Galileo
ITALIAN PHILOSOPHER, ASTRONOMER AND MATHEMATICIAN


Galileo, in full Galileo Galilei, (born February 15, 1564, Pisa [Italy]
He was italian natural philosopher, astronomer, and mathematician who made fundamental contributions to the sciences of motion, astronomy, and strength of materials and to the development of the scientific method. His formulation of (circular) inertia, the law of falling bodies, and parabolic trajectories marked the beginning of a fundamental change in the study of motion. His insistence that the book of nature was written in the language of mathematics changed natural philosophy from a verbal, qualitative account to a mathematical one in which experimentation became a recognized method for discovering the facts of nature. Finally, his discoveries with the telescope revolutionized astronomy and paved the way for the acceptance of the Copernican heliocentric system, but his advocacy of that system eventually resulted in an Inquisition process against him.

Early Life And Career

was born in Pisa, Tuscany, on February 15, 1564, the oldest son of Vincenzo Galilei, a musician who made important contributions to the theory and practice of music and who may have performed some experiments with Galileo in 1588–89 on the relationship between pitch and the tension of strings. The family moved to Florence in the early 1570s, where the Galilei family had lived for generations. In his middle teens Galileo attended the monastery school at Vallombrosa, near Florence, and then in 1581 matriculated at the University of Pisa, where he was to study medicine. However, he became enamoured with mathematics and decided to make the mathematical subjects and philosophy his profession, against the protests of his father. Galileo then began to prepare himself to teach Aristotelian philosophy and mathematics, and several of his lectures have survived. In 1585 Galileo left the university without having obtained a degree, and for several years he gave private lessons in the mathematical subjects in Florence and Siena. During this period he designed a new form of hydrostatic balance for weighing small quantities and wrote a short treatise, La bilancetta (“The Little Balance”), that circulated in manuscript form. He also began his studies on motion, which he pursued steadily for the next two decades.

In 1588 Galileo applied for the chair of mathematics at the University of Bologna but was unsuccessful. His reputation was, however, increasing, and later that year he was asked to deliver two lectures to the Florentine Academy, a prestigious literary group, on the arrangement of the world in Dante’s Inferno. He also found some ingenious theorems on centres of gravity (again, circulated in manuscript) that brought him recognition among mathematicians and the patronage of Guidobaldo del Monte (1545–1607), a nobleman and author of several important works on mechanics. As a result, he obtained the chair of mathematics at the University of Pisa in 1589. There, according to his first biographer, Vincenzo Viviani (1622–1703), Galileo demonstrated, by dropping bodies of different weights from the top of the famous Leaning Tower, that the speed of fall of a heavy object is not proportional to its weight, as Aristotle had claimed. The manuscript tract De motu (On Motion), finished during this period, shows that Galileo was abandoning Aristotelian notions about motion and was instead taking an Archimedean approach to the problem. But his attacks on Aristotle made him unpopular with his colleagues, and in 1592 his contract was not renewed. His patrons, however, secured him the chair of mathematics at the University of Padua, where he taught from 1592 until 1610.

Discoveries

Telescopic Discoveries

Galileo pioneered the use of the telescope for observing the night sky. His discoveries undermined traditional ideas about a perfect and unchanging cosmos with the Earth at its centre.

Galileo used observation and experimentation to interrogate and challenge received wisdom and traditional ideas. For him it wasn’t enough that people in authority had been saying that something was true for centuries, he wanted to test these ideas and compare them to the evidence. At the time this was quite a shocking idea, and was one of the reasons that he got into trouble. He discovered..

1. Craters and mountains on the Moon

The Moon’s surface was not smooth and perfect as received wisdom had claimed but rough, with mountains and craters whose shadows changed with the position of the Sun. Galileo was able to use the length of the shadows to estimate the height of the lunar mountains, showing that they were similar to mountains on Earth. 

2. The phases of Venus

The planet Venus showed changing crescent phases like those of the Moon, but their geometry could only be explained if Venus was moving around the Sun rather than the Earth. This undermined the idea that everything in the heavens revolved around the Earth (although it was consistent with the Tychonic system as well as the Copernican one).

3. Jupiter’s moons

The planet Jupiter was accompanied by four tiny satellites which moved around it. These are now known as the Galilean moons: Io, Ganymede, Europa and Callisto. Again, this showed that not everything in the heavens revolved around the Earth.

4. The stars of the Milky Way 

Galileo saw that the Milky Way was not just a band of misty light, it was made up of thousands of individual stars.

5. The first pendulum clock

If that wasn’t enough, as well as Galileo’s contributions to astronomy, he also designed a major component for the first pendulum clock, Galileo’s escapement. This design, however, went unbuilt until after the construction of the first working pendulum clock by Christiaan Huygens.

Other Discoveries of Galileo Galilei

The Law of Falling Bodies

Earth's Orbit

Mathematical Paradigm of Natural Law.

Death

 suffering fever and heart palpitations, he died on 8 January 1642, aged 77.

Isaac Newton

 (25 December 1642 – 20 March 1726)

 Isaac Newton was an English mathematician, physicist, astronomer, theologian, and author (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time and as a key figure in the scientific revolution. His book Mathematical Principles of Natural Philosophy, first published in 1687, laid the foundations of classical mechanics. Newton also made seminal contributions to optics, and shares credit with Gottfried Wilhelm Leibniz for developing the infinitesimal calculus.

 Sir Isaac Newton began developing his theories on light, calculus and celestial mechanics while on break from Cambridge University. Years of research culminated with the 1687 publication of “Principia,” a landmark work that established the universal laws of motion and gravity. Newton’s second major book, “Optics,” detailed his experiments to determine the properties of light. Also a student of Biblical history and alchemy, the famed scientist served as president of the Royal Society of London and master of England’s Royal Mint until his death in 1727.

Isaac Newton: Early Life and Education

Isaac Newton was born on January 4, 1643, in Woolsthorpe, Lincolnshire, England. The son of a farmer who died three months before he was born, Newton spent most of his early years with his maternal grandmother after his mother remarried. His education was interrupted by a failed attempt to turn him into a farmer, and he attended the King’s School in Grantham before enrolling at the University of Cambridge’s Trinity College in 1661.

Newton studied a classical curriculum at Cambridge, but he became fascinated by the works of modern philosophers such as René Descartes, even devoting a set of notes to his outside readings he titled “Quaestiones Quaedam Philosophicae” (“Certain Philosophical Questions”). When the Great Plague shuttered Cambridge in 1665, Newton returned home and began formulating his theories on calculus, light and color, his farm the setting for the supposed falling apple that inspired his work on gravit

 apple that inspired his work on gravity.

Middle years

Newton's work has been said "to distinctly advance every branch of mathematics then studied." His work on the subject usually referred to as fluxions or calculus, seen in a manuscript of October 1666, is now published among Newton's mathematical papers. The author of the manuscript De analysi per aequationes numero terminorum infinitas, sent by Isaac Barrow to John Collins in June 1669, was identified by Barrow in a letter sent to Collins in August of that year as "[...] of an extraordinary genius and proficiency in these things."

Newton later became involved in a dispute with Leibniz over priority in the development of calculus (the Leibniz–Newton calculus controversy). Most modern historians believe that Newton and Leibniz developed calculus independently, although with very different mathematical notations. Occasionally it has been suggested that Newton published almost nothing about it until 1693, and did not give a full account until 1704, while Leibniz began publishing a full account of his methods in 1684. Leibniz's notation and "differential Method", nowadays recognised as much more convenient notations, were adopted by continental European mathematicians, and after 1820 or so, also by British mathematicians.^{[citation needed]}

Such a suggestion fails to account for the calculus in Book 1 of Newton's Principia itself and in its forerunner manuscripts, such as De motu corporum in gyrum of 1684; this content has been pointed out by critics of both Newton's time and modern times.

His work extensively uses calculus in geometric form based on limiting values of the ratios of vanishingly small quantities: in the Principia itself, Newton gave demonstration of this under the name of "the method of first and last ratios" and explained why he put his expositions in this form, remarking also that "hereby the same thing is performed as by the method of indivisibles."

Because of this, the Principia has been called "a book dense with the theory and application of the infinitesimal calculus" in modern times and in Newton's time "nearly all of it is of this calculus." His use of methods involving "one or more orders of the infinitesimally small" is present in his De motu corporum in gyrum of 1684 and in his papers on motion "during the two decades preceding 1684".

Newton in 1702 by Godfrey Kneller

Newton had been reluctant to publish his calculus because he feared controversy and criticism. He was close to the Swiss mathematician Nicolas Fatio de Duillier. In 1691, Duillier started to write a new version of Newton's Principia, and corresponded with Leibniz. In 1693, the relationship between Duillier and Newton deteriorated and the book was never completed.^{[citation needed]}

Starting in 1699, other members^[who?] of the Royal Society accused Leibniz of plagiarism. The dispute then broke out in full force in 1711 when the Royal Society proclaimed in a study that it was Newton who was the true discoverer and labelled Leibniz a fraud; it was later found that Newton wrote the study's concluding remarks on Leibniz. Thus began the bitter controversy which marred the lives of both Newton and Leibniz until the latter's death in 1716

Newton is generally credited with the generalised binomial theorem, valid for any exponent. He discovered Newton's identities, Newton's method, classified cubic plane curves (polynomials of degree three in two variables), made substantial contributions to the theory of finite differences, and was the first to use fractional indices and to employ coordinate geometry to derive solutions to Diophantine equations. He approximated partial sums of the harmonic series by logarithms (a precursor to Euler's summation formula) and was the first to use power series with confidence and to revert power series. Newton's work on infinite series was inspired by Simon Stevin's decimals.

When Newton received his MA and became a Fellow of the "College of the Holy and Undivided Trinity" in 1667, he made the commitment that "I will either set Theology as the object of my studies and will take holy orders when the time prescribed by these statutes [7 years] arrives, or I will resign from the college." Up until this point he had not thought much about religion and had twice signed his agreement to the thirty-nine articles, the basis of Church of England doctrine.

He was appointed Lucasian Professor of Mathematics in 1669, on Barrow's recommendation. During that time, any Fellow of a college at Cambridge or Oxford was required to take holy orders and become an ordained Anglican priest. However, the terms of the Lucasian professorship required that the holder not be active in the church – presumably,so as to have more time for science. Newton argued that this should exempt him from the ordination requirement, and Charles II, whose permission was needed, accepted this argument. Thus a conflict between Newton's religious views and Anglican orthodoxy was averted

Isaac Newton’s Telescope and Studies on Light

Newton returned to Cambridge in 1667 and was elected a minor fellow. He constructed the first reflecting telescope in 1668, and the following year he received his Master of Arts degree and took over as Cambridge’s Lucasian Professor of Mathematics. Asked to give a demonstration of his telescope to the Royal Society of London in 1671, he was elected to the Royal Society the following year and published his notes on optics for his peers.

Through his experiments with refraction, Newton determined that white light was a composite of all the colors on the spectrum, and he asserted that light was composed of particles instead of waves. His methods drew sharp rebuke from established Society member Robert Hooke, who was unsparing again with Newton’s follow-up paper in 1675. Known for his temperamental defense of his work, Newton engaged in heated correspondence with Hooke before suffering a nervous breakdown and withdrawing from the public eye in 1678. In the following years, he returned to his earlier studies on the forces governing gravity and dabbled in alchemy.

Isaac Newton’s Other Studies

OPTICS
Mechanics and gravitationClassification of cubics

Death of Isaac Newton

Newton was also an ardent student of history and religious doctrines, and his writings on those subjects were compiled into multiple books that were published posthumously. Having never married, Newton spent his later years living with his niece at Cranbury Park near Winchester, England. He died in his sleep on March 31, 1727, and was buried in Westminster Abbey.

A giant even among the brilliant minds that drove the Scientific Revolution, Newton is remembered as a transformative scholar, inventor and writer. He eradicated any doubts about the heliocentric model of the universe by establishing celestial mechanics, his precise methodology giving birth to what is known as the scientific method. Although his theories of space-time and gravity eventually gave way to those of Albert Einstein, his work remains the bedrock on which modern physics was built.

Isaac Newton Quotes

• “If I have seen further it is by standing on the shoulders of Giants.”
• “I can calculate the motion of heavenly bodies but not the madness of people.”
• “What we know is a drop, what we don't know is an ocean.”
• “Gravity explains the motions of the planets, but it cannot explain who sets the planets in motion.”
• “No great discovery was ever made without a bold guess.”

 Issac Newton’s last words

 

 “I don’t know what I may seem to the world. But as to myself I seem to have been only like a boy playing on the seashore and diverting myself now and then in finding a smoother pebble or a prettier shell than the ordinary, whilst the great ocean of truth lay all undiscovered before me.”