short essay on galileo galilei

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Galileo Galilei

By: History.com Editors

Updated: June 6, 2023 | Original: July 23, 2010

Galileo Galilei (1564-1642) is considered the father of modern science and made major contributions to the fields of physics, astronomy, cosmology, mathematics and philosophy. Galileo invented an improved telescope that let him observe and describe the moons of Jupiter, the rings of Saturn, the phases of Venus, sunspots and the rugged lunar surface. His flair for self-promotion earned him powerful friends among Italy’s ruling elite and enemies among the Catholic Church’s leaders. Galileo’s advocacy of a heliocentric universe brought him before religious authorities in 1616 and again in 1633, when he was forced to recant and placed under house arrest for the rest of his life.

Galileo’s Early Life, Education and Experiments

Galileo Galilei was born in Pisa in 1564, the first of six children of Vincenzo Galilei, a musician and scholar. In 1581 he entered the University of Pisa at age 16 to study medicine, but was soon sidetracked by mathematics. He left without finishing his degree. In 1583 he made his first important discovery, describing the rules that govern the motion of pendulums.

Did you know? After being forced during his trial to admit that the Earth was the stationary center of the universe, Galileo allegedly muttered, "Eppur si muove!" ("Yet it moves!" ). The first direct attribution of the quote to Galileo dates to 125 years after the trial, though it appears on a wall behind him in a 1634 Spanish painting commissioned by one of Galileo's friends.

From 1589 to 1610, Galileo was chair of mathematics at the universities of Pisa and then Padua. During those years he performed the experiments with falling bodies that made his most significant contribution to physics.

Galileo had three children with Marina Gamba, whom he never married: Two daughters, Virginia (Later “Sister Maria Celeste”) and Livia Galilei, and a son, Vincenzo Gamba. Despite his own later troubles with the Catholic Church, both of Galileo’s daughters became nuns in a convent near Florence.

Galileo, Telescopes and the Medici Court

In 1609 Galileo built his first telescope, improving upon a Dutch design. In January of 1610 he discovered four new “stars” orbiting Jupiter—the planet’s four largest moons. He quickly published a short treatise outlining his discoveries, “Siderius Nuncius” (“The Starry Messenger”), which also contained observations of the moon’s surface and descriptions of a multitude of new stars in the Milky Way. In an attempt to gain favor with the powerful grand duke of Tuscany, Cosimo II de Medici, he suggested Jupiter’s moons be called the “Medician Stars.”

“The Starry Messenger” made Galileo a celebrity in Italy. Cosimo II appointed him mathematician and philosopher to the Medicis , offering him a platform for proclaiming his theories and ridiculing his opponents.

Galileo’s observations contradicted the Aristotelian view of the universe, then widely accepted by both scientists and theologians. The moon’s rugged surface went against the idea of heavenly perfection, and the orbits of the Medician stars violated the geocentric notion that the heavens revolved around Earth.

Galileo Galilei’s Trial

In 1616 the Catholic Church placed Nicholas Copernicus ’s “De Revolutionibus,” the first modern scientific argument for a heliocentric (sun-centered) universe, on its index of banned books. Pope Paul V summoned Galileo to Rome and told him he could no longer support Copernicus publicly.

In 1632 Galileo published his “Dialogue Concerning the Two Chief World Systems,” which supposedly presented arguments for both sides of the heliocentrism debate. His attempt at balance fooled no one, and it especially didn’t help that his advocate for geocentrism was named “Simplicius.”

Galileo was summoned before the Roman Inquisition in 1633. At first he denied that he had advocated heliocentrism, but later he said he had only done so unintentionally. Galileo was convicted of “vehement suspicion of heresy” and under threat of torture forced to express sorrow and curse his errors.

Nearly 70 at the time of his trial, Galileo lived his last nine years under comfortable house arrest, writing a summary of his early motion experiments that became his final great scientific work. He died in Arcetri near Florence, Italy on January 8, 1642 at age 77 after suffering from heart palpitations and a fever.

What Was Galileo Famous For? 

Galileo’s laws of motion, made from his measurements that all bodies accelerate at the same rate regardless of their mass or size, paved the way for the codification of classical mechanics by Isaac Newton . Galileo’s heliocentrism (with modifications by Kepler ) soon became accepted scientific fact. His inventions, from compasses and balances to improved telescopes and microscopes, revolutionized astronomy and biology. Galilleo discovered craters and mountains on the moon, the phases of Venus, Jupiter’s moons and the stars of the Milky Way. His penchant for thoughtful and inventive experimentation pushed the scientific method toward its modern form.

In his conflict with the Church, Galileo was also largely vindicated. Enlightenment thinkers like Voltaire used tales of his trial (often in simplified and exaggerated form) to portray Galileo as a martyr for objectivity. Recent scholarship suggests Galileo’s actual trial and punishment were as much a matter of courtly intrigue and philosophical minutiae as of inherent tension between religion and science.

In 1744 Galileo’s “Dialogue” was removed from the Church’s list of banned books, and in the 20th century Popes Pius XII and John Paul II made official statements of regret for how the Church had treated Galileo.

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• Scientific Methods
• Famous Physicists

Galileo Galilei

Galileo Galilei was an Italian philosopher, astronomer, and mathematician who made essential contributions to the sciences of astronomy, motion and strength of the material and several developments of scientific methods. Galileo Galilei played a vital role in the history of science. Galileo Galilei provided several scientific perceptions that lay essential groundwork for future scientists. His examination of the laws of motion and enhancements of the telescope also helped a lot to understand the world and universe around.

Table of Contents

About galileo galilei, telescopic discoveries of galileo, earth’s orbit, the law of falling bodies, the principle of pendulum.

Galileo was born on February 15, 1564, in Pisa, Tuscany. In his middle teens, Galileo joined a monastery school near Florence, and then in 1581, he enrolled at the University of Pisa, where he was going to study medicine. However, he was more inclined towards mathematics and decided to make a profession in mathematical subject and philosophy.

Galileo has been regarded as a hero from the seventeenth century. If we talk about his discoveries, he was the first person to report telescopic observations of the mountains on the moon, the rings of Saturn, the moons of Jupiter and the phases of Venus. He calculated the law of free fall, conceived by the principle of inertia ; he also determined the parabolic trajectory of projectiles and promoted the relativity of motion.

Galileo’s significant contributions were observational data, which he obtained with a telescope he made himself. He was the first astrophysicist to scan the spaces with a light-magnifying instrument; he is also referred to as the father of observational astronomy.

Galileo was not only the first inventor of the reflecting telescope , but he also significantly enhanced its power . What set Galileo apart was that he quickly figured out how to improve the instrument.

Galileo was the first to observe the rough, cratered surface of the moon; Jupiter’s four largest satellites named the Galilean moons; dark spots on the sun’s surface, known as sunspots; and the phases of the phases of Venus with his unprecedentedly powerful telescopes.

Soon after the invention of the telescope in the Netherlands, Galileo created his own from improvised spectacle lenses. He learned how to make unprecedentedly powerful telescopes, which he used to study the solar phases of the planet Venus. He also concluded that the sun is the central point of the solar system, not the Earth, as was formerly assumed, after noticing and studying the similar phases of Venus and the moon. Such discoveries of Galileo took the world of inventions to another level.

The Ancient Greek philosopher Aristotle taught that heavier objects fall faster than lighter ones, but Galileo wasn’t convinced. By climbing to the top of the Leaning Tower of Pisa, Galileo demonstrated this theory by dropping items of various weights off the side, which states that every object will fall at an equal rate. All items hit the ground simultaneously. This law of falling bodies was his crucial contribution in the field of motion .

The law of the pendulum was discovered by Galileo Galilei, which made the young scientist famous. Galileo observed that no matter how big the swings are, the time it will take for each swing to complete will be the same because the kinetic energy left in the pendulum will always be the same; it is just shifted from one direction to the other. This law is eventually used to regulate clocks.

For more such interesting articles, Stay tuned with BYJU’S. Also, register to “BYJU’S – The Learning App” for loads of interactive, engaging Physics-related videos and an unlimited academic assist.

Frequently Asked Questions

What was galileo famous for.

Galileo was the first inventor of refracting telescopes; he was also a natural philosopher, astronomer and mathematician.

What are the three things that Galileo discovered in space?

The moon, Jupiter’s moon and Sunspots.

What is the law of a simple pendulum?

The time period of a simple pendulum is directly proportional to the square root of its length.

What were the major tools invented by Galileo?

Galileo invented the Engineering compass, Microscope, telescope.

When was the pendulum first discovered?

In 1656 by Dutch mathematician, astronomer, physicist Christiaan Huygens.

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Galileo Galilei

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Galileo Galilei (1564-1642) was an Italian mathematician, physicist, astronomer, and natural philosopher. He created a superior telescope with which he made new observations of the night sky, notably that the surface of the Moon has mountains, that Jupiter has four satellite moons, and that the sunspots of the Sun, under careful observation, reveal that it is a moving sphere.

Besides astronomy, Galileo conducted many other scientific experiments over his long lifetime as he was greatly interested in physics. Testing age-old theories and coming up with new ones after meticulous experimentation, the scientist fell foul of the Catholic Church for questioning the accepted Ptolemaic view of the universe. Found guilty of heresy in a trial in 1633, Galileo was obliged to live his final years under house arrest at his villa in Tuscany. His discoveries and, above all, his approach to experimentation and testing hypotheses made Galileo an influential figure in the Scientific Revolution .

Galileo Galilei was born in Pisa, Italy , on 15 February 1564. His family belonged to the minor nobility but was rather down on its luck. Galileo inherited an interest in science from his father, Vincenzo Galilei (c. 1520-1591), who wrote treatises based on his practical experiments in musical science. Vincenzo might have earned acclaim in music , but he earned money as a cloth merchant, the family of his wife and Galileo's mother Giulia being in that trade . From 1581, Galileo studied medicine at the University of Pisa, but it was the mathematics part of the course (then part of a traditional education in medicine) that appealed to him most. So much so that Galileo left Pisa without graduating and took up a post as a mathematics teacher in Florence. Galileo was keen to make his mark , and his private studies resulted in his first contribution to the ever-growing knowledge of the Scientific Revolution. Galileo studied the action of pendulums and formed his theory of constant motion. Such was Galileo's expertise in mathematics that he was awarded a position in that field at the University of Pisa in 1589; three years later, he was made the professor of mathematics at the University of Padua.

It was at Padua that Galileo began a life-long friendship with the philosopher Cesare Cremonini (1550-1631). Galileo also met Marina Gamba in Padua, and although they never married, they had three children together: Virginia (b. 1600), Livia (b. 1601), and Vincenzio (b. 1606). Galileo was never far from financial distress, and he supplemented his meagre lecturer's income with private lessons and the occasional detailed horoscope. In 1613, when his daughters reached their teens, Galileo, unable to live openly with his mistress, entered Virginia and Livia into a nunnery outside Florence (both became nuns when reaching maturity). Galileo supported his daughters in the nunnery, buying better rooms and supplying them with food grown on his own estate to supplement the rather meagre standard fare of the nunnery. Virginia, by then known as Maria Celeste, was a great help to her father in his old age.

From Theory to Practice: A New Science

Mathematics was crucial to Galileo's understanding of the universe, as here he explains in his The Assayer of 1623:

One cannot understand it unless one first learns to understand the language and recognize the characters in which it is written. It is written in mathematical language and the characters are triangles, circles and other geometrical figures; without these means it is humanly impossible to understand a word of it; without these there is only clueless scrabbling around in a dark labyrinth . (Wootton, 163).

But Galileo was an all-round thinker interested in any discipline of thought that would provide the answers to the problems he wished to solve. His first biographer, Vincenzo Viviani, notes the following (paraphrased by Heilbron):

[He] could compete with the best lunatists in Tuscany, advise painters and poets on matter of artistic taste, and recite vast stretches of Petrarch , Dante , and Ariosto by heart. But his great strength, Galileo said when negotiating for a post at the Medici court in 1610, was philosophy , on which he had spent more years of study than he had months on mathematics. (v)

In short, Galileo "was no more (or less!) a mathematician than he was a musician, artist, writer, philosopher, or gadgeteer…Galileo would have done well in any of several professions" ( ibid ).

It was in the 1590s that Galileo began to move away from pure mathematical studies towards experimentation, although the story he dropped cannonballs from the Leaning Tower of Pisa is apocryphal. Rejecting the old Aristotelian understanding of physics, Galileo studied such subjects as uniform acceleration, inertia, and mechanics in his private workshop. He discovered all sorts of startling physical facts, such as a falling object has the same rate of acceleration regardless of its weight (which means, if air resistance is removed, two falling objects, though of different weight, will hit the ground at the same time), that a projectile follows a parabola in its path from one spot to another, and that a body moving on a perfectly smooth surface rolls on at a constant speed and, in a vacuum, would do so indefinitely. This latter point was used by Galileo to explain an age-old problem. If the Earth revolves around the Sun, then what causes it to move? Galileo demonstrated that, assuming God had started it off at the Creation, no continuous force was needed.

Galileo became deeply interested in astronomy and, from 1597, began an enduring correspondence with that other great thinker and astronomer Johannes Kepler (1571-1630). These two men would find the physical evidence to confirm the controversial theories of Nicolaus Copernicus (1473-1543) and finally bury the outdated ones of Ptolemy (c. 100 to c. 170). Copernicus believed the Earth revolved around the Sun, while Ptolemy believed the Sun revolved around the Earth (a view favoured by the Church). Galileo rejected the traditional working methods of the medieval astronomer, which was to create meticulous charts and tables using complex mathematics, and instead focussed his telescope on direct observation and discovery. In this sense, "Galileo fundamentally changed the notion of what astronomy was about" (Burns, 63).

Galileo's Telescope

The first telescope was invented in the Netherlands around 1608, perhaps by Hans Lippershey (c. 1570 to c. 1619). The simple idea of using a convex and concave lens at either end of a tube soon spread around Europe , and it reached Galileo's ears within a year or two. Galileo built his own version using superb lenses, which he ground himself (although he would not tell anyone exactly how). Going through several prototypes, Galileo arrived at a telescope with a magnification of 33 diameters, far more powerful than any in possession of his contemporaries. Galileo's telescope, what he called his occhiale ('eyeglass'), had two lenses set at either end of a lead tube around 60 cm (24 in) long. It was so powerful and well-made that other scientists had trouble believing what Galileo claimed to see through it since their own telescopes failed to spot what the Italian could see. Galileo even invented a pair of binoculars, but the idea did not catch on. Other gadgets Galileo invented early versions of include the thermometer (actually a thermoscope), a hydrostatic balance, and a compass (what we today would call a military compass or sector). It was the telescope, though, which revolutionised thought in the 17th century.

Galileo used his new telescope to study the heavens in tremendous detail, publishing the fruit of his research in Sidereus Nuncius ( The Starry Messenger ) in 1610. Galileo was able to observe the Moon and note that its surface seemed similar to Earth's with mountains and valleys, suggesting it was not, as many had previously thought, made of some entirely different matter. Galileo spotted for the first time the four largest moons of Jupiter (we now know there are more), studied the composition of the Milky Way, and identified the phases of Venus , which proved that it orbits the Sun. Galileo built theories on what he saw, such as the movement of Jupiter's moons must mean they orbit Jupiter (and not some other body like the Sun). He believed (correctly) that just as we can see the shine of the Moon, so on the Moon one should be able to see the shine of the Earth, that is the reflected light of the Sun. These new discoveries made Galileo as famous as Christopher Columbus (1451-1506), the discoverer of the New World, with whom, as the discoverer of a new Cosmos, Galileo was frequently compared.

Galileo's most important discovery, though, was not the details of the Moon or Jupiter's satellites but his observation of the sunspots on the Sun, using his telescope. The sunspots had been noted in antiquity, but Galileo could now, using filters, see things nobody had ever seen before. Galileo described what he saw:

The dark spots seen in the solar disk by means of the telescope are not at all distant from its surface, but are either contiguous to it or separated by an interval so small as to be quite imperceptible…They vary in duration from one or two days to thirty or forty. For the most part they are of most irregular shape, and their shapes continually change, some quickly and violently, others more slowly and moderately…Besides all these disordered movements they have in common a general uniform motion across the face of the sun in parallel lines. From special characteristics of this motion one may learn that the sun is absolutely spherical, that it rotates from west to east and around its own centre, carries the spots along with it in parallel circles, and completes an entire revolution in about a lunar month. (Fermi, 57).

In order to secure a position at the court of Cosimo II de' Medici, Grand Duke of Tuscany (r. 1609-1621), Galileo cleverly named the moons of Jupiter he had discovered the 'Medicean stars' in honour of the Medici family. Sure enough, in 1610, Galileo was appointed the duke's official mathematician and natural philosopher (the latter title now allowed Galileo to present theories on the place of Earth in the universe, something a lowly mathematician could not do). In 1611, Galileo was admitted into the prestigious scientific society in Rome called the Academia dei Lincei. In 1612, Galileo's Discourse on Floating Bodies attacked Aristotelian natural philosophy. In 1613, Galileo presented his pro-Copernicus theories in Letters on Sunspots , a work that landed the scientist into serious trouble.

The Trial of Galileo

Ptolemy had presented the theory that Earth was the centre of the universe with everything revolving around it. The Christian Church liked this idea since it put humanity at the centre of things. Copernicus presented his theory that it was the Sun which was at the centre and Earth and other planets revolved around it. This the Catholic Church, in particular, did not like. When Galileo sided with Copernicus, whose work was put on the Catholic Church's Index of Forbidden Books in 1616, he opened himself to the possibility of formal censure for heresy. Galileo was not denying the existence of God but, perhaps crucially, he had made many personal enemies over the years besides institutional ones. There was, for example, a notable feud with the Jesuit astronomer Christoph Scheiner (1573-1650). Galileo, it seems, had a particular skill for rubbing up people the wrong way (this was one reason why he left Pisa for Padua back in 1592). His delight in poking fun at the beliefs of others and his skill at philosophical discussion where he pulled such beliefs apart made him as few friends as Socrates had done in 5th-century BCE Athens . On the other side, Galileo was also good at gaining friends and supporters since he was "a forceful publicist of his own ideas and a superb communicator of technical ideas" (Henry, 29). In short, Galileo was a sticky problem to handle for the Church.

Most astronomers were not actually interested in challenging religious orthodoxy and did not view their new discoveries using telescopes and other instruments as necessarily challenging a universe created as described in the Bible . Galileo considered theology and natural philosophy as entirely different subjects. What he was doing was showing that the physical world on Earth was entirely related in terms of matter and physical laws to what could be seen in the heavens. This went against the traditional Aristotelian view. In the end, Galileo's writings were not banned by the Church, but he was taken to one side and privately admonished by Cardinal Robert Bellarmine (1542-1621). Galileo was by now a public figure, especially since he wrote his works in Italian rather than the more audience-restricted Latin most other great thinkers used. Galileo's works were also translated into several other languages shortly after publication. In a meeting on 26 February 1616, Galileo was encouraged not to pursue his pro-Copernicus theories, which appeared to contradict the Bible. This he did, for a while, but the Copernicus view of the universe was now becoming more and more widely accepted following the work of other astronomers. There was, too, some middle ground, with Tycho Brahe (1546-1601) famously endorsing a compromise view that the Sun orbited Earth and the other planets orbited the Sun. In short, the problem of what revolved around what was not going away, no matter how much the Church wanted to brush the investigations of the astronomers under the ecclesiastical carpet of accepted doctrine.

In 1632, Galileo wrote his Dialogue on the Two Chief Systems of the World . Here, he has two great thinkers, one pro-Ptolemy and the other pro-Copernicus, argue the matter of which bodies revolve around what in our galaxy (and by now, Galileo was convinced what we could see through a telescope was only a galaxy and not the entire universe). There is a third character, a neutral thinker who is ultimately persuaded to accept the Copernicus model. Tellingly, the pro-Ptolemy philosopher is called Simplicio (suspiciously like 'simpleton'), and the other, really Galileo himself, is called Salviati (hinting at salvation through correct knowledge). The Dialogue was a step too far for the Church, and Galileo was accused of heresy. He was hauled before a panel for trial in 1633. Found guilty, Galileo had to desist from promoting pro-Copernicus theories, and he was obliged to stay under house arrest in his home in Florence for the remainder of his life. He also had to recite the Penitential Psalms once every week for the next three years, a minor but no doubt annoying punishment for a man who so valued his time.

Galileo might have become an enemy of Catholicism, but his case has certain unique features, not least the long line of enemies the scientist had created who now took their opportunity for revenge. As the historian J. Henry notes, "The Galileo affair should not be taken as a general indicator of relations between science and religion in the early modern period" (86).

Death & Legacy

Galileo spent his remaining time designing a pendulum clock, and he wrote a summary of all his work in physics in Discourse on Two New Sciences , completed in 1638, but, because of his trial and punishment, published in Leiden in the Netherlands. Galileo eventually lost his eyesight (endlessly peering through lenses might have been responsible for this), and he suffered from arthritis. The tranquillity of his forced retirement was only broken by occasional visits from outsiders such as the poet John Milton.

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Galileo still pressed on with his studies, especially the pendulum and the attempt to find a working navigational aid for mariners, but just as his visual world had diminished from the stars to the hand before his face, the end was closing in. "I do not stop with my speculations, although with considerable damage to my health, since along with my other troubles they deprive me of sleep, which increases my melancholy at night" (Heilbron, 348). Galileo died on 8 January 1642; he was 77 years old. His remains were buried in the Church of Sante Croce in Florence.

Other thinkers came along and built upon and very often corrected the ideas that Galileo had presented. Johannes Kepler created a new model of the universe where the planets moved in elliptical orbits, not in perfect circles as Galileo had thought. Isaac Newton (1642-1727) discovered the force of gravity, and this explained phenomena that had puzzled Galileo, such as how the planets rotate, maintain their satellite moons, and move at different speeds depending on their distance from the Sun. Galileo, though, had made a much more lasting contribution to world knowledge than any specific discovery or theory. Galileo had uniquely combined the theory of mathematics, the observations of natural philosophy, and the use of repeated experiments to test hypotheses. As a consequence, he created a new and more rigorous methodology of inquiry that became the standard approach adopted by all other serious thinkers during the Scientific Revolution, a period when science relentlessly sought out new and definitive answers to questions humanity had been posing for millennia.

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Bibliography

• Burns, William E. The Scientific Revolution in Global Perspective. Oxford University Press, 2015.
• Burns, William E. The Scientific Revolution. ABC-CLIO, 2001.
• Fermi, Laura & Bernardini, Gilberto. Galileo and the Scientific Revolution. Dover Publications, 2013.
• Heilbron, John L. Galileo. Oxford University Press, 2012.
• Henry. The Scientific Revolution and the Origins of Modern Science . Red Globe Press, 2008.
• Jardine, Lisa. Ingenious Pursuits. Anchor, 2000.
• Rundle, D. (ed). The Hutchinson Encyclopedia of the Renaissance. Helicon, 2023.
• Wootton, David. The Invention of Science. Harper, 2015.

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Galileo Galilei

Justus Sustermans

Galileo Galilei was the founder of modern physics. To assess such a claim requires that we make a giant leap of the imagination to transport us to a state of ignorance about even the most elementary principles of physics. Today, the simple laws of motion as defined by  Isaac Newton , for example, are known to the most modest students, yet Galileo spent his life unravelling these mysteries.

His many discoveries include the law of inertia later used by Isaac Newton as the first law of motion, the parabola as the path of a projectile, the relationships between distance and velocity and between distance and time and at the continuity of acceleration. He struggled towards an understanding of continuity, though the work had to wait for Newton and Gottfried Leibnitz to produce an infinitesimal calculus to master this difficulty.

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Galileo and the renaissance.

Galileo lived at a time when the centuries-old Almagest of the Egyptian scholar Claudius Ptolemy , written in 139AD, was still being used by the Church as “evidence” and “confirmation” for the Aristotelian idea that the Earth was at the centre of the Universe. Galileo was part of the Renaissance, the centuries-long ferment accelerated and intensified by the invention of printing in the middle of the 15th century. He was not alone. More or less contemporary with him were physicists and mathematicians Willebrord Snell (the Dutchman who conceived the law of light refraction), the Belgian Simon Stevin and the four Frenchmen Marin Mersenne, Pierre de Fermat, Rene Descartes and Blaise Pascale. Yet it is Galileo’s name that survives as the “founder” of physics.

We must understand, however briefly, the sociological, political and religious climates of Galileo’s time. Italy, for instance, was no longer the great Roman Empire. It was divided into small states often warring with one another. The one in which Galileo was born was an autocracy, the Grand Duchy of Tuscany, with its capital at Florence and the second city at Pisa, his birthplace. The de Medici family ruled. Next to Tuscany was the state led by Venice – the Venetian Republic – as near as anyone came to a democracy in the 16th century. It refused to give in to the authority of Rome and the Church. It expelled the Jesuits and defied the Pope. It had its famous university at Padua (from which, it may be remembered, the learned doctor Bellario was to come to defend Antonio against Shylock in The Merchant of Venice , which William Shakespeare wrote in 1594, when Galileo was at Padua).

As a young student at Pisa, Galileo was highly intelligent, observant and questioning, a joy to the first-class teacher and a pest to the second rate, who as usual formed the majority. He wrote poetry and was a skilled musician and painter. He was highly cultured and came of a family of minor nobility. Vincenzio Galilei, his father, was also a musician, with original views, as well as being something of a mathematician. Galileo was to read medicine and so be able to earn a living. However, the biting winter winds of Florence at that time forced the court to relocate to Pisa. The court mathematician, Matteo Ricci, went with it. Galileo came upon Ricci teaching the young pages about Euclid and was at once entranced. Meeting Ricci later, Galileo also learned about Archimedes, a Latin version of whose work had been published in 1543. That was that. Archimedes became “that divine man” and Galileo saw in Euclid the wonder of geometry, especially in the work on ratios, which Galileo was to expand and use to its limit later.

His mind was alerted to the excitement and importance of mathematics applied to practical problems, that is in effect, physics. He timed the swinging of chandeliers in the cathedral and at once abstracted the essence of the problem, so that he made pendulums of string and small weights and established the relationship between length and time of swing, using his own pulse for measurement, for there existed no device for fine accurate timing. Later on Galileo utilised the phenomenon to make his pulsilogium , a device timing the human pulse, and on his deathbed 70 years later he designed a pendulum-regulated escapement for a proposed clock.

Leaving the university, he kept himself by teaching privately and lecturing, and then produced his first scientific paper at the age of 22. It was concerned with the story that Archimedes had found a way of discovering if a crown made for King Hiero of Syracuse was in fact of pure gold, as it was supposed to be, or had been adulterated with a cheaper metal. This he had done, according to the story, by finding the weight of water displaced from a full bowl. Galileo could not believe that a genius such as Archimedes would have used such a crude method. So Galileo set out to devise a method of considerable precision.

The Bilancetta

He made for himself a special balance with which he could measure the exact proportions of two metals in a mixture or alloy. He realised that fine-enough markings would be too difficult to read so he wound along a part of one arm of the balance a tight spiral of very fine brass wire, extending from where the suspended weight would balance metal A (suspended in water) to where it would balance metal B (suspended in water). He then balanced the immersed mixture by sliding the weight along. He measured the number of turns along his spiral by passing along it a fine stiletto knife, each winding making an audible “ping”. Thus, with his fine musical ear, he could count the number of turns, and therefore the distance. So he was able to state the proportion of A to B in the mixture. This tiny essay, which he called La Bilancetta , is enchanting.

In this little original work there is much of what we need to know about Galileo’s methods. There is first of all his outstanding and delicate manual skill. More important, there is always his insistence on accurate measurements and also repeatable measurements. And there is the use of mathematics, in this case the principle of the lever, which he was to use many a time in later work. Moreover his mathematical basis was Euclid and Archimedes.

Across his work Galileo was original in dynamics, hydrostatics, mechanics and the strength of materials, optics and astronomy. He continued to develop, correcting earlier errors, admitting his ignorance on “mysteries” and abhorring abstract notions. He was interested only in what he could see or hear or touch and, above everything, measure.

The spy-glass and Galileo’s telescopes

In 1609 came the most sensational discovery of his life. He heard of a Fleming who made a “spy-glass” and he rushed to experiment, not wishing to be outdone. And he succeeded in making a telescope of the sort familiar to everyone today who has seen an elementary book on optics. It astonished and delighted everyone, and when he succeeded in making one of eight magnifications and then even of 20 (grinding his own lenses!) he made celestial observations that shook the world of astronomy as well as the most learned of the Peripatetics (Aristotelian philosophers). He saw mountains on the Moon (very anti-Aristotle this), then satellites orbiting Jupiter, which he mapped with such accuracy that his orbital times are hardly different from those calculated today. That he saw sunspots and described their variations. Finally he observed that Venus showed phases very like those of the Moon, an observation that clinched the Copernican argument. In 1610 he published The Starry Messenger . He presented telescopes to the Doge of Venice (and had ageing councillors climbing bell towers to see merchant ships out at sea) and to his former pupil and friend Cosimo II, Grand Duke of Tuscany. He became famous all over Europe. He was the equivalent in science of a Nobel prize winner today.

When he left Padua and Venice, he returned to his home near Florence and completed his book on hydrostatics, in which it is interesting to see that he was nonplussed by the fact that a thin flake of ebony, though denser than water would nonetheless float. This pleased his Peripatetic opponents who asserted with Aristotle that sinking or floating was merely a matter of shape. Galileo did have the insight to perceive that the effect was probably the same as that when a drop of water would remain on a cabbage leaf. Of course surface tension was an unknown phenomenon.

The Galileo affair

A year later he published his three letters on sunspots. He was by now a very powerful man and had created jealousy and resentment. He had so many appreciative friends in high places, including former pupils, that he probably considered himself safe. Most of his enemies worked quietly like rats in a cellar, but some did not. There was, for example, the hateful person Christopher Scheiner, a Jesuit, who claimed priority in seeing sunspots and of course gave an Aristotelian explanation of them. His book challenged Galileo in the most spiteful way.

It looks like there was an opinion on high to leave Galileo alone, but then he made a mistake. He wrote a letter to his friend and former pupil Benedetto Castelli in which he discussed the Bible, especially the passage that stated that Joshua had commanded the Sun to stand still, a fact that would have proved that the Sun must previously have been moving, as Aristotle and Ptolemy had said. Galileo’s comment was that though the Bible was the word of God it must not be taken too literally, word for word, being written not for intellectuals but for common people. The spies were about and a Dominican in some way unknown secured a copy and sent it to the Inquisition at Rome.

Almost at the same time a loud-voiced and unpopular Dominican priest made an outspoken attack against all mathematicians and Galileo supporters. Galileo saw the danger and hurried to Rome. There, Cardinal Bellarmine after some talk persuaded Galileo to agree not to teach the Copernican theory as truth. In fact nobody knows exactly what Galileo did promise at this meeting in 1616, but his enemies, by a gangster-like trick, did much later produce an unsigned document (long after Bellarmine was dead) claiming that Galileo had promised not to teach or publicise the Copernican doctrine. He did not enter controversy again until 1623 when he produced a now-famous polemic book called The Assayer , acclaimed as the height of controversial writing. It was against a Jesuit who had written about comets and was a manifesto for intellectual freedom in science.

In 1623 his friend in Florence, Maffeo Barberini, was elected Pope and Galileo could not wait to get to Rome to see him, and the reception was cordial. Everything seemed to be going well, and it must have looked as if the weight of Galileo and the rest of the scientific world might succeed and get a thorough revision of orthodox science. Galileo produced his famous book called in brief A Dialogue etc. between a Peripatetic aptly called Simplicio, a Venetian gentleman Sagredo (actually Galileo’s close friend of the old days) and a scientifically informed Florentine, Salvatio, who was really voicing the opinions of Galileo himself. The subject of the dialogue was the two world systems, that of Ptolemy and that of Copernicus.

The imprimatur, the official licence to print the book, was obtained from the Papal censor and the book was published in 1632. Galileo had written a pious preface in which he ridiculed the Copernican theory as wild and fantastic and contrary to Holy Scripture. In this form the censor permitted the book to pass. The censor lost his job when the pious preface brought laughter down on the Church that had been duped by such an obvious pretence. All over Europe people read Galileo while the Pope and cardinals fumed.

It is said that Scheiner, on hearing this in a Rome bookshop, turned purple and shook violently. But he and his fellow haters and intriguers were not beaten. In fact they succeeded. It seems likely that the Inquisition would have liked to do nothing but was forced to do so by the detailed and documented evidence claiming that Galileo was in fact a heretic. There was another fact working against Galileo as well. It was that the Pope grew angry and anti-Galileo when he learned of the events of 1616, of which he had never been informed. He thought himself tricked by Galileo’s artfulness. Galileo was ordered to appear before the Inquisition.

Galileo’s recantation

Though ill, old and partially blind, he went, having been offered a horse-drawn “litter” by the Duke of Tuscany, though Venice had offered sanctuary. In Rome he was housed comfortably and on 13 April at the first hearing he pleaded ignorance of the unsigned document and promised to produce that signed by Bellarmine in 1616. He almost won the day. There followed considerable activity behind the scenes — the Cardinals probably detested the Scheiners — and Francesco Barberini, the Pope’s brother, who remained a loyal and admiring friend to Galileo throughout, was very active. He appeared once more and was then kept in suspense for months. The Pope eventually decided on life imprisonment. Of the 10 cardinals, three had refused to sign the verdict, Francesco had demanded a pardon and when it was refused he persuaded his brother to make life “imprisonment” that of house arrest in the home of a sympathetic bishop. To pay for this, Galileo was made to kneel and admit to being vain and ambitious and to renounce the Copernican doctrine as being wrong.

“I Galileo Galilei, being in my seventieth year having before my eyes the Holy Gospel, which I touch with my hands, abjure [renounce], curse and detest the error and heresy of the movement of the Earth.”

“And yet it moves”

The churchmen published Galileo’s recantation throughout Europe to demonstrate their power to make men recant. It was an enormous humiliation and Galileo was left a broken man, almost mentally deranged by the months of pressure. But the kindly bishop Ascanio Piccolomini nursed him back to mental health and at length the authorities in Rome allowed him to go home, though still under house arrest. It was possibly on this occasion that Galileo defiantly made his famous outburst: “Eppur si muove” (And yet it moves).

Why did Galileo make this adjuration at the trial, admitting what he knew to be a lie? Was he a coward? Did he think it more important to get back to his life work? Who are we to judge?

It was at his home that Galileo renewed his life work, that on mechanics and motion. The book Two New Sciences etc. published in 1638 can be considered his memorial. He died on 8 January 1642. Less than a year later Isaac Newton was born.

This article by C L Boltz was originally published in New Scientist on 7 April 1983

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Galileo Galilei

Galileo Galilei (1564–1642) has always played a key role in any history of science and, in many histories of philosophy, he is a, if not the, central figure of the scientific revolution of the 17 th Century. His work in physics or natural philosophy, astronomy, and the methodology of science still evoke debate after over 400 years. His role in promoting the Copernican theory and his travails and trials with the Roman Church are stories that still require re-telling. This article attempts to provide an overview of these aspects of Galileo’s life and work, but does so by focusing in a new way on his arguments concerning the nature of matter.

1. Brief Biography

2. introduction and background, 3. galileo’s scientific story, 4. galileo and the church, other internet resources, related entries.

Galileo was born on February 15, 1564 in Pisa. By the time he died on January 8, 1642 (but see problems with the date, Machamer 1998, pp. 24–5) he was as famous as any person in Europe. Moreover, when he was born there was no such thing as ‘science’, yet by the time he died science was well on its way to becoming a discipline and its concepts and method a whole philosophical system.

Galileo and his family moved to Florence in 1572. He started to study for the priesthood, but left and enrolled for a medical degree at the University of Pisa. He never completed this degree, but instead studied mathematics notably with Ostilio Ricci, the mathematician of the Tuscan court. Later he visited the mathematician Christopher Clavius in Rome and started a correspondence with Guildobaldo del Monte. He applied and was turned down for a position in Bologna, but a few years later in 1589, with the help of Clavius and del Monte, he was appointed to the chair of mathematics in Pisa.

In 1592 he was appointed, at a much higher salary, to the position of mathematician at the University of Padua. While in Padua he met Marina Gamba, and in 1600 their daughter Virginia was born. In 1601 they had another daughter Livia, and in 1606 a son Vincenzo.

It was during his Paduan period that Galileo worked out much of his mechanics and began his work with the telescope. In 1610 he published The Starry Messenger , and soon after accepted a position as Mathematician,a non-teaching post at University of Pisa and Philosopher to the Grand Duke of Tuscany. A facsimile copy of The Library of Congress’ manuscript of The Starry Messenger and a symposium discussing details about the manuscript, may be found in Hessler and DeSimone 2013. Galileo had lobbied hard for this position at the Medici court and even named the moons of Jupiter, which he discovered, after the Medici. There were many reasons hewanted move, but he says he did not like the wine in the Venice area and he had to teach too many students. Late in 1610, the Collegio Romano in Rome, where Clavius taught, certified the results of Galileo’s telescopic observations. In 1611 he became a member of what is perhaps the first scientific society, the Academia dei Lincei.

In 1612 Galileo published a Discourse on Floating Bodies , and in 1613, Letters on the Sunspots . In this latter work he first expressed his position in favor of Copernicus. In 1614 both his daughters entered the Franciscan convent of Saint Mathew, near Florence. Virginia became Sister Maria Celeste and Livia, Sister Arcangela. Marina Gamba, their mother, had been left behind in Padua when Galileo moved to Florence.

In 1613–4 Galileo entered into discussions of Copernicanism through his student Benedetto Castelli, and wrote a Letter to Castelli . In 1616 he transformed this into the Letter to the Grand Duchess Christina . In February 1616, the Sacred Congregation of the Index condemned Copernicus’ book On the Revolution of the Heavenly Orbs , pending correction. Galileo then was called to an audience with Cardinal Robert Bellarmine and advised not to teach or defend Copernican theory.

In 1623 Galileo published The Assayer dealing with the comets and arguing they were sublunary phenomena. In this book, he made some of his most famous methodological pronouncements including the claim the book of nature is written in the language of mathematics.

The same year Maffeo Barberini, Galileo’s supporter and friend, was elected Pope Urban VIII. Galileo felt empowered to begin work on his Dialogues concerning the Two Great World Systems . It was published with an imprimatur from Florence (and not Rome) in 1632. Shortly afterwards the Inquisition banned its sale, and Galileo was ordered to Rome for trial. In 1633 he was condemned. There is more about these events and their implications in the final section of this article, Galileo and the Church .

In 1634, while Galileo was under house arrest, his daughter, Maria Celeste died (cf. Sobel 1999). At this time he began work on his final book, Discourses and Mathematical Demonstrations concerning Two New Sciences . This book was smuggled out of Italy and published in Holland. Galileo died early in 1642. Due to his conviction, he was buried obscurely until 1737.

For detailed biographical material, the best and classic work dealing with Galileo’s life and scientific achievements is Stillman Drake’s Galileo at Work (1978). More recently, J.L. Heilbron has written a magnificent biography, Galileo , that touches on all the multiple facets of Galileo’s life (2010). A strange popularization based somewhat on Heilbron’s book, by Adam Gopik, appeared in The New Yorker in 2013.

For many people, in the Seventeenth Century as well as today, Galileo was and is seen as the ‘hero’ of modern science. Galileo discovered many things: with his telescope, he first saw the moons of Jupiter and the mountains on the Moon; he determined the parabolic path of projectiles and calculated the law of free fall on the basis of experiment. He is known for defending and making popular the Copernican system, using the telescope to examine the heavens, inventing the microscope, dropping stones from towers and masts, playing with pendula and clocks, being the first ‘real’ experimental scientist, advocating the relativity of motion, and creating a mathematical physics. His major claim to fame probably comes from his trial by the Catholic Inquisition and his purported role as heroic rational, modern man in the subsequent history of the ‘warfare’ between science and religion. This is no small set of accomplishments for one 17 th -century Italian, who was the son of a court musician and who left the University of Pisa without a degree.

One of the good things about dealing with such momentous times and people is that they are full of interpretive fecundity. Galileo and his work provide one such occasion. Since his death in 1642, Galileo has been the subject of manifold interpretations and much controversy. The use of Galileo’s work and the invocations of his name make a fascinating history (Segre 1991, Palmerino and Thijssen 2004,  Finocchiaro 2005), but this is not our topic here.

Philosophically, Galileo has been used to exemplify many different themes, usually as a side bar to what the particular writer wished to make the hallmark of the scientific revolution or the nature of good science. Whatever was good about the new science or science in general, it was Galileo who started it. One early 20th Century tradition of Galileo scholarship used to divvy up Galileo’s work into three or four parts: (1) his physics, (2) his astronomy, and (3) his methodology, which could include his method of Biblical interpretation and his thoughts about the nature of proof or demonstration. In this tradition, typical treatments dealt with his physical and astronomical discoveries and their background and/or who were Galileo’s predecessors. More philosophically, many would ask how his mathematics relates to his natural philosophy? How did he produce a telescope and use his telescopic observations to provide evidence in favor of Copernicanism (Reeves 2008)? Was he an experimentalist (Settle 1961, 196, 1983, 1992; Palmieri 2008), a mathematical Platonist (Koyré 1939), an Aristotelian emphasizing experience (Geymonat 1954), precursor of modern positivist science (Drake 1978), or maybe an Archimedean (Machamer 1998), who might have used a revised Scholastic method of proof (Wallace 1992)? Or did he have no method and just fly like an eagle in the way that geniuses do (Feyerabend 1975)? Behind each of these claims there was some attempt to place Galileo in an intellectual context that brought out the background to his achievements. Some emphasize his debt to the artisan/engineer practical tradition (Rossi 1962), others his mathematics (Giusti1993, Peterson 2011,, Feldhay 1998, Palmieri 2001, 2003, Renn 2002, Palmerino 2015,), some his mixed (or subalternate) mathematics (Machamer 1978, 1998, Lennox 1986, Wallace 1992), others his debt to atomism (Shea 1972, Redondi 1983), and some his use of Hellenistic and Medieval impetus theory (Duhem 1954, Claggett 1966, Shapere 1974) or the idea that discoveries bring new data into science (Wootton (2015).

Yet most everyone in this tradition seemed to think the three areas—physics, astronomy and methodology—were somewhat distinct and represented different Galilean endeavors. More recent historical research has followed contemporary intellectual fashion and shifted foci bringing new dimensions to our understanding of Galileo by studying his rhetoric (Moss 1993, Feldhay 1998, Spranzi 2004), the power structures of his social milieu (Biagioli 1993, 2006), his personal quest for acknowledgment (Shea and Artigas 2003) and more generally has emphasized the larger social and cultural history, specifically the court and papal culture, in which Galileo functioned (Redondi 1983, Biagioli 1993, 2006, Heilbron 2010).

In an intellectualist recidivist mode, this entry will outline his investigations in physics and astronomy and exhibit, in a new way, how these all cohered in a unified inquiry. In setting this path out I shall show why, at the end of his life, Galileo felt compelled (in some sense of necessity) to write the Discourses Concerning the Two New Sciences , which stands as a true completion of his overall project and is not just a reworking of his earlier research that he reverted to after his trial, when he was blind and under house arrest. Particularly, we shall try to show why both of the two new sciences, especially the first, were so important (a topic not much treated except recently by Biener 2004 and Raphael 2011). In passing, we shall touch on his methodology and his mathematics (and here refer you to some of the recent work by Palmieri 2001, 2003). At the end we shall have some words about Galileo, the Catholic Church and his trial.

The philosophical thread that runs through Galileo’s intellectual life is a strong and increasing desire to find a new conception of what constitutes natural philosophy and how natural philosophy ought to be pursued. Galileo signals this goal clearly when he leaves Padua in 1611 to return to Florence and the court of the Medici and asks for the title Philosopher as well as Mathematician . This was not just a status-affirming request, but also a reflection of his large-scale goal. What Galileo accomplished by the end of his life in 1642 was a reasonably articulated replacement for the traditional set of analytical concepts connected with the Aristotelian tradition of natural philosophy. He offered, in place of the Aristotelian categories, a set of mechanical concepts that were accepted by most everyone who afterwards developed the ‘new sciences’, and which, in some form or another, became the hallmark of the new philosophy. His way of thinking became the way of the scientific revolution (and yes, there was such a ‘revolution’ pace Shapin 1996 and others, cf. selections in Lindberg 1990, Osler 2000.)

Some scholars might wish to describe what Galileo achieved in psychological terms as an introduction of new mental models (Palmieri 2003) or a new model of intelligibility (Machamer 1998, Adams et al . 2017). However phrased, Galileo’s main move was to de-throne the Aristotelian physical categories of the one celestial (the aether or fifth element) and four terrestrial elements (fire, air, water and earth) and their differential directional natures of motion (circular,  and up and down). In their place he left only one element, corporeal matter, and a different way of describing the properties and motions of matter in terms of the mathematics of the equilibria of proportional relations (Palmieri 2001) that were typified by the Archimedian simple machines—the balance, the inclined plane, the lever, and, he includes, the pendulum (Machamer 1998, Machamer and Hepburn 2004, Palmieri 2008). In doing so Galileo changed the acceptable way of talking about matter and its motion, and so ushered in the mechanical tradition that characterizes so much of modern science, even today. But this would take more explaining (Dijksterhuis 1950, Machamer et al. 2000, Gaukroger 2009).

As a main focus underlying Galileo’s accomplishments, it is useful to see him as being interested in finding a unified theory of matter, a mathematical theory of the material stuff that constitutes the whole of the cosmos. Perhaps he didn’t realize that this was his grand goal until the time he actually wrote the Discourses on the Two New Sciences in 1638. Despite working on problems of the nature of matter from 1590 onwards, he could not have written his final work much earlier than 1638, certainly not before The Starry Messenger of 1610, and actually not before the Dialogues on the Two Chief World Systems of 1632. Before 1632, he did not have the theory and evidence he needed to support his claim about unified, singular matter. He had thought deeply about the nature of matter before 1610 and had tried to work out how best to describe matter, but the idea of unified matter theory had to wait on the establishment of principles of matter’s motion on a moving earth. And this he did not do until the Dialogues .

Galileo began his critique of Aristotle in the 1590 manuscript, De Motu . The first part of this manuscript deals with terrestrial matter and argues that Aristotle’s theory has it wrong. For Aristotle, sublunary or terrestrial matter is of four kinds [earth, air, water, and fire] and has two forms, heavy and light, which by nature are different principles of (natural) motion, down and up. Galileo, using an Archimedian model of floating bodies and later the balance, argues that there is only one principle of motion, the heavy ( gravitas ), and that lightness (or levitas ) is to be explained by the heavy bodies moving so as to displace or extrude other bits of matter in such a direction that explains why the other bits rise. So on his view heaviness (or gravity) is the cause of all natural terrestrial motion. But this left him with a problem as to the nature of the heavy, the nature of gravitas ? In De Motu , he argued that the moving arms of a balance could be used as a model for treating all problems of motion. In this model heaviness is the proportionality of weight of one object on one arm of a balance to that of the weight of another body on the other arm of the balance. In the context of floating bodies, weight is the ‘weight’ of one body minus weight of the medium.

Galileo realized quickly these characterizations were insufficient, and so began to explore how heaviness was relative to the different specific gravities of bodies having the same volume. He was trying to figure out what is the concept of heaviness that is characteristic of all matter. What he failed to work out, and this was probably the reason why he never published De Motu , was this positive characterization of heaviness. There seemed to be no way to find standard measures of heaviness that would work across different substances. So at this point he did not have useful replacement categories.

A while later, in his 1600 manuscript, Le Mecaniche (Galileo 1600/1960) he introduces the concept of momento , a quasi force concept that applies to a body at a moment and which is somehow proportional to weight or specific gravity (Galluzzi 1979). Still, he has no good way to measure or compare specific gravities of bodies of different kinds and his notebooks during this early 17 th -century period reflect his trying again and again to find a way to bring all matter under a single proportional measuring scale. He tries to study acceleration along an inclined plane and to find a way to think of what changes acceleration brings. In this regard and during this period he attempts to examine the properties of percussive effect of bodies of different specific gravities, or how they have differential impacts. Yet the details and categories of how to properly treat weight and movement elude him.

One of Galileo’s problems was that the Archimedian simple machines that he was using as his model of intelligibility, especially the balance, are not easily conceived of in a dynamic way (but see Machamer and Woody 1994). Except for the inclined plane, time is not a property of the action of simple machines that one would normally attend to. In discussing a balance, one does not normally think about how fast an arm of the balance descends nor how fast a body on the opposite arm is rising (though Galileo in his Postils to Rocco ca. 1634–45 does; see Palmieri 2005). The converse is also true. It is difficult to model ‘dynamic’ phenomena that deal with the rate of change of different bodies as problems of balance arms moving upwards or downwards because of differential weights. So it was that Galileo’s classic dynamic puzzle about how to describe time and the force of percussion, or the force of body’s impact, would remain unsolved, He could not, throughout his life find systematic relations among specific gravities, height of fall and percussive forces. In the Fifth Day of the Discouses, he presciently explores the concept of the force of percussion . This concept will become, after his death, one of the most fecund ways to think about matter.

In 1603–9, Galileo worked long at doing experiments on inclined planes and most importantly with pendula. The pendulum again exhibited to Galileo that acceleration and, therefore, time is a crucial variable. Moreover, isochrony—equal times for equal lengths of string, despite different weights—goes someway towards showing that time is a possible form for describing the equilibrium (or ratio) that needs to be made explicit in representing motion. It also shows that in at least one case time can displace weight as a crucial variable. Work on the force of percussion and inclined planes also emphasized acceleration and time, and during this time (ca. 1608) he wrote a little treatise on acceleration that remained unpublished.

We see from this period that Galileo’s law of free fall arises out of this struggle to find the proper categories for his new science of matter and motion. Galileo accepts, probably as early as the 1594 draft of Le Mecaniche , that natural motions might be accelerated. But that accelerated motion is properly measured against time is an idea enabled only later, chiefly through his failure to find any satisfactory dependence on place and specific gravity. Galileo must have observed that the speeds of bodies increase as they move downwards and, perhaps, do so naturally, particularly in the cases of the pendulum, the inclined plane, in free fall, and during projectile motion. Also at this time he begins to think about percussive force, the force that a body acquires during its motion that shows upon impact. For many years he thinks that the correct science of these changes should describe how bodies change according to where they are on their paths. Specifically, it seems that height is crucial. Percussive force is directly related to height and the motion of the pendulum seems to involve essentially equilibrium with respect to the height of the bob (and time also, but isochrony did not lead directly to a recognition of time’s importance.)

The law of free fall, expressed as time squared, was discovered by Galileo through the inclined plane experiments (Drake 1999, v. 2), but he attempted to find an explanation of this relation, and the equivalent mean proportional relation, through a velocity-distance relation. His later and correct definition of natural acceleration as dependent on time is an insight gained through recognizing the physical significance of the mean proportional relation (Machamer and Hepburn 2004; for a different analysis of Galileo’s discovery of free fall see Renn et al. 2004.) Yet Galileo would not publish anything making time central to motion until 1638, in Discourses on the Two New Sciences (Galileo 1638/1954.) But let us return to the main matter.

In 1609 Galileo begins his work with the telescope. Many interpreters have taken this to be an interlude irrelevant to his physics. The Starry Messenger , which describes his early telescopic discoveries, was published in 1610. There are many ways to describe Galileo’s findings but for present purposes they are remarkable as his start at dismantling of the celestial/terrestrial distinction (Feyerabend 1975). Perhaps the most unequivocal case of this is when he analogizes the mountains on the moon to mountains in Bohemia. The abandonment of the heaven/earth dichotomy implied that all matter is of the same kind, whether celestial or terrestrial. Further, if there is only one kind of matter there can be only one kind of natural motion, one kind of motion that this matter has by nature. So it has to be that one law of motion will hold for earth, fire and the heavens. This is a far stronger claim than he had made back in 1590. In addition, he described of his discovery of the four moons circling Jupiter, which he called politically the Medicean stars (after the ruling family in Florence, his patrons). In the Copernican system, the earth having a moon revolve around it was unique and so seemingly problematic. Jupiter’s having planets made the earth-moon system non-unique and so again the earth became like the other planets.  Some fascinating background and treatments of this period of Galileo’s life and motivations have recently appeared (Biagoli 2006, Reeves 2008, and the essays in Hessler and De Simone 2013).

In 1611, at the request of Cardinal Robert Bellarmine, the professors at the Collegio Romano confirmed Galileo’s telescopic observations, with a slight dissent from Father Clavius, who felt that the moon’s surface was probably not uneven. Later that year Clavius changed his mind.

A few years later in his Letters on the Sunspots (1612), Galileo enumerated more reasons for the breakdown of the celestial/terrestrial distinction. Basically the ideas here were that the sun has spots ( maculae ) and rotated in circular motion, and, most importantly Venus had phases just like the moon, which was the spatial key to physically locating Venus as being between the Sun and the earth, and as revolving around the Sun. In these letters he claimed that the new telescopic evidence supported the Copernican theory. Certainly the phases of Venus contradicted the Ptolemaic ordering of the planets.

Later in 1623, Galileo argued for a quite mistaken material thesis. In The Assayer , he tried to show that comets were sublunary phenomena and that their properties could be explained by optical refraction. While this work stands as a masterpiece of scientific rhetoric, it is somewhat strange that Galileo should have argued against the super-lunary nature of comets, which the great Danish astronomer Tycho Brahe had demonstrated earlier.

Yet even with all these changes, two things were missing. First, he needed to work out some general principles concerning the nature of motion for this new unified matter. Specifically, given his Copernicanism, he needed to work out, at least qualitatively, a way of thinking about the motions of matter on a moving earth. The change here was not just the shift from a Ptolemaic, Earth-centered planetary system to a Sun-centered Copernican model. For Galileo, this shift was also from a mathematical planetary model to a physically realizable cosmography. It was necessary for him to describe the planets and the earth as real material bodies. In this respect Galileo differed dramatically from Ptolemy, Copernicus, or even Tycho Brahe, who had demolished the crystalline spheres by his comets-as-celestial argument and flirted with physical models (Westman 1976). So on the new Galilean scheme there is only one kind of matter, and it may have only one kind of motion natural to it. Therefore, he had to devise (or shall we say, discover) principles of local motion that will fit a central sun, planets moving around that sun, and a daily whirling earth.

This he did by introducing two new principles. In Day One of his Dialogues on the Two Chief World Systems (1632), Galileo argued that all natural motion is circular. Then, in Day Two, he introduced his version of the famous principle of the relativity of observed motion. This latter held that motions in common among bodies could not be observed. Only those motions differing from a shared common motion could be seen as moving. The joint effect of these two principles was to say that all matter shares a common motion, circular, and so only motions different from the common, say up and down motion, could be directly observed. Of course, neither of the principles originated with Galileo. They had predecessors. But no one needed them for the reasons that he did, namely that they were necessitated by a unified cosmological matter.

In Day Three, Galileo dramatically argues for the Copernican system. Salviati, the persona of Galileo, has Simplicio, the ever astounded Aristotelian, make use of astronomical observations, especially the facts that Venus has phases and that Venus and Mercury are never far from the Sun, to construct a diagram of the planetary positions. The resulting diagram neatly corresponds to the Copernican model. Earlier in Day One, he had repeated his claims from The Starry Messenger , noting that the earth must be like the moon in being spherical, dense and solid, and having rugged mountains. Clearly the moon could not be a crystalline sphere as held by some Aristotelians.

In the Dialogues , things are more complicated than we have just sketched. Galileo, as noted, argues for a circular natural motion, so that all things on the earth and in the atmosphere revolve in a common motion with the earth so that the principle of the relativity of observed motion will apply to phenomena such as balls dropped from the masts of moving ships. Yet he also introduces at places a straight-line natural motion. For example, in Day Three, he gives a quasi account for a Coriolis-type effect for the winds circulating about the earth by means of this straight-line motion (Hooper 1998). Further, in Day Four, when he is giving his proof of the Copernican theory by sketching out how the three-way moving earth mechanically moves the tides, he nuances his matter theory by attributing to the element water the power of retaining an impetus for motion such that it can provide a reciprocal movement once it is sloshed against a side of a basin. This was not Galileo’s first dealing with water. We saw it in De Motu in 1590, with submerged bodies, but more importantly he learned much more while working through his dispute over floating bodies ( Discourse on Floating Bodies , 1612). In fact a large part of this debate turned on the exact nature of water as matter, and what kind of mathematical proportionality could be used to correctly describe it and bodies moving in it (cf. Palmieri, 1998, 2004a).

The final chapter of Galileo’s scientific story comes in 1638 with the publication of Discourses of the Two New Sciences . The second science, discussed (so to speak) in the last two days, dealt with the principles of local motion. These have been much commented upon in the Galilean literature. Here is where he enunciates the law of free fall, the parabolic path for projectiles and his physical “discoveries” (Drake 1999, v. 2). But the first two days, the first science, has been much misunderstood and little discussed. This first science, misleadingly, has been called the science of the strength of materials, and so seems to have found a place in history of engineering, since such a course is still taught today. However, this first science is not about the strength of materials per se . It is Galileo’s attempt to provide a mathematical science of his unified matter. (See Machamer 1998, Machamer and Hepburn 2004, and the detailed work spelling this out by Biener 2004.) Galileo realizes that before he can work out a science of the motion of matter, he must have some way of showing that the nature of matter may be mathematically characterized. Both the mathematical nature of matter and the mathematical principles of motion he believes belong to the science of mechanics, which is the name he gives for this new way of philosophizing. Remember that specific gravities did not work.

So it is in Day One that he begins to discuss how to describe, mathematically (or geometrically), the causes of how beams break. He is searching for the mathematical description of the essential nature of matter. He rules out certain questions that might use infinite atoms as basis for this discussion, and continues on giving reasons for various properties that matter has. Among these are questions of the constitution of matter, properties of matter due to its heaviness, the properties of the media within which bodies move and what is the cause of a body’s coherence as a single material body. The most famous of these discussions is his account of acceleration of falling bodies, that whatever their weight would fall equally fast in a vacuum. The Second Day lays out the mathematical principles concerning how bodies break. He does this all by reducing the problems of matter to problems of how a lever and a balance function. Something he had begun back in 1590, though this time he believes he is getting it right, showing mathematically how bits of matter solidify and stick together, and do so by showing how they break into bits. The ultimate explanation of the “sticking” eluded him since he felt he would have to deal with infinitesimals to really solve this problem.

The second science, Days Three and Four of Discorsi , dealt with proper principles of local motion, but this was now motion for all matter (not just sublunary stuff) and it took the categories of time and acceleration as basic. Interestingly Galileo, here again, revisited or felt the need to include some anti-Aristotelian points about motion as he had done back in 1590. The most famous example of his doing this, is his “beautiful thought experiment”, whereby he compares two bodies of the same material of different sizes and points out that according to Aristotle they fall at different speeds, the heavier one faster. Then, he says, join the bodies together. In this case the lightness of the small one ought to slow down the faster larger one, and so they together fall as a speed less than the heavy fell in the first instance. Then his punch line: but one might also conceive of the two bodies joined as being one larger body, in which case it would fall even more quickly. So there is a contradiction in the Aristotelian position (Palmieri 2005). His projected Fifth Day would have treated the grand principle of the power of matter in motion due to impact. He calls it the force of percussion, which deals with two bodies interacting. This problem he does not solve, and it won’t be solved until René Descartes, probably following Isaac Beeckman, turns the problem into finding the equilibrium points for colliding bodies.

The sketch above provides the basis for understanding Galileo’s changes. He has a new science of matter, a new physical cosmography, and a new science of local motion. In all these he is using a mathematical mode of description based upon, though somewhat changed from, the proportional geometry of Euclid, Book VI and Archimedes (for details on the change see Palmieri 2002).

It is in this way that Galileo developed the new categories of the mechanical new science, the science of matter and motion. His new categories utilized some of the basic principles of traditional mechanics, to which he added the category of time and so emphasized acceleration. But throughout, he was working out the details about the nature of matter so that it could be understood as uniform and treated in a way that allowed for coherent discussion of the principles of motion. That a unified matter became accepted and its nature became one of the problems for the ‘new science’ that followed was due to Galileo. Thereafter, matter really mattered.

No account of Galileo’s importance to philosophy can be complete if it does not discuss Galileo’s condemnation and the Galileo affair (Finocchiaro 1989). The end of the episode is simply stated. In late 1632, after publishing Dialogues on the Two Chief World Systems , Galileo was ordered to go to Rome to be examined by the Holy Office of the Inquisition. In January 1633, a very ill Galileo made an arduous journey to Rome. Finally, in April 1633 Galileo was called before the Holy Office. This was tantamount to a charge of heresy, and he was urged to repent (Shea and Artigas, 183f). Specifically, he had been charged with teaching and defending the Copernican doctrine that holds that the Sun is at the center of the universe and that the earth moves. This doctrine had been deemed heretical in 1616, and Copernicus’ book had been placed on the Index of Prohibited Books, pending correction.

Galileo was called four times for a hearing; the last was on June 21, 1633. The next day, 22 June, Galileo was taken to the church of Santa Maria sopra Minerva, and ordered to kneel while his sentence was read. It was declared that he was “vehemently suspect of heresy”. Galileo was made to recite and sign a formal abjuration:

I have been judged vehemently suspect of heresy, that is, of having held and believed that the sun in the centre of the universe and immoveable, and that the earth is not at the center of same, and that it does move. Wishing however, to remove from the minds of your Eminences and all faithful Christians this vehement suspicion reasonably conceived against me, I abjure with a sincere heart and unfeigned faith, I curse and detest the said errors and heresies, and generally all and every error, heresy, and sect contrary to the Holy Catholic Church. (Quoted in Shea and Artigas 194)

Galileo was not imprisoned but had his sentence commuted to house arrest. In December 1633 he was allowed to retire to his villa in Arcetri, outside of Florence. During this time he finished his last book, Discourses on the Two New Sciences , which was published in 1638, in Holland, by Louis Elzivier. The book does not mention Copernicanism at all, and Galileo professed amazement at how it could have been published. He died on January 8, 1642.

There has been much controversy over the events leading up to Galileo’s trial, and it seems that each year we learn more about what actually happened. There is also controversy over the legitimacy of the charges against Galileo, both in terms of their content and judicial procedure. The summary judgment about this latter point is that the Church most probably acted within its authority and on ‘good’ grounds given the condemnation of Copernicus, and, as we shall see, the fact that Galileo had been warned by Cardinal Bellarmine earlier in 1616 not to defend or teach Copernicanism. There were also a number of political factors given the Counter Reformation, the 30 Years War (Miller 2008), and the problems with the papacy of Urban VIII that served as further impetus to Galileo’s condemnation (McMullin, ed. 2005). It has even been argued (Redondi 1983) that the charge of Copernicanism was a compromise plea bargain to avoid the truly heretical charge of atomism. Though this latter hypothesis has not found many willing supporters.

Legitimacy of the content, that is, of the condemnation of Copernicus, is much more problematic. Galileo had addressed this problem in 1615, when he wrote his Letter to Castelli (which was transformed into the Letter to the Grand Duchess Christina ). In this letter he had argued that, of course, the Bible was an inspired text, yet two truths could not contradict one another. So in cases where it was known that science had achieved a true result, the Bible ought to be interpreted in such a way that makes it compatible with this truth. The Bible, he argued, was an historical document written for common people at an historical time, and it had to be written in language that would make sense to them and lead them towards the true religion.

Much philosophical controversy, before and after Galileo’s time, revolves around this doctrine of the two truths and their seeming incompatibility. Which of course, leads us right to such questions as: “What is truth?” and “How is truth known or shown?”

Cardinal Bellarmine was willing to countenance scientific truth if it could be proven or demonstrated (McMullin 1998). But Bellarmine held that the planetary theories of Ptolemy and Copernicus (and presumably Tycho Brahe) were only hypotheses and due to their mathematical, purely calculatory character were not susceptible to physical proof. This is a sort of instrumentalist, anti-realist position (Duhem 1985, Machamer 1976). There are any number of ways to argue for some sort of instrumentalism. Duhem (1985) himself argued that science is not metaphysics, and so only deals with useful conjectures that enable us to systematize the phenomena. Subtler versions, without an Aquinian metaphysical bias, of this position have been argued subsequently and more fully by van Fraassen (1996) and others. Less sweepingly, it could reasonably be argued that both Ptolemy and Copernicus’ theories were primarily mathematical, and that what Galileo was defending was not Copernicus’ theory per se, but a physical realization of it. In fact, it might be better to say the Copernican theory that Galileo was constructing was a physical realization of parts of Copernicus’ theory, which, by the way, dispensed with all the mathematical trappings (eccentrics, epicycles, Tusi couples and the like). Galileo would be led to such a view by his concern with matter theory. Of course, put this way we are faced with the question of what constitutes identity conditions for a theory, or being the same theory. There is clearly a way in which Galileo’s Copernicus is not Copernicus and most certainly not Kepler.

The other aspect of all this which has been hotly debated is: what constitutes proof or demonstration of a scientific claim? In 1616, the same year that Copernicus’ book was placed on the Index of Prohibited Books, Galileo was called before Cardinal Robert Bellarmine, head of the Holy Office of the Inquisition and warned not to defend or teach Copernicanism. During this year Galileo also completed a manuscript, On the Ebb and Flow of the Tides . The argument of this manuscript will turn up 17 years later as day Four of Galileo’s Dialogues concerning the Two Chief World Systems . This argument, about the tides, Galileo believed provided proof of the truth of the Copernican theory. But insofar as it possibly does, it provides an argument for the physical plausibility of Galileo’s Copernican theory. Let’s look more closely at his argument.

Galileo argues that the motion of the earth (diurnal and axial) is the only conceivable (or maybe plausible) physical cause for the reciprocal regular motion of the tides. He restricts the possible class of causes to mechanical motions, and so rules out Kepler’s attribution of the moon as a cause. How could the moon without any connection to the seas cause the tides to ebb and flow? Such an explanation would be the invocation of magic or occult powers. So the motion of the earth causes the waters in the basins of the seas to slosh back and forth, and since the earth’s diurnal and axial rotation is regular, so are the periods of the tides; the backward movement is due to the residual impetus built up in the water during its slosh. Differences in tidal flows are due to the differences in the physical conformations of the basins in which they flow (for background and more detail, see Palmieri 1998).

Albeit mistaken, Galileo’s commitment to mechanically intelligible causation makes this is a plausible argument. One can see why Galileo thinks he has some sort of proof for the motion of the earth, and therefore for Copernicanism. Yet one can also see why Bellarmine and the instrumentalists would not be impressed. First, they do not accept Galileo’s restriction of possible causes to mechanically intelligible causes. Second, the tidal argument does not directly deal with the annual motion of the earth about the sun. And third, the argument does not touch anything about the central position of the sun or about the periods of the planets as calculated by Copernicus. So at its best, Galileo’s argument is an inference to the best partial explanation of one point in Copernicus’ theory. Yet when this argument is added to the earlier telescopic observations that show the improbabilities of the older celestial picture, to the fact that Venus has phases like the moon and so must revolve around the sun, to the principle of the relativity of perceived motion which neutralizes the physical motion arguments against a moving earth, it was enough for Galileo to believe that he had the necessary proof to convince the Copernican doubters. Unfortunately, it was not until after Galileo’s death and the acceptance of a unified material cosmology, utilizing the presuppositions about matter and motion that were published in the Discourses on the Two New Sciences, that people were ready for such proofs. But this could occur only after Galileo had changed the acceptable parameters for gaining knowledge and theorizing about the world. 

To read many of the documents of Galileo’s trial see Finocchiaro 1989, and Mayer 2012. To understand the long, tortuous, and fascinating aftermath of the Galileo affair see Finocchiaro 2005, and for John Paul II’s attempt see George Coyne’s article in McMullin 2005.

Primary Sources: Galileo’s Works

The main body of Galileo’s work is collected in Le Opere di Galileo Galilei , Edizione Nazionale, 20 vols., edited by Antonio Favaro, Florence: Barbera, 1890-1909; reprinted 1929-1939 and 1964–1966.

• 1590, On Motion , translated I.E. Drabkin, Madison: University of Wisconsin Press, 1960.
• 1600, On Mechanics , S. Drake (trans.), Madison: University of Wisconsin Press, 1960.
• 1610, The Starry Messenger , A. van Helden (ed.), Chicago: University of Chicago Press, 1989.
• 1613, Letters on the Sunspots , selections in S. Drake, (ed.), The Discoveries and Opinions of Galileo , New York: Anchor, 1957.
• 1623, Il Saggiatore , The Assayer , translated by Stillman Drake, in The Controversy of the Comets of 1618 , Philadelphia: The University of Pennsylvania Press 1960.
• 1632, Dialogue Concerning the Two Chief World Systems , S. Drake (trans.), Berkeley: University of California Press, 1967.
• 1638, Dialogues Concerning Two New Sciences , H. Crew and A. de Salvio (trans.), Dover Publications, Inc., New York, 1954, 1974. A better translation is: Galilei, Galileo. [ Discourses on the ] Two New Sciences , S. Drake (trans.), Madison: University of Wisconsin Press, 1974; 2nd edition, 1989 & 2000 Toronto: Wall and Emerson.

Secondary Sources

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• –––, 1967, Galileo and the Measure of Time , Florence: Olschki.
• Biagioli, Mario, 1993, Galileo Courtier , Chicago: University of Chicago Press.
• –––, 1990, “Galileo’s System of Patronage,” History of Science , 28: 1–61.
• –––, 2006, Galileo’s Instruments of Credit :Tekescopes, Images, Secrecy , Chicago: University of Chicago Press.
• Biener, Zvi, 2004, “Galileo’s First New Science: the Science of Matter,” Perspectives on Science , 12(3): 262–287.
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• Claggett, Marshall, 1966, The Science of Mechanics in the Middle Ages , Madison: University of Wisconsin Press.
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• Dijksterhuis, E.J., 1961 [1950], The Mechanization of the World Picture , translated by C Dikshoorn, Oxford: Oxford University Press.
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• –––, 1978, Galileo at Work: His Scientific Biography , Chicago: University of Chicago Press.
• –––, 1999, Essays on Galileo and the history and philosophy of science , N.M. Swerdlow and T.H. Levere, eds., 3 volumes, Toronto: University of Toronto Press.
• Duhem, Pierre, 1954, Le Systeme du monde , 6 volumes, Paris: Hermann.
• –––, 1985, To Save the Phenomena: An Essay on the Idea of Physical Theory from Plato to Galileo , translated Roger Ariew, Chicago: University of Chicago Press.
• Feldhay, Rivka, 1995, Galileo and the Church: Political Inquisition or Critical Dialogue , New York, NY: Cambridge University Press.
• –––, 1998, “The use and abuse of mathematical entities: Galileo and the Jesuits revisited,” in Machamer 1998.
• Feyerabend, Paul, 1975, Against Method , London: Verso, and New York: Humanities Press.
• Finocchiaro, Maurice A., 2005, Retrying Galileo, 1633–1992 , Berkeley: University of California Press
• –––, 1989, The Galileo Affair , Berkeley and Los Angeles: University of California Press,
• –––, 1980, Galileo and the Art of Reasoning , Dordrecht: Reidel.
• Galluzzi, Paolo, 1979, Momento: Studi Galileiani , Rome: Ateno e Bizzarri.
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• Giusti, Enrico, 1993, Euclides Reformatus. La Teoria delle Proporzioni nella Scuola Galileiana , Torino: Bottati-Boringhieri.
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• Hooper, Wallace, 1998, “Inertial problems in Galileo’s preinertial framework,” in Machamer 1998.
• Koyré, Alexander, 1939, Etudes Galileennes , Paris Hermann; translated John Mepham, Galileo Studies , Atlantic Highlands, N.J.: Humanities Press, 1978
• Lennox, James G., 1986, “Aristotle, Galileo and the ‘Mixed Sciences’ in William Wallace, ed. Reinterpreting Galileo , Washington, D.C.: The Catholic University of America Press.
• Lindberg, David C. and Robert S. Westman (eds.), 1990, Reappraisals of the Scientific Revolution , Cambridge: Cambridge University Press.
• Machamer, Peter, 1976, “Fictionalism and Realism in 16th Century Astronomy,” in R.S. Westman (ed.), The Copernican Achievement , Berkeley: University of California Press, 346–353.
• –––, 1978, “Galileo and the Causes,” in Robert Butts and Joseph Pitt (eds.), New Perspectives on Galileo , Dordrecht: Kleuwer.
• –––, 1991, “The Person Centered Rhetoric of the 17th Century,” in M. Pera and W. Shea (eds.), Persuading Science: The Art of Scientific Rhetoric , Canton, MA: Science History Publications.
• –––, and Andrea Woody, 1994, “A Model of intelligibility in Science: Using Galileo’s Balance as a Model for Understanding the Motion of Bodies,” Science and Education , 3: 215–244.
• ––– (ed.), 1998, “Introduction,” and “Galileo, Mathematics and Mechanism,” Cambridge Companion to Galileo , Cambridge: Cambridge University Press.
• –––, 1999, “Galileo’s Rhetoric of Relativity,” Science and Education , 8(2): 111–120; reprinted in Enrico Gianetto, Fabio Bevilacqua and Michael Matthews, eds. Science Education and Culture: The Role of History and Philosophy of Science , Dordrecht: Kluwer, 2001.
• Machamer, P., Lindley Darden, and Carl Craver, 2000, “Thinking about Mechanisms,” Philosophy of Science , 67: 1–25.
• Machamer, P., and Brian Hepburn, 2004, “Galileo and the Pendulum; Latching on to Time,” Science and Education , 13: 333–347; also in Michael R. Matthews (ed.), Proceedings of the International Pendulum Project (Volume 2), Sydney, Australia: The University of South Wales, 2002, 75–83.
• McMullin, Ernan (ed.), 1964, Galileo Man of Science , New York: Basic Books.
• –––, 1998, “Galileo on Science and Scripture,” in Machamer 1998.
• ––– (ed.), 2005, The Church and Galileo: Religion and Science , Notre Dame: University of Notre Dame Press.
• Mayer, Thomas F. (ed.), 2012, The Trial of Galileo 1612-1633 , North York, Ontario: The University of Toronto Press.
• Miller, David Marshall, 2008, “The Thirty Years War and the Galileo Affair,” History of Science , 46: 49-74.
• Moss, Jean Dietz, 1993, Novelties in the Heavens , Chicago, University of Chicago Press.
• Osler, Margaret, ed., 2000, Rethinking the Scientific Revolution , Cambridge: Cambridge University Press
• Palmerino, Carla Rita, 2016, “Reading the Book of Nature: The Ontological and Epistemological Underpinnings of Galileo’s Mathematical Realism,” in G. Gorham, B. Hill, E. Slowik and K. Watters (eds.), The Language of Nature: Reassessing the Mathematization of Natural Philosophy the Seventeenth Century , Minneapolis: University of Minnesota Press, pp. 29-50.
• Palmerino, Carla Rita and J.M.M.H. Thijssen, 2004, The Reception of the Galilean Science of Motion in Seventeenth-Century Europe , Dordrecht: Kluwer.
• Palmieri, Paolo, 2008, Reenacting Galileo’s Experiments: Rediscovering the Techniques of Seventeenth-Century Science , Lewiston, NY: Edwin Mellen Press
• –––, 1998, “Re-examining Galileo’s Theory of Tides,” Archive for History of Exact Sciences , 53: 223–375.
• –––, 2001, “The Obscurity of the Equimultiples: Clavius’ and Galileo’s Foundational Studies of Euclid’s Theory of Proportions,” Archive for the History of the Exact Sciences , 55(6): 555–597.
• –––, 2003, “Mental Models in Galileo’s Early Mathematization of Nature,” Studies in History and Philosophy of Science , 34: 229–264.
• –––, 2004a, “The Cognitive Development of Galileo’s Theory of Buoyancy,” Archive for the History of the Exact Sciences , 59: 189–222.
• –––, 2005, “‘Spuntar lo scoglio piu duro’: did Galileo ever think the most beautiful thought experiment in the history of science?” Studies in History and Philosophy of Science , 36(2): 223–240.
• Peterson Mark A., 2011, Galileo’s Muse: Renaissance Mathematics and the Arts , Cambridge, MA: Harvard University Press.
• Redondi, Pietro, 1983, Galileo eretico , Torino: Einaudi; translated by Raymond Rosenthal, Galileo Heretic , Princeton: Princeton University Press, 1987.
• Raphael, Renee Jennifer, 2011, “Making sense of Day 1 of the Two New Sciences: Galileo’s Aristotelian-inspired agenda and his Jesuit readers,” Studies in History and Philosophy of Science , 42: 479-491.
• Renn, J. & Damerow, P. & Rieger, S., 2002, ‘Hunting the White Elephant: When and How did Galileo Discover the Law of Fall?’, in J. Renn (ed.), Galileo in Context , Cambridge University Press, Cambridge, 29–149.
• Reeves, Eileen, 2008, Galileo’s Glass Works: The telescope and the mirror , Cambridge, MA: Harvard University Press.
• Rossi, Paolo, 1962, I Filosofi e le Macchine , Milan: Feltrinelli; 1970, translated by S. Attanasio, Philosophy, Technology and the Arts in the Early Modern Era , New York: Harper.
• Segré, Michael, 1998, “The Neverending Galileo Story” in Machamer 1998.
• –––, 1991, In the Wake of Galileo , New Brunswick: Rutgers University Press.
• Settle, Thomas B., 1967, “Galileo’s Use of Experiment as a Tool of Investigation,” in McMullin 1967.
• –––, 1983, “Galileo and Early Experimentation,” in Springs of Scientific Creativity: Essays on Founders of Modern Science , Rutherford Aris, H. Ted Davis, and Roger H. Stuewer (eds.), Minneapolis: University of Minnesota Press, pp. 3–20.
• –––, 1992, “Experimental Research and Galilean Mechanics,” in Galileo Scientist: His Years at Padua and Venice , Milla Baldo Ceolin (ed.), Padua: Istituto Nazionale di Fisica Nucleare; Venice: Istituto Venet o di Scienze, Lettere ed Arti; Padua: Dipartimento di Fisica, pp. 39–57.
• Shapere, Dudley, 1974, Galileo: A Philosophical Study , Chicago: University of Chicago Press.
• Shapin, Steve, 1996, The Scientific Revolution , Chicago: University of Chicago Press.
• Shea, William, 1972, Galileo’s Intellectual Revolution: Middle Period (1610–1632) , New York: Science History Publications.
• Shea, William & Marinao Artigas, 2003, Galileo in Rome: The Rise and fall of a Troublesome Genius , Oxford: Oxford University Press.
• Sobel, Dava, 1999, Galileo’s Daughter , New York: Walker and company
• Spranzi, Marta, 2004, Galilee: “Le Dialogues sur les deux grands systemes du monde”: rhetorique, dialectique et demenstration , Paris: PUF.
• Van Fraassen, Bas C., 1996, The Scientific Image , Oxford: Oxford University Press.
• Wallace, William A., 1984, Galileo and his Sources: The Heritage of the Collegio Romano in Galileo’s Science , Princeton: Princeton University Press.
• –––, 1992, Galileo’s Logic of Discovery and Proof: The Background, Content and Use of His Appropriated Treatises on Aristotle’s Posterior Analytics , Dordrecht; Boston: Kluwer Academic.
• Westman, Robert (ed.), 1976, The Copernican Achievement , University of California Press.
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• Woottron, David, 2015, The Invention of Science , New York: Harper.

How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up this entry topic at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

• Galileo Galilei’s Notes on Motion , Joint Project of Biblioteca Nazionale Centrale, Florence Istituto e Museo di Storia della Scienza, Florence Max Planck Institute for the History of Science, Berlin.
• The Galileo Project , contains Dava Sobel’s translations of all 124 letters from Suor Maria Celeste to Galileo in the sequence in which they were written, maintained by Albert Van Helden.
• Galileo Galilei , The Institute and Museum of the History of Science of Florence, Italy.

Copernicus, Nicolaus | -->matter --> | natural philosophy: in the Renaissance | religion: and science

Acknowledgments

Thanks to Zvi Biener and Paolo Palmieri for commenting on earlier drafts of this entry.

Copyright © 2017 by Peter Machamer < machamerpeter @ gmail . com >

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How Galileo Changed Your Life

Galileo ’s contributions to the fields of astronomy, physics, mathematics, and philosophy have led many to call him the father of modern science. But his controversial theories, which impacted how we see and understand the solar system and our place within it, led to serious conflict with the Catholic Church and the long-time suppression of his achievements.

Galileo developed one of the first telescopes

Galileo didn’t invent the telescope — it was invented by Dutch eyeglass makers — but he made significant improvements to it. After learning about the Dutch invention, he was able to develop one of his own, teaching himself how to ground lenses. His first version magnified distant objects by three times. By that fall, he could produce lenses with a 20x magnification.

His innovations brought him both professional and financial success. He was given a lifetime tenure position at the University of Padua, where he had been teaching for several years, at double his salary. And he received a contract to produce his telescopes for a group of Venetian merchants, eager to use them as a navigational tool.

He helped created modern astronomy

Galileo turned his new, high-powered telescope to the sky. In early 1610, he made the first in a remarkable series of discoveries. He spent several weeks observing a set of stars near Jupiter as they revolved around the planet. He had discovered Jupiter’s four moons, which he named the Medicean Stars (after his patrons, the powerful Medici family), but which have since been renamed the Galilean moons, in his honor. Galileo’s close study of orbits of Jupiter’s moons and their eclipses helped create more accurate time table and measurements that later mapmakers built upon for the practice of cartography.

While the scientific doctrine of the day held that space was perfect, unchanging environments created by God, Galileo’s telescope helped change that view. His studies and drawings showed the Moon had a rough, uneven surface that was pockmarked in some places, and was actually an imperfect sphere. Galileo also observed the phases of planet Venus and the existence of far more stars in the Milky Way that weren't visible to the naked eye.

He was also one of the first people to observe the phenomena known as sunspots, thanks to his telescope which allowed him to view the sun for extended periods of time without damaging the eye. This discovery also saw one of his first scientific clashes, as he used his evidence to debate fellow scientists who argued that the sunspots were actually satellites of the sun and not irregularities.

Galileo helped prove that the Earth revolved around the sun

In 1610, Galileo published his new findings in the book Sidereus Nuncius , or Starry Messenger , which was an instant success. The Medicis helped secure him an appointment as a mathematician and philosopher in his native Tuscany.

He became close with a number of other leading scientists, including Johannes Kepler. A German astronomer and mathematician, Kepler’s work helped lay the foundations for the later discoveries of Isaac Newton and others.

Kepler’s experiments had led him to support the idea that the planets, Earth included, revolved around the sun. This heliocentric theory, as well as the idea of Earth’s daily rotational turning, had been developed by Polish astronomer Nicolaus Copernicus half a century earlier. Galileo and Kepler exchanged correspondence around Kepler’s ideas of planetary motion, and their detailed studies and observations helped spur the Scientific Revolution.

Their belief that the Sun, and not the Earth, was the gravitational center of the universe, upended almost 2,000 years of scientific thinking, dating back to theories about the fixed, unchanging universe put forth by the Greek philosopher and scientist Aristotle . Galileo had been testing Aristotle’s theories for years, including an experiment in the late 16th century in which he dropped two items of different masses from the Leaning Tower of Pisa, disproving Aristotle’s belief that objects would fall at differing speeds based on their weight (Newton later improved upon this work).

Galileo paid a high price for his contributions

But challenging the Aristotelian or Ptolemaic theories about the Earth’s role in the universe was dangerous stuff. Geocentrism was, in part, a theoretical underpinning of the Roman Catholic Church. Galileo’s work brought him to the attention of Church authorities, and in 1615, he was called before the Roman Inquisition, accused of heresy for beliefs which contradicted Catholic scripture. The following year, the Church banned all works that supported Copernicus’ theories and forbade Galileo from publicly discussing his works.

Galileo kept quiet for more than 15 years, during which he quietly continued his experiments. In 1632, after the election of a new pope who he considered more liberal, he published another book, Dialogue on the Two Chief World Systems, Ptolemaic and Copernican , which argued both sides of the scientific (and religious) debate but fell squarely on the side of Copernicus’ heliocentrism. Galileo was once again summoned to Rome. In 1633, following a trial, he was found guilty of suspected heresy, forced to recant his views and sentenced to house arrest until his death in 1642.

It took nearly 200 years after Galileo’s death for the Catholic Church to drop its opposition to heliocentrism. In 1992, after a decade-long process and 359 years after his heresy conviction, Pope John Paul II formally expressed the Church’s regret over Galileo’s treatment. In 1995, an unmanned NASA spacecraft named Galileo landed on Jupiter to begin a multi-year study of the planet and its moons, which Galileo had helped identify in 1610.

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Biography of Galileo Galilei, Renaissance Philosopher and Inventor

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The University of Pisa

Becoming a mathematician, the leaning tower of pisa, the university of padua, building a spyglass (telescope).

• Galileo's Observations of the Moon
• Discovery of Jupiter's Satellites
• Seeing Saturn's Rings

Charged With Heresy

The final trial, inquisition and death, the vatican pardons galileo in 1992.

Galileo Galilei (February 15, 1564–January 8, 1642) was a famous inventor , mathematician, astronomer, and philosopher whose inventive mind and stubborn nature ran him into trouble with the Inquisition.

Fast Facts: Galileo Galilei

• Known For : Italian Renaissance philosopher, inventor, and polymath who faced the wrath of the Inquisition for his astronomical studies
• Born : February 15, 1564 in Pisa, Italy
• Parents : Vincenzo and Giulia Ammannati Galilei (m. July 5, 1562)
• Died : January 8, 1642 in Arcetri, Italy
• Education : Privately tutored; Jesuit monastery, University of Pisa
• Published Works : "The Starry Messenger"
• Spouse : None; Marina Gamba, mistress (1600–1610)
• Children : Virginia (1600), Livia Antonia (1601), Vincenzo (1606)

Galileo was born in Pisa, Italy on February 15, 1564, the oldest of seven children of Giulia Ammannati and Vincenzo Galilei. His father (c. 1525–1591) was a gifted lute musician and wool trader and wanted his son to study medicine because there was more money in that field. Vincenzo was attached to the court and was often traveling. The family was originally named Bonaiuti, but they had an illustrious ancestor named Galileo Bonaiuti (1370–1450) who was a physician and public officer in Pisa. One branch of the family broke off and began calling itself Galilei ("of Galileo"), and so Galileo Galilei was doubly named after him.

As a child, Galileo made mechanical models of ships and watermills, learned to play the lute to a professional standard, and showed an aptitude for painting and drawing. Originally tutored by a man named Jacopo Borghini, Galileo was sent to the Camaldlese monastery at Vallambroso to study grammar, logic, and rhetoric. He found the contemplative life to his liking, and after four years he joined the community as a novice. This was not exactly what his father had in mind, so Galileo was hastily withdrawn from the monastery. In 1581 at the age of 17, he entered the University of Pisa to study medicine , as his father wished.

At age 20, Galileo noticed a lamp swinging overhead while he was in a cathedral. Curious to find out how long it took the lamp to swing back and forth, he used his pulse to time large and small swings. Galileo discovered something that no one else had ever realized: the period of each swing was exactly the same. The law of the pendulum, which would eventually be used to regulate clocks , made Galileo Galilei instantly famous.

Except for mathematics , Galileo was soon bored with the university and the study of medicine. Uninvited, he attended the lecture of court mathematician Ostilio Ricci—who had been assigned by the Duke of Tuscany to teach the court attendants in math, and Galileo was not one of those. Galileo followed up the lecture by reading Euclid on his own; he sent a set of questions to Ricci, the content of which greatly impressed the scholar.

Galileo's family considered his mathematical studies subsidiary to medicine, but when Vincenzo was informed that their son was in danger of flunking out, he worked out a compromise so that Galileo could be tutored in mathematics by Ricci full-time. Galileo's father was hardly overjoyed about this turn of events because a mathematician's earning power was roughly around that of a musician, but it seemed that this might yet allow Galileo to successfully complete his college education. The compromise didn't work out, for Galileo soon left the University of Pisa without a degree.

After he flunked out, Galileo started tutoring students in mathematics to earn a living. He did some experimenting with floating objects, developing a balance that could tell him that a piece of gold, for example, was 19.3 times heavier than the same volume of water. He also started campaigning for his life's ambition: a position on the mathematics faculty at a major university. Although Galileo was clearly brilliant, he had offended many people in the field and they would choose other candidates for vacancies.

Ironically, it was a lecture on literature that would turn Galileo's fortunes. The Academy of Florence had been arguing over a 100-year-old controversy: what were the location, shape, and dimensions of Dante's Inferno? Galileo wanted to seriously answer the question from the point of view of a scientist. Extrapolating from Dante's line that the giant Nimrod's "face was about as long/and just as wide as St. Peter's cone in Rome," Galileo deduced that Lucifer himself was 2,000 arm-lengths long. The audience was impressed, and within the year, Galileo had received a three-year appointment to the University of Pisa, the same university that never granted him a degree.

When Galileo arrived at the University, some debate had started up on one of Aristotle's "laws" of nature: that heavier objects fell faster than lighter objects. Aristotle's word had been accepted as gospel truth, and there had been few attempts to actually test Aristotle's conclusions by actually conducting an experiment.

According to legend, Galileo decided to try. He needed to be able to drop the objects from a great height. The perfect building was right at hand—the Tower of Pisa , which was 54 meters (177 feet) tall. Galileo climbed to the top of the building carrying a variety of balls of varying sizes and weights and dumped them off the top. They all landed at the base of the building at the same time (legend says that the demonstration was witnessed by a huge crowd of students and professors). Aristotle was wrong.

It might have helped the junior member of the faculty if Galileo had not continued to behave rudely toward his colleagues. "Men are like wine flasks," he once said to a group of students, "Look at…bottles with the handsome labels. When you taste them, they are full of air or perfume or rouge. These are bottles fit only to pee into!" Perhaps not surprisingly, the University of Pisa chose not to renew Galileo's contract.

Galileo Galilei moved on to the University of Padua. By 1593, he was desperate and in need of additional cash. His father had died, so Galileo was now head of his family. Debts were pressing down on him, most notably the dowry for one of his sisters, which was to be paid in installments over decades. (A dowry could be thousands of crowns, and Galileo's annual salary was 180 crowns.) Debtor's prison was a real threat if Galileo returned to Florence.

What Galileo needed was to come up with some sort of device that could make him a tidy profit. A rudimentary thermometer (which, for the first time, allowed temperature variations to be measured) and an ingenious device to raise water from aquifers found no market. He found greater success in 1596 with a military compass that could be used to accurately aim cannonballs. A modified civilian version that could be used for land surveying came out in 1597 and ended up earning a fair amount of money for Galileo. It helped his profit margin that the instruments were sold for three times the cost of manufacture, he offered classes on how to use the instrument, and the actual toolmaker was paid dirt-poor wages.

Galileo needed the money to support his siblings, his mistress (21-year-old Marina Gamba), and his three children (two daughters and a boy). By 1602, Galileo's name was famous enough to help bring in students to the University, where Galileo was busily experimenting with magnets .

During a vacation to Venice in 1609, Galileo Galilei heard rumors that a Dutch spectacle-maker had invented a device that made distant objects seem near at hand (at first called the spyglass and later renamed the  telescope ). A patent had been requested, but not yet granted. The methods were being kept secret because it was obviously of tremendous military value for Holland.

Galileo Galilei was determined to attempt to construct his own spyglass. After a frantic 24 hours of experimentation, working only on instinct and bits of rumors—he had never actually seen the Dutch spyglass—he built a three-power telescope. After some refinement, he brought a 10-power telescope to Venice and demonstrated it to a highly impressed Senate. His salary was promptly raised, and he was honored with proclamations.

Galileo's Observations of the Moon

If he had stopped here and become a man of wealth and leisure, Galileo Galilei might be a mere footnote in history. Instead, a revolution started when, one fall evening, the scientist trained his telescope on an object in the sky that all people at that time believed must be a perfect, smooth, polished heavenly body—the moon.

To his astonishment, Galileo Galilei viewed a surface that was uneven, rough, and full of cavities and prominences. Many people insisted that Galileo Galilei was wrong, including a mathematician who insisted that even if Galileo was seeing a rough surface on the Moon, that only meant that the entire moon had to be covered in invisible, transparent, smooth crystal.

Discovery of Jupiter's Satellites

Months passed, and his telescopes improved. On January 7, 1610, he turned his 30-power telescope toward Jupiter and found three small, bright stars near the planet. One was off to the west, the other two were to the east, all three in a straight line. The following evening, Galileo once again took a look at Jupiter and found that all three of the "stars" were now west of the planet, still in a straight line.

Observations over the following weeks led Galileo to the inescapable conclusion that these small "stars" were actually small satellites that were rotating around Jupiter. If there were satellites that didn't move around the Earth, wasn't it possible that the Earth was not the center of the universe? Couldn't the  Copernican  idea of the sun resting at the center of the solar system be correct?

Galileo Galilei published his findings in a small book titled "The Starry Messenger." A total of 550 copies were published in March 1610, to tremendous public acclaim and excitement. It was the only one of Galileo's writings in Latin; most of his work was published in Tuscan.

Seeing Saturn's Rings

There continued to be more discoveries via the new telescope: the appearance of bumps next to the planet Saturn (Galileo thought they were companion stars; the "stars" were actually the edges of Saturn's rings), spots on the Sun's surface (though others had actually seen the spots before), and seeing Venus change from a full disk to a sliver of light.

For Galileo Galilei, saying that the Earth went around the Sun changed everything since he was contradicting the teachings of the Catholic Church. While some of the church's mathematicians wrote that his observations were clearly correct, many members of the church believed that he must be wrong.

In December 1613, one of the scientist's friends told him how a powerful member of the nobility said that she could not see how his observations could be true since they would contradict the Bible. The woman quoted a passage in Joshua in which God causes the sun to stand still and lengthen the day. How could this mean anything other than that the sun went around the Earth?

Galileo was a religious man and agreed that the Bible could never be wrong. However, he said, the interpreters of the Bible could make mistakes, and it was a mistake to assume that the Bible had to be taken literally. That was one of Galileo's major mistakes. At that time, only church priests were allowed to interpret the Bible or define God's intentions. It was absolutely unthinkable for a mere member of the public to do so.

Some of the church clergy started responding, accusing him of heresy. Some clerics went to the Inquisition, the Catholic Church court that investigated charges of heresy, and formally accused Galileo Galilei. This was a very serious matter. In 1600, a man named Giordano Bruno was convicted of being a heretic for believing that the Earth moved about the sun and that there were many planets throughout the universe where life—living creations of God—existed. Bruno was burned to death.

However, Galileo was found innocent of all charges and was cautioned not to teach the Copernican system. Sixteen years later, all that would change.

The following years saw Galileo work on other projects. With his telescope he watched the movements of Jupiter's moons , recorded them as a list, and then came up with a way to use these measurements as a navigation tool. He developed a contraption that would allow a ship captain to navigate with his hands on the wheel, but the contraption looked like a horned helmet.

As another amusement, Galileo started writing about ocean tides. Instead of writing his arguments as a scientific paper, he found that it was much more interesting to have an imaginary conversation, or dialogue, between three fictional characters. One character, who would support Galileo's side of the argument, was brilliant. Another character would be open to either side of the argument. The final character, named Simplicio, was dogmatic and foolish, representing all of Galileo's enemies who ignored any evidence that Galileo was right. Soon, he wrote up a similar dialogue called "Dialogue on the Two Great Systems of the World." This book talked about the Copernican system .

"Dialogue" was an immediate hit with the public, but not, of course, with the church. The pope suspected that he was the model for Simplicio. He ordered the book banned and also ordered the scientist to appear before the Inquisition in Rome for the crime of teaching the Copernican theory after being ordered not to do so.

Galileo Galilei was 68 years old and sick. Threatened with torture, he publicly confessed that he had been wrong to have said that the Earth moves around the Sun. Legend then has it that after his confession, Galileo quietly whispered, "and yet, it moves."

Unlike many less famous prisoners, he was allowed to live under house arrest in his house outside of Florence and near one of his daughters, a nun. Until his death in 1642, he continued to investigate other areas of science. Amazingly, he even published a book on force and motion although he had been blinded by an eye infection.

The Church eventually lifted the ban on Galileo's Dialogue in 1822—by that time, it was common knowledge that the Earth was not the center of the Universe. Still later, there were statements by the Vatican Council in the early 1960s and in 1979 that implied that Galileo was pardoned and that he had suffered at the hands of the church. Finally, in 1992, three years after Galileo Galilei's namesake had been launched on its way to Jupiter, the Vatican formally and publicly cleared Galileo of any wrongdoing.

• Drake, Stillman. "Galileo at Work: His Scientific Biography." Mineola, New York: Dover Publications Inc., 2003.
• Reston, Jr., James. "Galileo: A Life." Washington DC: BeardBooks, 2000. 
• Van Helden, Albert. "Galileo: Italian Philosopher, Astronomer and Mathematician." Encyclopedia Britannica , February 11, 2019.
• Wootton, David. Galileo: "Watcher of the Skies." New Haven, Connecticut: Yale University Press, 2010.
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Galileo (Galilei) summary

Galileo (Galilei) , (born Feb. 15, 1564, Pisa—died Jan. 8, 1642, Arcetri, near Florence), Italian mathematician, astronomer, and physicist. Son of a musician, he studied medicine before turning his attention to mathematics. His invention of the hydrostatic balance ( c. 1586) made him famous. In 1589 he published a treatise on the centre of gravity in solids, which won him the post of mathematics lecturer at the University of Pisa. There he disproved the Aristotelian contention that bodies of different weights fall at different speeds; he also proposed the law of uniform acceleration for falling bodies and showed that the path of a thrown object is a parabola. The first to use a telescope to study the skies, he discovered (1609–10) that the surface of the Moon is irregular, that the Milky Way is composed of stars, and that Jupiter has moons ( see Galilean satellite). His findings led to his appointment as philosopher and mathematician to the grand duke of Tuscany. During a visit to Rome (1611), he spoke persuasively for the Copernican system, which put him at odds with Aristotelian professors and led to Copernicanism’s being declared false and erroneous (1616) by the church. Obtaining permission to write about the Copernican system so long as he discussed it noncommittally, he wrote his Dialogue Concerning the Two Chief World Systems (1632). Though considered a masterpiece, it enraged the Jesuits, and Galileo was tried before the Inquisition , found guilty of heresy, and forced to recant. He spent the rest of his life under house arrest, continuing to write and conduct research even after going blind in 1637.

 MacTutor

Galileo galilei.

About ten months ago a report reached my ears that a certain Fleming 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 believed while other denied them. A few days later the report was confirmed by a letter I received from a Frenchman in Paris, Jacques Badovere, which caused me to apply myself wholeheartedly to investigate means by which I might arrive at the invention of a similar instrument. This I did soon afterwards, my basis being the doctrine of refraction.

In about two months, December and January, he made more discoveries that changed the world than anyone has ever made before or since.

I hold that the Sun is located at the centre of the revolutions of the heavenly orbs and does not change place, and that the Earth rotates on itself and moves around it. Moreover ... I confirm this view not only by refuting Ptolemy 's and Aristotle 's arguments, but also by producing many for the other side, especially some pertaining to physical effects whose causes perhaps cannot be determined in any other way, and other astronomical discoveries; these discoveries clearly confute the Ptolemaic system, and they agree admirably with this other position and confirm it.

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth.

I assume that the speed acquired by the same movable object over different inclinations of the plane are equal whenever the heights of those planes are equal.

The time in which a certain distance is traversed by an object moving under uniform acceleration from rest is equal to the time in which the same distance would be traversed by the same movable object moving at a uniform speed of one half the maximum and final speed of the previous uniformly accelerated motion.

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Additional Resources ( show )

Other pages about Galileo Galilei:

• Preface to Letters from Galileo
• Galileo's Confession
• Galileo's Dialogue
• The title page from Discorsi (1638)
• ... and another page
• ... and yet another page
• Multiple entries in The Mathematical Gazetteer of the British Isles ,
• Astronomy: The Dynamics of the Solar System
• Astronomy: The Structure of the Solar System
• Anstruther Solar System model
• Sci Hi blog
• Miller's postage stamps
• Heinz Klaus Strick biography

Other websites about Galileo Galilei:

• Dictionary of Scientific Biography
• Encyclopaedia Britannica
• Science Museum Florence
• The Galileo Project
• Michael Fowler ( Dialogue concerning two new sciences )
• The Catholic Encyclopedia
• Sci Hi blog ( Jupiter's moons )
• Sci Hi blog ( Galileo's telescope )
• Internet Encyclopedia of Philosophy
• Openculture ( Galileo's so-called "moon drawings" )
• MathSciNet Author profile

Honours ( show )

Honours awarded to Galileo Galilei

• Lunar features Crater Galilaei and Rima Galilaei
• Paris street names Rue Galilée ( = Galileo ) (16 th Arrondissement )
• Popular biographies list Number 9

Cross-references ( show )

• History Topics: A brief history of cosmology
• History Topics: A history of time: Classical time
• History Topics: A mathematical walk around Bologna
• History Topics: An overview of the history of mathematics
• History Topics: Christianity and the Mathematical Sciences - the Heliocentric Hypothesis
• History Topics: Galileo's Difesa
• History Topics: General relativity
• History Topics: Infinity
• History Topics: Kepler's Planetary Laws
• History Topics: Light through the ages: Ancient Greece to Maxwell
• History Topics: Longitude and the Académie Royale
• History Topics: Mathematical discovery of planets
• History Topics: Mathematics and the physical world
• History Topics: Science in the 17 th century: From Europe to St Andrews
• History Topics: The Size of the Universe
• History Topics: The brachistochrone problem
• History Topics: The function concept
• History Topics: The mathematician and the forger
• History Topics: Theories of gravitation
• History Topics: Thomas Harriot's manuscripts
• History Topics: Weather forecasting
• Famous Curves: Catenary
• Famous Curves: Cycloid
• Famous Curves: Parabola
• Societies: Lincei Accademia
• Societies: Paris Academy of Sciences
• Other: 17th December
• Other: 1908 ICM - Rome
• Other: 1924 ICM - Toronto
• Other: 1928 ICM - Bologna
• Other: 1950 ICM - Cambridge USA
• Other: 2009 Most popular biographies
• Other: 20th January
• Other: 21st February
• Other: 22nd June
• Other: 25th July
• Other: 28th December
• Other: 31st October
• Other: 5th March
• Other: 7th January
• Other: Earliest Known Uses of Some of the Words of Mathematics (C)
• Other: Earliest Known Uses of Some of the Words of Mathematics (Q)
• Other: Earliest Uses of Symbols for Fractions
• Other: Jeff Miller's postage stamps
• Other: London Learned Societies
• Other: London Museums
• Other: London Scientific Institutions
• Other: London individuals H-M
• Other: Most popular biographies – 2024
• Other: Other London Institutions outside the centre
• Other: Oxford Institutions and Colleges
• Other: Popular biographies 2018
• Other: The Dynamics of the Solar System
• Other: The Structure of the Solar System

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Galileo Galilei often known, as Galileo was a very famous scholar and an Italian scientist who pioneered astronomy and modern physics. He was born in Pisa, Italy on 15 February 1564 and spent valuable time of his life by providing the services as professor of mathematics. He was the sixth child of Giulia Ammannati and well known and famous musician of his time Vincenzo Galilei. Spending very early years of his life in Italy, Galileo shifted along with his family in the year 1574 in Florence and there began his proper education at the Camaldolese Monastery in Vallombrosa (Sis, 2000). In the year 1583, with high passion of acquiring well education, he admitted in university of Pisa to begin the studies of medicine. Young Galileo had a keen interest towards exploring plenty of subjects and thus he finally took a halt of putting his intelligence and talent towards mathematics and physics.

He studied physics and went deep down into the subject’s elements to bring various observations related to nature. At Pisa University Galileo spent an outstanding time of learning a lot and studied according to the Aristotle’s view of the world. His career took a lead when he was offered to teach in his university even before completing his degree but unfortunately, he was compelled to leave his studies due to immense financial troubles. However, he continued to explore mathematics and joined various teaching positions so that he could make his both ends meet. His study towards exploring motion of objects and introducing principles of weighing smaller quantities were included in his publication named as “The Little Balance” that proved very attractive and brought him to a lime light. Gaining little fame, he accepted the offer from Pisa University to work as lecturer. That was the place that allowed him to do various experiments but Galileo in search of good results went against the principles and studies of Aristotle. As a result, no one supported him and he could not get a renewal of his contract in Pisa University in 1592.

Galileo was a talented man with potential to go beyond and do something exceptional. He gained a good position of teaching mathematics, astronomy, and mechanics at the University of Padua. However, the offer proved lucky for him but with the news of his father’s death. Overcoming the grief, Galileo devoted himself towards supporting family and completing his mission to provide good services as teacher, attracting huge mass of followers, and giving valuable and knowledgeable lectures (Wood, 1091). His positive intention and struggle helped him to reach at high position where he got increasing fame, respect, honor, and recognition of his talent and intellectual. Galileo was quite impressed by the technology and thus applied his experiments to technological applications and merging his skills published “The Operations of the Geometrical and Military Compass.”

His work was not confined to this but he went further to develop hydrostatic balance that could measure small objects quite easily. His exceptional and remarkable inventions were one of their kinds. As a result, he got overwhelming response and recognition and then switched over to other observations out of which he invented his own telescope. His curiosity to know more about the world and universe took him to the discovery of Jupiter, Venus, and moon and the things all around them. He explored that the moon was not flat but a sphere, Venus rotated around the sun, and Jupiter had various moons all around it. Galileo championed Heliocentrism but it proved controversial (Fayyazuddin, pp. 15-18). However, after facing some time of controversy he finally defended himself through “Dialogue concerning the two chief world systems.”

Galileo was forced to live under house arrest in which he wrote the work of “Two new Sciences.” This particular work was a summary of his forty years learning and knowledge related to strength of materials and Kinematics. Galileo’s innovative combination is still useful in the present time and will continue to be like that even for the coming generations and centuries. He died at the age of 77 after suffering from heart palpitations and fever, on eighth of January 1642.

Works Cited

Fayyazuddin, Ansar. "The Courage Of Rational Thinking: Galileo's Revolution." Against The Current 29.3 (2014): pp. 15-18. Sis, Peter. Starry messenger: Galileo Galilei. Turtleback Books Distributed by Demco Media, 2000. Wood, C. G. "Renaissance Genius: Galileo Galilei & His Legacy to Modern Science." Choice 47.6 (2010): pp. 1091.

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Collection Finding Our Place in the Cosmos: From Galileo to Sagan and Beyond

Galileo and the telescope.

The invention of the telescope played an important role in advancing our understanding of Earth's place in the cosmos. While there is evidence that the principles of telescopes were known in the late 16th century, the first telescopes were created in the Netherlands in 1608. Spectacle makers Hans Lippershey & Zacharias Janssen and Jacob Metius independently created telescopes. The telescope emerged from a tradition of craftsmanship and technical innovation around spectacles and developments in the science of optics traced back through Roger Bacon and a series of Islamic scientists, in particular Al-Kindi (c. 801–873), Ibn Sahl (c. 940-1000) and Ibn al-Haytham (965–1040).

The story of Galileo's telescopic observations illustrates how a tool for seeing and collecting evidence can dramatically change our understanding of the cosmos.

Early telescopes were primarily used for making Earth-bound observations, such as surveying and military tactics. Galileo Galilei (1564-1642) was part of a small group of astronomers who turned telescopes towards the heavens. After hearing about the "Danish perspective glass" in 1609, Galileo constructed his own telescope. He subsequently demonstrated the telescope in Venice. His demonstration of the telescope earned him a lifetime lectureship.

After his initial success, Galileo focused on refining the instrument. The initial telescope he created (and the Dutch ones it was based on) magnified objects three diameters. That is, it made things look three times larger than they did with the naked eye. Through refining the design of the telescope he developed an instrument that could magnify eight times, and eventually thirty times.

This increased magnification of heavenly objects had a significant and immediate impact.  These new observations were by no means exclusive to Galileo.  The story of Galileo and the telescope is a powerful example of the key role that technologies play in enabling advances in scientific knowledge. With that said, the telescope isn't the only technology at play in this story. Galileo deftly used the printed book and the design of prints in his books to present his research to the learned community.  This is not a story of a lone thinker theorizing and piecing together a new model of the cosmos. Quite the contrary, an array of individuals in the early 17th century took the newly created telescopes and pointed them toward the heavens. Unlike those other observers, however, Galileo rapidly published his findings.  In some cases, Galileo understood the significance and importance of these observations more readily than his contemporaries. It was this understanding, and foresight to publish, that made Galileo's ideas stand the test of time.

Starry Messenger , Galileo's Rapidly Published Findings

Shortly after his first telescopic observations of the heavens, Galileo began sketching his observations. He wanted to get his findings out. His observations and interpretations of stars, the moon, Jupiter, the sun and the phases of the planet Venus, were critical in refining our understanding of the cosmos. In March of 1610, Galileo published the initial results of his telescopic observations in Starry Messenger ( Sidereus Nuncius ) , this short astronomical treatise quickly traveled to the corners of learned society.

The Moon is not a Perfect Sphere

The engravings of the Moon, created from Galileo's artfully drawn sketches, presented readers with a radically different perspective on the Moon. Due to Galileo's training in Renaissance art and an understanding of chiaroscuro (a technique for shading light and dark) he quickly understood that the shadows he was seeing were actually mountains and craters. From his sketches, he made estimates of their heights and depths. These observations, only possible by the magnifying power of the telescope, clearly suggested that the Aristotelian idea of the Moon as a translucent perfect sphere (or as Dante had suggested an "eternal pearl") were wrong. The Moon was no longer a perfect heavenly object; it now clearly had features and a topology similar in many ways to the Earth. The notion that the moon had a topology like the Earth led to speculation on what life might be like on the Moon .

It's now understood that English astronomer Thomas Harriot, (1560-1621) made the first recorded observations of the Moon through a telescope, a month before Galileo in July of 1609. Moreover, the map Harriot created of the Moon in 1612 or 1613 is more detailed than Galileo's. Harriot observed the Moon first, and the maps he created included more information, but he did not broadly distribute his work. However, over 500 copies of the Starry Messenger were printed and sold, solidifying Galileo's legacy in astronomy. 

Jupiter has its Own Moons

When Galileo turned his telescope to observe Jupiter, he saw what he initially thought to be three previously unobserved fixed stars. After continued observations it became clear that they were not fixed, and in a matter of days he had come to the conclusion that these new stars were in fact orbiting Jupiter. He had discovered three of the largest moons of Jupiter.

The implications of this discovery, of objects orbiting a planet, were part of what pushed Galileo to argue for a sun-centered cosmos . Jupiter's moons countered a key argument against the Earth orbiting the sun. Critics of Copernicus' sun-centered cosmos asked, how could the Earth drag the moon across the heavens? Remember, the idea of the underlying mechanism of gravity wouldn't come until Newton's Principia Mathematica in 1687, which makes this both a reasonable and important question. Since there was wide agreement that Jupiter was already in motion, the fact that Jupiter clearly had its own moons offered a clear refutation of an important critique of the heliocentric system.

In Mundus Jovialis (1614) , Simon Marius claimed that he, not Galileo, had first discovered the moons of Jupiter. In his times, Marius was publicly condemned as a plagiarist. Galileo had published his results already in 1610 and was rather well known and powerful in renaissance court. Only in the 19th century, would historians return to examine the evidence. It turns out that Marius had not plagiarized Galileo. Clearly his observations were different; in fact he had more accurately charted the orbits of Jupiter's moons. It's now broadly understood that Marius was an independent observer of Jupiter's moons.

A Spotted Rotating Sun

In observing the sun, Galileo saw a series of "imperfections". He had discovered sunspots. Monitoring these spots on the sun demonstrated that the sun in fact rotated. Furthermore, later observations by Francesco Sizzi in 1612 suggested that the spots on the sun actually changed over time. It would seem that the Sun, like the Moon, was not the perfect sphere that learned Europeans thought of as a key feature of their universe.

These sunspots were also independently observed by the Jesuit priest and astronomer Christoph Scheiner (1575-1650). Scheiner observed sunspots in 1611 and published his results in 1612. Over the course of their careers Galileo and Schiener feuded over who should get credit for the discovery. Unbeknownst to either of them, Thomas Harriot had observed them in 1610 and the German theologian, David Fabricius and his son Johanes likely beat both Scheiner and Galileo to the publication of the discovery with their Apparente earum cum Sole Conversione Narratio in June of 1611. However, their publication was not widely circulated and thus remained obscure in its times. Outside the western tradition of science. Chinese astronomers have long observed sunspots, going back to at least 165 BC.