having obtained a clear notion of acceleration and of the independence of different motions, was able to prove that projectiles move in parabolic curves. Up to his time it was believed that a cannon-ball moved forward at first in a straight line and then suddenly fell vertically to the ground. Galileo had an understanding of centrifugal forces, and gave a correct definition of momentum. Though he formulated the fundamental principles of statics, known as the parallelogram of forces, yet he did not fully recognise its scope. The principle of virtual velocities was partly conceived by Guido Ubaldo (died 1607), and afterwards more fully by Galileo.”

“It is impossible to exaggerate the effects of his telescopic discoveries on Galileo's life, so profound were they. Not only is it true of Galileo's personal life and thought, but it equally true of their influence on the history of scientific thought. Galileo had the experience of beholding the heavens as they actually are for perhaps the first time, and wherever he looked he found evidence to support the Copernican system against the Ptolemaic, or at least weaken the authority of the ancients. This shattering experience—of observing the depths of the universe, of being the first mortal to know what the heavens are actually like—made so deep an impression... that it is only by considering the events of 1609... that one can understand the subsequent direction of his life.”

“Koyré's exaltation of the "Platonic and Pythagorean" elements of the Scientific Revolution... was based on a demonstrably false understanding of how Galileo reached his conclusions. Koyré asserted that Galileo merely used experiments as a check on the theories he devised by mathematical reasoning. But later research has definitively established that Galileo's experiments preceded his attempts to give a mathematical account of their results.”

“For measurements of time he collected and weighed water flowing from a container at a constant rate of about three fluid ounces per second, He recorded weights of water in grains and, and defined his time unit, called a tempo, to be the time for 16 grains of water to flow, which was equivalent to 1/92 second. These units were small enough so Galileo's measurements of distance and time always resulted in large numbers. That was a necessity because decimal numbers were not part of his mathematical equipment; the only way he could add significant digits in his calculations was to make the numbers larger.”

“Galileo was the first scientist to recognise clearly that the only way to further our understanding of the physical world was to resort to experiment. ...the Greeks, in spite of their proficiency in geometry, never seem to have realised the importance of experiment (Democritus and Archimedes excepted). ...an excuse ...can scarcely be put forward when the elementary nature of Galileo's experiments and observations is recalled. Watching a lamp oscillate in the cathedral of Pisa, dropping bodies from the leaning tower of Pisa, rolling balls down inclined planes, noticing the magnifying effect of water in a spherical glass vase... might just as well have been performed by the Greeks.”

“It is to the Italian astronomer, forced in old age by the Inquisition to turn aside from the more dangerous study of the machinery of the heavens, that we owe the first exposition of many of the problems of mechanics and statics, published... in 1638. Not only did Galileo put together whatever the sixteenth century had learned in the sciences affecting building construction, but from his study of the bending strength of a beam there dates a new branch of science—the theory of the strength of materials.”

“Conclusions obtained by purely rational processes are, so far as Reality is concerned, entirely empty. It was because he recognized this, and especially because he impressed it upon the scientific world that Galileo became the father of modern physics and in fact of the whole of modern natural science.”

“Galileo was no idiot. Only an idiot could believe that science requires martyrdom — that may be necessary in religion, but in time a scientific result will establish itself.”

“The beginning of astronomy, except observations, I think is not to be derived from farther time than from Nicolaus Copernicus; who in the age next preceding the present revived the opinion of Pythagoras, Aristarchus, and Philolaus. After him, the doctrine of the motion of the earth being now received, and a difficult question thereupon arising concerning the descent of heavy bodies, Galileus in our time, striving with that difficulty, was the first that opened to us the gate of natural philosophy universal, which is the knowledge of the nature of motion. So that neither can the age of natural philosophy be reckoned higher than to him.”

“A light was kindled amongst the investigators of nature when Galilei let balls of a definite weight roll down the inclined plane. For they saw that they only understand what is produced according to a predetermined plan or hypothesis... for otherwise planless observations made according to no ideas could never be brought into the form of a law which reason demands and seeks. ...Thus physics was brought into the position of a certain science after groping about blindly for so many hundred years.”

“Copernicus, Kepler and Galileo were ‘revisionists’ in rejecting the geocentric system of Ptolemy (which held sway for some 1500 years) and, against an oppressive and repressive mainstream opinion (and officialdom), reinstated—with improvements—the heliocentric system of Aristarchos of Samos (3rd cent BCE).”

“Galileo's program offers us a dead world: Out go sight, sound, taste, touch, and smell, and along with them have since gone esthetic and ethical sensibility, values, quality, soul, consciousness, spirit. Experience as such is cast out of the realm of scientific discourse. Hardly anything has changed our world more during the past four hundred years than Galileo's audacious program. We had to destroy the world in theory before we could destroy it in practice.”

“Galileo deduced the laws of freely falling bodies and the parabolic paths of projectiles, initiating an era of applications of mathematics to physics. In his book Two New Sciences, he used indivisible methods to study the motion of a falling body, and he planned, but never wrote, an entire book on indivisibles.”

“The first mathematician to consider the nature of the resistance of solids to rupture was Galileo. Although he treated solids as inelastic, not being in possession of any law connecting the displacements produced with the forces producing them, or of any physical hypothesis capable of yielding such a law, yet his enquiries gave the direction which was subsequently followed by many investigators.”

“History can be helpful in making sense of the world we live in. It can also be fascinating, even fun. How can even the best novelist or playwright invent someone like Augustus Caesar or Catherine the Great, Galileo or Florence Nightingale? How can screenwriters create better action stories or human dramas than exist, thousand upon thousand, throughout the many centuries of recorded history? There is a thirst out there both for knowledge and to be entertained, and the market has responded with enthusiasm.”

“Galileo's comprehension of the concept of acceleration, which he defined as a change of velocity either in magnitude or direction... was an abstract idea that no one seems to have thought much about before. And in using it to test the still accepted Aristotelian precept that a moving object requires a force to maintain it, Galileo easily demonstrated that it is not motion but rather acceleration which cannot occur without an external force. Deliberately rejecting common sense as a prejudiced witness, he let nature herself speak in the form of a "hard, smooth and very round ball" rolling down a "very straight" ideal groove lined with polished parchment, and then rolling up another groove, clocking each roll "hundreds or times"... he showed that, while downward motion (helped by gravity force) makes speed increase and upward motion (hindered by gravity force) makes speed decrease, there is always a "boundary case" in between... where speed remains constant (without any appreciable force)—and that, by reducing friction, this boundary case can be made to approach a horizontal level where gravity has no effect. Similarly testing... he also drafted a law of falling bodies: "that the distances traversed, during equal intervals of time... stand to one another in the same ratio as the odd numbers beginning with unity." And his beautiful analysis of a cannonball's trajectory into horizontal and vertical components... was one day to be of enormous help to Isaac Newton in solving the riddle of gravity.”

“It was in Galileo's time that firearms were invented... What is the path of a cannonball? ...Characteristically, Galileo was engrossed with the problem; characteristically, he solved it. The outcome of his ingenuity we know today as the method of superposition.”

“Galileo's head was on the block... The crime was looking up for truth... And then you had to bring up reincarnation... How long 'til my soul gets it right... Can any human being ever reach that kind of light... I call on the resting soul of Galileo... King of night vision, king of insight... I'm not making a joke, you know me...I take everything so seriously... If we wait for the time 'til all souls get it right... Then at least I know there'll be no nuclear annihilation... Can any human being ever reach the highest light... Except for Galileo — God rest his soul... Except for the resting soul of Galileo... King of night vision, king of insight.”

“If Galileo had been willing to face the idea of a plurality of worlds, instead of resting on that of the Sun as the natural "centre of things," he might have been impelled to develop his system in the Newtonian sense. ...The position of the satellites in the Copernican scheme proved the existence of a multiplicity of centers. But the way that led from there was fraught with danger.”

“To give us the science of motion God and Nature have joined hands and created the intellect of Galileo.”

“The old Greek philosophy, which in Europe in the later middle ages was synonymous with the works of Aristotle, considered motion as a thing for which a cause must be found: a velocity required a force to produce and to maintain it. The great discovery of Galileo was that not velocity, but acceleration requires a force. This is the law of inertia of which the real content is: the natural phenomena are described by differential equations of the second order.”

“[T]he mathematical habit of mind and the mathematical procedure... had to be generated; otherwise Newton could never have thought of a formula representing the force between any two masses at any distance. ...Throughout the middle ages, under the influence of Aristotle, the science was entirely misconceived. Newton had the advantage of coming after a series of great men, notably Galileo... who in the previous two centuries had reconstructed the science and had invented the right way of thinking about it. He completed their work.”

“In Galileo's time, professors of philosophy and theology—the subjects were inseparable—produced grand discourses on the nature of reality... all based on sophisticated metaphysical arguments. Meanwhile, Galileo measured how fast balls roll down inclined planes. How mundane! But the learned discourses, while grand, were vague. Galileo's investigations were clear and precise. The old metaphysics never progressed, while Galileo's work bore abundant, and at length spectacular, fruit. Galileo too cared about the big questions, but he realized that getting the genuine answers requires patience and humility before the facts.”

“How does the world recognizes England, the United Kingdom, as the country that gave birth to the modern age? It was not Newton but Galilei who opened the Moderna age.”

“As a believing scientist [...] it is my deep conviction that it is our task to search nature and the universe, as Galileo Galilei, the father of modern science, did, for the footprints of God.”