Early life of Isaac Newton
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Sir Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, theologian, and author (described in his time as a "natural philosopher"), widely recognised as one of the great ...
, the English mathematician and scientist, author of the '' Principia''. It portrays the years after Newton's birth in 1642, his education, as well as his early scientific contributions, before the writing of his main work, the ''
Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. ...
'', in 1685.


Overview of Newton's Life

Sir Isaac Newton is known for many scientific findings. Some of these discoveries include the laws of motion, the theory of gravity, and basic calculus. Although Newton was predominantly known for his discoveries in mathematics and physics, he also put much effort and study into chemistry, biblical history and optics. One of Newton's most famous writing was the ''Principia'' where he described some of his major findings of time, physics, mathematics and calculus. Although his theories soon became universal, he faced much opposition with some of his early theories. Specifically, his theory of gravity faced criticism from leading scientists such as Christiaan Huygens and Leibniz. After a few years of debate, Newton's concept of gravity became universally accepted as he became the dominant figure in the European continent.


Birth and education

Isaac Newton was born on
Christmas Christmas is an annual festival commemorating Nativity of Jesus, the birth of Jesus, Jesus Christ, observed primarily on December 25 as a religious and cultural celebration among billions of people Observance of Christmas by country, around t ...
Day, 25 December 1642
Old Style Old Style (O.S.) and New Style (N.S.) indicate dating systems before and after a calendar change, respectively. Usually, this is the change from the Julian calendar to the Gregorian calendar as enacted in various European countries between 158 ...
(which was 4 January 1643 on the
Gregorian calendar The Gregorian calendar is the calendar used in most parts of the world. It was introduced in October 1582 by Pope Gregory XIII as a modification of, and replacement for, the Julian calendar. The principal change was to space leap years dif ...
, which is now used)During Newton's lifetime, two calendars were in use in Europe: the
Julian Julian may refer to: People * Julian (emperor) (331–363), Roman emperor from 361 to 363 * Julian (Rome), referring to the Roman gens Julia, with imperial dynasty offshoots * Saint Julian (disambiguation), several Christian saints * Julian (give ...
or '
Old Style Old Style (O.S.) and New Style (N.S.) indicate dating systems before and after a calendar change, respectively. Usually, this is the change from the Julian calendar to the Gregorian calendar as enacted in various European countries between 158 ...
' in Britain and parts of northern Europe (Protestant) and eastern Europe, and the Gregorian or '
New Style Old Style (O.S.) and New Style (N.S.) indicate dating systems before and after a calendar change, respectively. Usually, this is the change from the Julian calendar to the Gregorian calendar as enacted in various European countries between 158 ...
', in use in Roman Catholic Europe and elsewhere. At Newton's birth, Gregorian dates were ten days ahead of Julian's dates: thus Newton was born on Christmas Day, 25 December 1642 by the Julian calendar, but on 4 January 1643 by the Gregorian. By the time he died, the difference between the calendars had increased to eleven days. Moreover, before the adoption of the Gregorian calendar in the UK in 1752, the English new year began (for legal and some other civil purposes) on 25 March ('
Lady Day In the Western liturgical year, Lady Day is the traditional name in some English-speaking countries of the Feast of the Annunciation, which is celebrated on 25 March, and commemorates the visit of the archangel Gabriel to the Virgin Mary, durin ...
', i.e. the feast of the Annunciation: sometimes called 'Annunciation Style') rather than on 1 January (sometimes called 'Circumcision Style'). Unless otherwise noted, the remainder of the dates in this article follow the Julian Calendar.
at
Woolsthorpe Manor Woolsthorpe Manor in Woolsthorpe-by-Colsterworth, near Grantham, Lincolnshire Lincolnshire (abbreviated Lincs.) is a county in the East Midlands of England, with a long coastline on the North Sea to the east. It borders Norfolk to the so ...
in
Woolsthorpe-by-Colsterworth Woolsthorpe-by-Colsterworth (to distinguish it from Woolsthorpe-by-Belvoir in the same county) is a hamlet in the South Kesteven district of Lincolnshire, England. It is best known as the birthplace of Sir Isaac Newton. Woolsthorpe-by-Colsterw ...
, a
hamlet ''The Tragedy of Hamlet, Prince of Denmark'', often shortened to ''Hamlet'' (), is a tragedy written by William Shakespeare sometime between 1599 and 1601. It is Shakespeare's longest play, with 29,551 words. Set in Denmark, the play depicts ...
in the county of
Lincolnshire Lincolnshire (abbreviated Lincs.) is a county in the East Midlands of England, with a long coastline on the North Sea to the east. It borders Norfolk to the south-east, Cambridgeshire to the south, Rutland to the south-west, Leicestershire ...
. (At the time of Newton's birth, England had not adopted the Gregorian calendar and therefore his date of birth was recorded as 25 December, according to the
Julian calendar The Julian calendar, proposed by Roman consul Julius Caesar in 46 BC, was a reform of the Roman calendar. It took effect on , by edict. It was designed with the aid of Greek mathematicians and astronomers such as Sosigenes of Alexandr ...
.) Newton was born three months after the death of his father, a prosperous farmer also named Isaac Newton. His father was described as a "wild and extravagant man". Born prematurely, young Isaac was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside a
quart The quart (symbol: qt) is an English unit of volume equal to a quarter gallon. Three kinds of quarts are currently used: the liquid quart and dry quart of the US customary system and the of the British imperial system. All are roughly equal ...
mug. When Newton was three, his mother remarried and went to live with her new husband, the Reverend Barnabus Smith, leaving her son in the care of his maternal grandmother, Margery Ayscough. The young Isaac disliked his stepfather and held some enmity towards his mother for marrying him, as revealed by this entry in a list of sins committed up to the age of 19: "Threatening my father and mother to burn them and the house over them." Later on his mother returned after her husband died. From age 12 to age 16, Newton resided with William Clarke,
apothecary ''Apothecary'' () is a mostly archaic term for a medical professional who formulates and dispenses '' materia medica'' (medicine) to physicians, surgeons, and patients. The modern chemist (British English) or pharmacist (British and North Ameri ...
, in
Grantham Grantham () is a market and industrial town in the South Kesteven district of Lincolnshire, England, situated on the banks of the River Witham and bounded to the west by the A1 road. It lies some 23 miles (37 km) south of the Lincoln and ...
, where he acquired his interest in chemistry. While living with the Clarke family, Newton was educated at
The King's School, Grantham The King's School is a British grammar school with academy status, in the market town of Grantham, Lincolnshire, England. The school's history can be traced to 1329, and was re-endowed by Richard Foxe in 1528. Located on Brook Street, the sch ...
(where his signature can still be seen upon a library window sill). He spent much of his time on independent pursuits, and did poorly in school. Newton was also captivated with mechanical devices and drawing. Not only did he analyze drawings and machines, he actually constructed them himself. From windmills to clocks, Newton constructed models of many objects that surrounded him in his everyday life. He was removed from school, and by October 1659 he was to be found at Woolsthorpe-by-Colsterworth, where his mother, widowed by now for a second time, attempted to make a farmer of him. He hated farming. Henry Stokes, master at the King's School, persuaded his mother to send him back to school so that he might complete his education. Newton's uncle also had an influence in persuading his mother to send him back to school as he could see the natural ability of Isaac. This he did at the age of eighteen, achieving an admirable final report. Newton lived his childhood during some of the most turbulent times in England as the Civil War began in 1642. Although the effects of the countries issues may not have directly affected Newton, the school and universities in England were certainly impacted. Whether it was for the better or worse was to be determined, but Newton was certainly going to have a unique schooling due to the country's unbalance. Manuscript evidence shows that Newton's earliest known piece writing, a Latin phrasebook, as well as the first letter in his hand which has yet been found, addressed to a ‘Loving friend’, were copied from an unpublished version of a work on Latin pedagogy by William Walker, a schoolmaster and rector whose acquaintance with Newton is documented from 1665. This suggests an early influence of the schoolmaster on the natural philosopher when he was still a schoolboy. In June 1661, he was admitted to
Trinity College, Cambridge Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by Henry VIII, King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge ...
as a
sizar At Trinity College, Dublin and the University of Cambridge, a sizar is an undergraduate who receives some form of assistance such as meals, lower fees or lodging during his or her period of study, in some cases in return for doing a defined jo ...
—a sort of work-study role. At that time, the college's teachings were based on those of
Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...
, whom Newton supplemented with modern philosophers such as Descartes and
astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, natural satellite, moons, comets and galaxy, g ...
s such as
Copernicus Nicolaus Copernicus (; pl, Mikołaj Kopernik; gml, Niklas Koppernigk, german: Nikolaus Kopernikus; 19 February 1473 – 24 May 1543) was a Renaissance polymath, active as a mathematician, astronomer, and Catholic canon, who formulated ...
,
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
, and
Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws o ...
. In 1665, he discovered the generalised
binomial theorem In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial. According to the theorem, it is possible to expand the polynomial into a sum involving terms of the form , where the ...
and began to develop a mathematical theory that later became
infinitesimal calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
. Soon after Newton had obtained his degree in August 1665, the University closed down as a precaution against the
Great Plague of London The Great Plague of London, lasting from 1665 to 1666, was the last major epidemic of the bubonic plague to occur in England. It happened within the centuries-long Second Pandemic, a period of intermittent bubonic plague epidemics that origi ...
. Although he had been undistinguished as a Cambridge student, Newton's private studies at his home in Woolsthorpe over the next two years saw the development of his theories on calculus, optics and the law of gravitation. In 1667 he returned to Cambridge as a fellow of Trinity. Newton had stated that when he had purchased a book on
astrology Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of Celestial o ...
at
Stourbridge fair Stourbridge fair was an annual fair held on Stourbridge Common in Cambridge, England. At its peak it was the largest fair in Europe and was the inspiration for Bunyan's "Vanity Fair". The fair was one of four important medieval fairs held in C ...
, near Cambridge, he was unable, on account of his ignorance of
trigonometry Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. T ...
, to understand a figure of the heavens which was drawn in the book. He, therefore, bought an English edition of Euclid's ''Elements'' which included an index of propositions, and, having turned to two or three which he thought might be helpful, found them so obvious that he dismissed it "as a trifling book", and applied himself to the study of
René Descartes René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ...
' ''Geometry''. It is reported that in his examination for a scholarship at Trinity, to which he was elected on 28 April 1664, he was examined in Euclid by Dr
Isaac Barrow Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for proof of the fundamental theorem ...
, who was disappointed in Newton's lack of knowledge of the subject. Newton was convinced to read the ''Elements'' again with care, and formed a more favourable opinion of Euclid's merit. Newton's study of Descartes' ''Geometry'' seems to have inspired him with a love of the subject, and introduced him to higher mathematics. In a small
commonplace book Commonplace books (or commonplaces) are a way to compile knowledge, usually by writing information into books. They have been kept from antiquity, and were kept particularly during the Renaissance and in the nineteenth century. Such books are simi ...
, dated January 1664, there are several articles on angular sections, and the squaring of curves and "crooked lines that may be squared", several calculations about
musical note In music, a note is the representation of a musical sound. Notes can represent the Pitch (music), pitch and Duration (music), duration of a sound in musical notation. A note can also represent a pitch class. Notes are the building blocks of much ...
s, geometrical propositions from
François Viète François Viète, Seigneur de la Bigotière ( la, Franciscus Vieta; 1540 – 23 February 1603), commonly know by his mononym, Vieta, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to i ...
and Frans van Schooten, annotations out of
John Wallis John Wallis (; la, Wallisius; ) was an English clergyman and mathematician who is given partial credit for the development of infinitesimal calculus. Between 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal ...
's ''Arithmetic of Infinities'', together with observations on
refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
, on the grinding of "spherical optic glasses", on the errors of
lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
es and the method of rectifying them, and on the extraction of all kinds of
root In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the sur ...
s, particularly those "in affected powers". In this same book the following entry made by Newton himself, many years afterward, gives a further account of the nature of his work during the period when he was an undergraduate: That Newton must have begun early to make careful observations of natural phenomena is shown by the following remarks about halos, which appear in his ''Optics'', book ii. part iv. obs. 13: He formulated the three laws of motion: * Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. * The relationship between an object's mass ''m'', its acceleration ''a'', and the applied force ''F'' is ''F'' = ''ma''. Acceleration and force are vectors (as sometimes indicated by their symbols being displayed in slant bold font); in this law, the direction of the force vector is the same as the direction of the acceleration vector. * For every action there is an equal and opposite reaction.


Academic career

In January 1665 Newton took the degree of
Bachelor of Arts Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four years ...
. The persons appointed (in conjunction with the proctors, John Slade of
Catharine Hall, Cambridge St Catharine's College is a constituent college of the University of Cambridge. Founded in 1473 as Katharine Hall, it adopted its current name in 1860. The college is nicknamed "Catz". The college is located in the historic city-centre of Camb ...
, and
Benjamin Pulleyn Benjamin Pulleyn (; died 1690) was the Cambridge tutor of Isaac Newton. Pulleyn served as Regius Professor of Greek from 1674 to 1686. He was known as a "pupil monger", meaning one who increased his income by accepting additional students. Pull ...
of Trinity College, Newton's tutor) to examine the questionists were
John Eachard John Eachard (1636?7 July 1697) was an English divine and satirist, noted for his humorous descriptions of the contemporary clergy. From Yoxford in Suffolk, he was educated at St Catharine's College, Cambridge, of which he became master in 1675 ...
of Catharine Hall and Thomas Gipps of Trinity University. It is a curious accident that we have no information about the respective merits of the candidates for a degree in this year since the "ordo senioritis" of the Bachelors of Arts for the year is omitted in the "Grace Book". It is supposed that it was in 1665 that the method of fluxións (his term for
calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...
) first occurred to Newton's mind. There are several papers in Newton's handwriting bearing dates 1665 and 1666 in which the method is described, in some of which dotted or dashed letters are used to represent fluxions (i.e. derivatives), and in some of which the method is explained without the use of dotted letters. Both in 1665 and 1666 Trinity College was dismissed on account of the
Great Plague of London The Great Plague of London, lasting from 1665 to 1666, was the last major epidemic of the bubonic plague to occur in England. It happened within the centuries-long Second Pandemic, a period of intermittent bubonic plague epidemics that origi ...
. On each occasion it was agreed, as shown by entries in the "Conclusion Book" of the college, dated 7 August 1665, and 22 June 1666, and signed by the master of the college, Dr Pearson, that all fellows and scholars who were dismissed on account of the pestilence be allowed one month's commons. Newton must have left college before August 1665, as his name does not appear in the list of those who received extra commons on that occasion, and he tells us himself in the extract from his commonplace book already quoted that he was "forced from Cambridge by the plague" in the summer of that year. He was elected a fellow of his college on 5 October 1667. There were nine vacancies, one caused by the death of
Abraham Cowley Abraham Cowley (; 161828 July 1667) was an English poet and essayist born in the City of London late in 1618. He was one of the leading English poets of the 17th century, with 14 printings of his ''Works'' published between 1668 and 1721. Early ...
the previous summer, and the nine successful candidates were all of the same academic standings. A few weeks after his election to a
fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...
ship Newton went to Lincolnshire and did not return to Cambridge till the February following. In March 1668 he took his
M.A. A Master of Arts ( la, Magister Artium or ''Artium Magister''; abbreviated MA, M.A., AM, or A.M.) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Tho ...
degree. During the years 1666 to 1669 Newton's studies were very diverse. He bought
prism Prism usually refers to: * Prism (optics), a transparent optical component with flat surfaces that refract light * Prism (geometry), a kind of polyhedron Prism may also refer to: Science and mathematics * Prism (geology), a type of sedimentary ...
s and lenses on two or three occasions, and also
chemical A chemical substance is a form of matter having constant chemical composition and characteristic properties. Some references add that chemical substance cannot be separated into its constituent elements by physical separation methods, i.e., wi ...
s and a
furnace A furnace is a structure in which heat is produced with the help of combustion. Furnace may also refer to: Appliances Buildings * Furnace (central heating): a furnace , or a heater or boiler , used to generate heat for buildings * Boiler, used t ...
, apparently for chemical experiments; but he also employed part of his time on the theory of fluxions and other branches of pure mathematics. He wrote a paper, ''De Analysi per Aequationes Numero Terminorum Infinitas'', which he put, probably in June 1669, into the hands of Isaac Barrow (then
Lucasian Professor of Mathematics The Lucasian Chair of Mathematics () is a mathematics professorship in the University of Cambridge, England; its holder is known as the Lucasian Professor. The post was founded in 1663 by Henry Lucas, who was Cambridge University's Member of Pa ...
), at the same time permitting him to communicate its contents to their common friend
John Collins John Collins may refer to: Arts and entertainment * John Collins (poet) (1742–1808), English orator, singer, and poet * John Churton Collins (1848–1908), English literary critic * John H. Collins (director) (1889–1918), American director an ...
(1624–1683), a mathematician of no mean order. Barrow did so on 31 July 1669, but kept the name of the author a secret, and merely told Collins that he was a friend staying at Cambridge, who had a powerful genius for such matters. In a subsequent letter on 20 August Barrow expressed his pleasure at hearing the favourable opinion which Collins had formed of the paper, and added, "the name of the author is Newton, a fellow of our college, and a young man, who is only in his second year since he took the degree of Master of Arts, and who, with an unparalleled genius (''examine quo est acumen''), has made very great progress in this branch of mathematics". Shortly afterward Barrow resigned his chair and was instrumental in securing Newton's election as his successor. Newton was elected Lucasian professor on 29 October 1670. It was his duty as professor to lecture at least once a week in term time on some portion of
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
,
arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...
,
astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
,
geography Geography (from Greek: , ''geographia''. Combination of Greek words ‘Geo’ (The Earth) and ‘Graphien’ (to describe), literally "earth description") is a field of science devoted to the study of the lands, features, inhabitants, and ...
,
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
,
statics Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with ...
, or some other
mathematical Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
subject, and also for two hours in the week to allow an audience to any student who might come to consult with the professor on any difficulties he had encountered. The subject which Newton chose for his lectures was optics. These lectures did little to expand his reputation, as they were remarkably sparsely attended; frequently leaving Newton to lecture at the walls of the classroom. An account of their content was presented to the
Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
in the spring of 1672. During the year 1684, Edmund Halley visited the home of Newton. While on his visit, Halley noted the remarkable development Newton had conducted regarding the path of object in space such as stars and planets. Newton was convinced to step forward and introduce his findings to the general public which soon became publicized. The publication, "Mathematical Principles of Natural Philosophy" introduced the three laws that Newton became famous for: law of inertia, summation of forces equals mass multiplied by acceleration and every action has an equal and opposite reaction. Prior to Newton, there were several other philosophers who proposed ideas to describe the motion of celestial bodies. Kepler and Galileo Galilei often studied the way objects fell in order to gain an understanding of the motion of the planets. However, it was Newton who had the most success out of them all as he was able to put his theories into laws. These laws as described in the previous paragraph are fundamental to education all around the world. Students learn these concepts in grade school and these laws have application from every aspect of life. Students ranging from grade school to graduate school in college use the three fundamental laws as they have changed the way humans think and act. Newton's development of these laws was one of the most beneficial contributions to society to date. In the year 1688, Newton was elected to the convention parliament at Cambridge University where he remained on board for two years. During his time at Cambridge, he was able to meet several famous people like John Locke and Nicolas Fatio de Duillier. Newton was able to form life-long bonds with these two figures in the matter of two years. Christiaan Huygens also came into the picture as Newton and him had disagreements in the past about gravity. The two figures had several extended arguments about their debate and were able to reach accord. Soon after, Newton entered a period of life where writing became his priority. He began by editing his book, ''Principia''. Despite the adjustments he made, the new version of ''Principia'' was abandoned by the year 1693 due to Newton's mental state. He decaled himself as having a mental breakdown which eradicated the adjustments he made to his famous writing. Newton had a different novel that he worked on during the same time period called ''Praxis.'' This text consists of five drafts of literature written by Newton having to do with chemistry. During this period, Newton studied several areas of work including religion, calculus and chemistry. According to
Alfred Rupert Hall Alfred Rupert Hall (1920–2009) was a prominent British historian of science, known as editor of a collection of Isaac Newton's unpublished scientific papers (1962), and Newton's correspondence, in 1977. Life Hall was born near Stoke-on-Trent ...
the first practical reflecting telescope was built by Newton in 1668.''Isaac Newton: adventurer in thought'', by Alfred Rupert Hall, 1996, page 67. Later on such prototype for a design came to be called a
Newtonian telescope The Newtonian telescope, also called the Newtonian reflector or just a Newtonian, is a type of reflecting telescope invented by the English scientist Sir Isaac Newton, using a concave primary mirror and a flat diagonal secondary mirror. Newton' ...
or
Newton's reflector The first reflecting telescope built by Sir Isaac Newton in 1668 is a landmark in the History of the telescope, history of telescopes, being the first known successful reflecting telescope. It was the prototype for a design that later came to be ...
. On 21 December 1671 he was proposed as a candidate for admission to the Royal Society by Dr Seth Ward,
bishop of Salisbury The Bishop of Salisbury is the ordinary of the Church of England's Diocese of Salisbury in the Province of Canterbury. The diocese covers much of the counties of Wiltshire and Dorset. The see is in the City of Salisbury where the bishop's seat ...
, and on 11 January 1672, he was elected a fellow of the Society. At the meeting at which Newton was elected, he read a description of a
reflecting telescope A reflecting telescope (also called a reflector) is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternati ...
which he had invented, and "it was ordered that a letter should be written by the secretary to Mr. Newton to acquaint him of his election into the Society, and to thank him for the communication of his
telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observe ...
, and to assure him that the Society would take care that all right should be done him concerning this invention." In his reply to the secretary on 18 January 1672, Newton writes: "I desire that in your next letter you would inform me for what time the society continue their weekly meetings; because, if they continue them for any time, I am purposing them to be considered of and examined an account of a philosophical discovery, which induced me to the making of the said telescope, and which I doubt not but will prove much more grateful than the communication of that instrument being in my judgment the oddest if not the most considerable detection which hath hitherto been made into the operations of nature." This promise was fulfilled in communication which Newton addressed to
Henry Oldenburg Henry Oldenburg (also Henry Oldenbourg) FRS (c. 1618 as Heinrich Oldenburg – 5 September 1677), was a German theologian, diplomat, and natural philosopher, known as one of the creators of modern scientific peer review. He was one of the for ...
, the secretary of the Royal Society, on 6 February 1672, and which was read before the society two days afterward. The whole is printed in No. 80 of the ''
Philosophical Transactions ''Philosophical Transactions of the Royal Society'' is a scientific journal published by the Royal Society. In its earliest days, it was a private venture of the Royal Society's secretary. It was established in 1665, making it the first journa ...
.'' Newton's "philosophical discovery" was the realisation that white light is composed of a
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
of colours. He realised that objects are coloured only because they absorb some of these colours more than others. After he explained this to the Society, he proceeded: "When I understood this, I left off my aforesaid glassworks; for I saw, that the perfection of telescopes was hitherto limited, not so much for want of glasses truly figured according to the prescriptions of Optics Authors (which all men have hitherto imagined), as because that light itself is a heterogeneous mixture of differently refrangible rays. So that was a glass so exactly figured as to collect any one sort of rays into one point, it could not collect those also into the same point, which has the same incidence upon the same medium are apt to suffer a different
refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomeno ...
. Nay, I wondered, that seeing the difference of refrangibility was so great, as I found it, telescopes should arrive at that perfection they are now at." This "difference in refrangibility" is now known as
dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...
. He then points out why "the object-glass of any telescope cannot collect all the rays which come from one point of an object, to make them convene at its focus in less room than in a circular space, whose diameter is the 50th part of the diameter of its aperture: which is an irregularity some hundreds of times greater, than a circularly figured lens, of so small a section as the object-glasses of long telescopes are, would cause by the unfitness of its figure, were light uniform." He adds: "This made me take
reflection Reflection or reflexion may refer to: Science and technology * Reflection (physics), a common wave phenomenon ** Specular reflection, reflection from a smooth surface *** Mirror image, a reflection in a mirror or in water ** Signal reflection, in s ...
s into consideration, and finding them regular so that the Angle of Reflection of all sorts of Rays was equal to their Angle of Incidence; I understood, that by their mediation optic instruments might be brought to any degree of perfection imaginable, provided a reflecting substance could be found, which would polish as finely as glass, and reflect as much light, as glass transmits, and the art of communicating to it a parabolic figure be also attained. But these seemed very great difficulties, and I have almost thought them insuperable, when I further considered, that every irregularity in a reflecting superficies makes the rays stray 5 or 6 times more out of their due course, than the like irregularities in a refracting one; so that a much greater curiosity would be here requisite, than in figuring glasses for refraction. "Amidst these thoughts, I was forced from Cambridge by the intervening Plague, and it was more than two years before I proceeded further. But then having thought on a tender way of polishing, proper for metal, whereby, as I imagined, the figure also would be corrected to the last; I began to try, what might be affected in this kind, and by degrees so far perfected an instrument (in the essential parts of it like that I sent to London), by which I could discern
Jupiter Jupiter is the fifth planet from the Sun and the List of Solar System objects by size, largest in the Solar System. It is a gas giant with a mass more than two and a half times that of all the other planets in the Solar System combined, but ...
's 4
Concomitant Concomitance is the condition of accompanying or coexisting. A concomitant is something that accompanies something else. Concomitant or concomitance may refer to: * Concomitance (doctrine), a Christian doctrine * Concomitant (classical algebraic ...
s, and showed them diverse times to two others of my acquaintance. I could also discern the
Moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
-like phase of
Venus Venus is the second planet from the Sun. It is sometimes called Earth's "sister" or "twin" planet as it is almost as large and has a similar composition. As an interior planet to Earth, Venus (like Mercury) appears in Earth's sky never fa ...
, but not very distinctly, nor without some niceness in disposing of the instrument. "From that time I was interrupted until this last autumn when I made the other. And as that was sensibly better than the first (especially for day-objects), so I doubt not, but they will be still brought to much greater perfection by their endeavours, who, as you inform me, are taking care of it at London."


Newton's theory of colour

After a remark that
microscope A microscope () is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science of investigating small objects and structures using a microscope. Microscopic means being invisibl ...
s seem as capable of improvement as telescopes, he adds: Further on, after some remarks on the subject of compound colours, he says: He concludes his communication with the words:


Controversies

The publication of these discoveries led to a series of controversies which lasted for several years, in which Newton had to contend with the eminent English physicist
Robert Hooke Robert Hooke FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using a compound microscope that ...
, Anthony Lucas (mathematical professor at the
University of Liège The University of Liège (french: Université de Liège), or ULiège, is a major public university of the French Community of Belgium based in Liège, Wallonia, Belgium. Its official language is French. As of 2020, ULiège is ranked in the 301 ...
), Franciscus Linus (a physician in
Liège Liège ( , , ; wa, Lîdje ; nl, Luik ; german: Lüttich ) is a major city and municipality of Wallonia and the capital of the Belgian province of Liège. The city is situated in the valley of the Meuse, in the east of Belgium, not far from b ...
), and many others. Some of his opponents denied the truth of his experiments, refusing to believe in the existence of the spectrum. Others criticised the experiments, saying that the length of the spectrum was never more than three and a half times the breadth, whereas Newton found it to be five times the breadth. It appears that Newton made the mistake of supposing that all prisms would give a spectrum of the same length; the objections of his opponents led him to measure carefully the lengths of spectra formed by prisms of different angles and different
refractive indices In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
, but he was not led thereby to the discovery of the different dispersive powers of different refractive substances. Newton carried on the discussion with the objectors with great courtesy and patience, but the pain which these long discussions gave to his sensitive mind may be estimated from his letter of 18 November 1676 to
Oldenburg Oldenburg may also refer to: Places *Mount Oldenburg, Ellsworth Land, Antarctica *Oldenburg (city), an independent city in Lower Saxony, Germany **Oldenburg (district), a district historically in Oldenburg Free State and now in Lower Saxony *Olde ...
: "I promised to send you an answer to Mr. Lucas this next Tuesday, but I find I shall scarce finish what I have designed, to get a copy taken of it by that time, and therefore I beg your patience a week longer. I see I have made myself a slave to philosophy, but if I get free of Mr. Lucas's business, I will resolutely bid adieu to it eternally, excepting what I do for my private satisfaction, or leave to come out after me; for I see a man must either resolve to put out nothing new or to become a slave to defend it." It was fortunate that these disputes did not damp Newton's ardour as much as he feared. He later published many papers in the Philosophical Transactions on various aspects of optics, and, although some of his views are erroneous, and are now almost universally rejected, his investigations led to discoveries which are of permanent value. He succeeded in explaining the colour of thin and of thick plates (
diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
), and the inflexion of light, and he wrote on double refraction,
light polarisation Polarization (also polarisation) is a property applying to transverse waves that specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the ...
and
binocular vision In biology, binocular vision is a type of vision in which an animal has two eyes capable of facing the same direction to perceive a single three-dimensional image of its surroundings. Binocular vision does not typically refer to vision where an ...
. He also invented a reflecting quadrant for observing the angles between the
moon The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
and the fixed stars— the same in every essential as the historically important navigational instrument more commonly known as
Hadley's quadrant The octant, also called a reflecting quadrant, is a reflecting instrument used in navigation. Etymology The name ''octant'' derives from the Latin ''octans'' meaning ''eighth part of a circle'', because the instrument's arc is one eighth of a ...
. This discovery was communicated by him to
Edmund Halley Edmond (or Edmund) Halley (; – ) was an English astronomer, mathematician and physicist. He was the second Astronomer Royal in Britain, succeeding John Flamsteed in 1720. From an observatory he constructed on Saint Helena in 1676–77, Ha ...
in 1700 but was not published, or communicated to the Royal Society, until after Newton's death, when a description of it was found among his papers.


Conflict over oratorship elections

In March 1673 Newton took a prominent part in a dispute in the university. The public oratorship fell vacant, and a contest arose between the heads of the colleges and the members of the
Senate A senate is a deliberative assembly, often the upper house or chamber of a bicameral legislature. The name comes from the ancient Roman Senate (Latin: ''Senatus''), so-called as an assembly of the senior (Latin: ''senex'' meaning "the el ...
as to the mode of electing to the office. The heads claimed the right of nominating two persons, one of whom was to be elected by the senate. The senate insisted that the proper mode was by an open election.
George Villiers, 2nd Duke of Buckingham George Villiers, 2nd Duke of Buckingham, 20th Baron de Ros, (30 January 1628 – 16 April 1687) was an English statesman and poet. Life Early life George was the son of George Villiers, 1st Duke of Buckingham, favourite of James I ...
, who was the chancellor of the university, endeavoured to effect a compromise which, he says, "I hope may for the present satisfy both sides. I propose that the heads may for this time nominate and the body comply, yet interposing (if they think fit) a protestation concerning their plea that this election may not hereafter pass for a decisive precedent in prejudice of their claim", and, "whereas I understand that the whole university has chiefly consideration for Dr
Henry Paman Henry Paman (1626–1695) was an English physician. Life Son of Robert Paman, he was born at his father's estate of Chevington, Suffolk. He entered as a sizar at Emmanuel College, Cambridge, on 22 June 1643, where William Sancroft was his tutor ...
of St John's College and Mr. Craven of Trinity College, I do recommend them both to be nominated." The heads, however, nominated Drs Paman and Ralph Sanderson (of St John's); the next day 121 members of the senate recorded their votes for Craven and ninety-eight for Paman. On the morning of the election, a protest in which Newton's name appeared was read and entered in the Regent House. But the vice-chancellor admitted Paman the same morning, and so ended the first contest of a non-scientific character in which Newton took part.


Newton's poverty

On 8 March 1673 Newton wrote to Oldenburg, the secretary of the Royal Society:
"Sir, I desire that you will procure that I may be put out from being any longer Fellow of the Royal Society: for though I honour that body, yet since I see I shall neither profit them nor (because of this distance) can partake of the advantage of their assemblies, I desire to withdraw."
Oldenburg replied to this with an offer to apply to the Society to excuse Newton the weekly payments, as in a letter of Newton's to Oldenburg, dated 23 June 1673, he says, "For your proffer about my quarterly payments, I thank you, but I would not have you trouble yourself to get them excused if you have not done it already." Nothing further seems to have been done in the matter until 28 January 1675, when Oldenburg informed the Society that "Mr. Newton is now in such circumstances that he desires to be excused from the weekly payments." Upon this "it was agreed to by the council that he be dispensed with, as several others are." On 18 February 1675 Newton was formally accepted into the Society. The most probable reason why Newton wished to be excused from these payments is that, as he was not in holy orders, his fellowship at Trinity College would lapse in autumn 1675, with a consequent reduction in his income. But he received a patent from the Crown in April 1675, allowing him as Lucasian professor to retain his fellowship without being required to take holy orders. This must have relieved Newton's financial worries since in November 1676 he donated £40 towards the building of the new library of Trinity College.


Universal law of gravitation

It is supposed that it was at Woolsthorpe in the summer of 1666 that Newton's thoughts were directed to the subject of gravity. They are said to have been inspired by Newton's seeing an apple fall from a tree on his mother's farm, a version for which there is reasonable historical evidence. In one version of the story, the apple is supposed to have fallen on Newton's head; this version appears to have been invented by
Isaac D'Israeli Isaac D'Israeli (11 May 1766 – 19 January 1848) was a British writer, scholar and the father of British Prime Minister Benjamin Disraeli. He is best known for his essays and his associations with other men of letters. Life and career Isaac wa ...
.
Voltaire François-Marie Arouet (; 21 November 169430 May 1778) was a French Age of Enlightenment, Enlightenment writer, historian, and philosopher. Known by his ''Pen name, nom de plume'' M. de Voltaire (; also ; ), he was famous for his wit, and his ...
is the authority for the former version of the story. He had his information from Newton's favourite niece
Catherine Barton Catherine Barton (1679–1739) was an English homemaker who oversaw the running of her uncle, scientist Isaac Newton's, household. She was reputed to be the source of the Isaac_Newton#Apple_incident, story of the apple inspiring Newton's work on gr ...
, who married
John Conduitt John Conduitt (; c. 8 March 1688 – 23 May 1737), of Cranbury Park, Hampshire, was a British landowner and Whig politician. He sat in the House of Commons from 1721 to 1737. He was married to the half-niece of Sir Isaac Newton, whom Conduitt s ...
, a fellow of the Royal Society, and one of Newton's intimate friends. How much truth there is in what is a plausible and a favourite story can never be known, but it is certain that tradition marked a tree as that from which the apple fell, until 1866, when, owing to decay, the tree was cut down and its wood carefully preserved.
Johannes Kepler Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
had proved by an elaborate series of measurements that * each
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
revolves in an
elliptical Elliptical may mean: * having the shape of an ellipse, or more broadly, any oval shape ** in botany, having an elliptic leaf shape ** of aircraft wings, having an elliptical planform * characterised by ellipsis (the omission of words), or by conc ...
orbit around the Sun, whose centre occupies one of the
foci Focus, or its plural form foci may refer to: Arts * Focus or Focus Festival, former name of the Adelaide Fringe arts festival in South Australia Film *''Focus'', a 1962 TV film starring James Whitmore * ''Focus'' (2001 film), a 2001 film based ...
of the ellipse, * that the radius vector of each planet drawn from the Sun sweeps out equal areas in equal times, * and that the squares of the periodic times of the planets are in the same proportion as the cubes of their mean distances from the Sun. The fact that heavy bodies have always a tendency to fall to the Earth, no matter at what height they are placed above the Earth's surface, seems to have led Newton to conjecture that the same tendency to fall to the Earth might have been the cause by which the Moon was retained in its orbit around the Earth. Newton, by calculating from
Kepler's laws In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits ...
, and supposing the orbits of the planets to be circles with the sun at the centre, had already proved that the force of the Sun acting upon the different planets must vary as the inverse square of the distances of the planets from the Sun. He was therefore led to inquire whether if the Earth's attraction extended to the Moon, the force at that distance would be of the exact magnitude necessary to retain the Moon in its orbit. He found that the Moon by its motion in its orbit was deflected from the tangent in every minute through a space of 13 feet (3.96 m). But by observing the distance through which a body would fall in one second at the Earth's surface, and by calculating from that on the supposition of the force diminishing in the ratio of the inverse square of the distance, he found that the Earth's attraction at the distance of the moon would draw a body through 15 ft. (4.57 metres) in one minute. Newton regarded the discrepancy between the results as proof of the inaccuracy of his conjecture, and "laid aside at that time any further thoughts of this matter". (See
Newton's cannonball Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his posthumously published 1728 work ''De mundi systemate'' (also ...
.) In November 1679,
Robert Hooke Robert Hooke FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using a compound microscope that ...
(after his appointment to manage the Royal Society's correspondence) began an exchange of letters with Newton: he wished to hear from members about their researches, or their views about the researches of others. The correspondence later led to controversy. Hooke and Newton disagreed about the form of the path of a body falling from a height, taking the motion of the Earth around its axis into consideration. Newton later acknowledged that the exchanges of 1679-80 had reawakened his dormant interest in astronomy.H W Turnbull (ed.) (1960), cited above, at pp.435-440. This led Newton to revert to his former conjectures on the Moon. The estimate Newton had used for the radius of the Earth, which had been accepted by geographers and navigators, was based on the very rough estimate that the
length of a degree of latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
of the Earth's surface measured along a meridian was 60 nautical miles. At a meeting of the Royal Society on 11 January 1672, Oldenburg, the secretary, read a letter from Paris describing the procedure followed by
Jean Picard Jean Picard (21 July 1620 – 12 July 1682) was a French astronomer and priest born in La Flèche, where he studied at the Jesuit Collège Royal Henry-Le-Grand. He is principally notable for his accurate measure of the size of the Earth, base ...
in measuring a degree, and specifically stating the precise length that he calculated it to be. It is probable that Newton had become acquainted with this measurement of Picard's, and that he was therefore led to make use of it when his thoughts were redirected to the subject. This estimate of the Earth's magnitude, giving 691 miles (1112  km) to 10°, made the two results, the discrepancy between which Newton had regarded as a disproof of his conjecture, to agree so exactly that he now regarded his conjecture as fully established. In January 1684, Sir
Christopher Wren Sir Christopher Wren PRS FRS (; – ) was one of the most highly acclaimed English architects in history, as well as an anatomist, astronomer, geometer, and mathematician-physicist. He was accorded responsibility for rebuilding 52 churches ...
, Halley and Hooke were led to discuss the law of gravity, and although they probably all agreed on the truth of the inverse square law, yet this truth was not looked upon as established. It appears that Hooke professed to have a solution of the problem of the path of a body moving around a centre of force attracting as the inverse square of the distance, but Halley declared after a delay of some months that Hooke "had not been so good as his word" in showing his solution to Wren and started for Cambridge, in August 1684, to consult Newton on the subject. Without mentioning the speculations which had been made, he asked Newton what would be the curve described by a planet around the Sun on the assumption that the Sun's force diminished as the square of the distance. Newton replied promptly, "an ellipse", and on being questioned by Halley as to the reason for his answer he replied, "Why, I have calculated it." He could not, however, put his hand upon his calculation, but he promised to send it to Halley. After the latter had left Cambridge, Newton set to work to reproduce the calculation. After making a mistake and producing a different result he corrected his work and obtained his former result. Next November, Newton redeemed his promise to Halley by sending him, by the hand of Mr. Paget, a fellow of Trinity College and mathematical master of
Christ's Hospital Christ's Hospital is a public school (English independent boarding school for pupils aged 11–18) with a royal charter located to the south of Horsham in West Sussex. The school was founded in 1552 and received its first royal charter in 1553 ...
, a copy of his demonstration; and very soon afterward Halley again visited Cambridge to confer with Newton about the problem. On his return to London on 10 December 1684, he informed the Royal Society "that he had lately seen Mr. Newton at Cambridge, who had shown him a curious treatise ''De Motu''", which at Halley's desire he promised to send to the Society to be entered upon their register. "Mr. Halley was desired to put Mr. Newton in mind of his promise for the securing this invention to himself, till he could be at leisure to publish it", and Paget was desired to join with Halley in urging Newton to do so. By the middle of February Newton had sent his paper to Aston, one of the secretaries of the Society, and in a letter to Aston dated 23 February 1685, Newton thanked him for "having entered on the register his notions about motion". This treatise ''De Motu'' was the starting point of the ''Principia'', and was meant to be a short account of what that work was intended to embrace. It occupies twenty-four
octavo Octavo, a Latin word meaning "in eighth" or "for the eighth time", (abbreviated 8vo, 8º, or In-8) is a technical term describing the format of a book, which refers to the size of leaves produced from folding a full sheet of paper on which multip ...
pages, and consists of four
theorem In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of th ...
s and seven problems, some of which are identical with some of the most important propositions of the second and third sections of the first book of the '' Principia''.


See also

*
Ismaël Bullialdus Ismaël Boulliau (; Latin: Ismaël Bullialdus; 28 September 1605 – 25 November 1694) was a 17th-century French astronomer and mathematician who was also interested in history, theology, classical studies, and philology. He was an active m ...
*
De Motu (Berkeley's essay) ''De Motu: Sive, de Motus Principio & Natura, et de Causa Communicationis Motuum'' (''On Motion: or The Principle and Nature of Motion and the Cause of the Communication of Motions''), or simply ''De Motu'', is an essay written by George Berkeley ...
* ''
Elements of the Philosophy of Newton ''Elements of the Philosophy of Newton'' (french: Éléments de la philosophie de Newton) is a book written by the philosopher Voltaire and co-authored by mathematician and physicist Emilie du Chatelet, Émilie du Châtelet in 1738 that helped t ...
'' *
Gauss–Newton algorithm The Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a non-linear function. Since a sum ...
*
History of calculus Calculus, originally called infinitesimal calculus, is a mathematical discipline focused on limits, continuity, derivatives, integrals, and infinite series. Many elements of calculus appeared in ancient Greece, then in China and the Middle East, a ...
*
List of independent discoveries Historians and sociologists have remarked upon the occurrence, in science, of "multiple independent discovery". Robert K. Merton defined such "multiples" as instances in which similar discoveries are made by scientists working independently of eac ...
*
Newton's cannonball Newton's cannonball was a thought experiment Isaac Newton used to hypothesize that the force of gravity was universal, and it was the key force for planetary motion. It appeared in his posthumously published 1728 work ''De mundi systemate'' (also ...
*
Newton disc The Newton disc, also known as the Disappearing Colour Disc, is a well-known physics experiment with a rotating disc with segments in different colors (usually Newton's primary colors: red, orange, yellow, green, blue, indigo, and violet or ROYGBI ...
*
Newton fractal The Newton fractal is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial or transcendental function. It is the Julia set of the meromorphic function which is given by Newton's method. ...
*
Newton's inequalities In mathematics, the Newton inequalities are named after Isaac Newton. Suppose ''a''1, ''a''2, ..., ''a'n'' are real numbers and let e_k denote the ''k''th elementary symmetric polynomial in ''a''1, ''a''2, ..., ''a' ...
*
Newton's laws of motion Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in moti ...
*
Newton's notation In differential calculus, there is no single uniform notation for differentiation. Instead, various notations for the derivative of a function or variable have been proposed by various mathematicians. The usefulness of each notation varies with t ...
*
Newton polygon In mathematics, the Newton polygon is a tool for understanding the behaviour of polynomials over local fields, or more generally, over ultrametric fields. In the original case, the local field of interest was ''essentially'' the field of formal Lau ...
*
Newton polynomial In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is an polynomial interpolation, interpolation polynomial for a given set of data points. The Newton polynomial is sometimes called Newton's ...
* Newton's religious views *
Newton series A finite difference is a mathematical expression of the form . If a finite difference is divided by , one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the ...
*
Newton's theorem of revolving orbits In classical mechanics, Newton's theorem of revolving orbits identifies the type of central force needed to multiply the angular speed of a particle by a factor ''k'' without affecting its radial motion (Figures 1 and 2). Newton applied his ...
*
Newton (unit) The newton (symbol: N) is the unit of force in the International System of Units (SI). It is defined as 1 kg⋅m/s, the force which gives a mass of 1 kilogram an acceleration of 1 metre per second per second. It is named after Isaac Newton in ...
*
Newton–Cotes formulas In numerical analysis, the Newton–Cotes formulas, also called the Newton–Cotes quadrature rules or simply Newton–Cotes rules, are a group of formulas for numerical integration (also called ''quadrature'') based on evaluating the integrand at ...
*
Newton–Euler equations In classical mechanics, the Newton–Euler equations describe the combined translational and rotational dynamics of a rigid body. Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rig ...
*
Newtonianism Newtonianism is a philosophical and scientific doctrine inspired by the beliefs and methods of natural philosopher Isaac Newton. While Newton's influential contributions were primarily in physics and mathematics, his broad conception of the unive ...
*
Scientific Revolution The Scientific Revolution was a series of events that marked the emergence of modern science during the early modern period, when developments in mathematics, physics, astronomy, biology (including human anatomy) and chemistry transfo ...
*
Writing of Principia Mathematica Isaac Newton composed ''Principia Mathematica'' during 1685 and 1686, and it was published in a first edition on 5 July 1687. Widely regarded as one of the most important works in both the science of physics and in applied mathematics during th ...


Notes


References

* *Hazen, Rober M. (2021). ''Sir Isaac Newton: Early life, Education and Work.'' The Great Courses Daily. {{Isaac Newton Isaac Newton Newton, Sir Isaac