The public domain consists of all the creative works to which no exclusive intellectual property rights apply. Those rights may have been forfeited, expressly waived, or may be inapplicable; the works of William Shakespeare and Beethoven, most early silent films, are in the public domain either by virtue of their having been created before copyright existed, or by their copyright term having expired. Some works are not covered by copyright, are therefore in the public domain—among them the formulae of Newtonian physics, cooking recipes, all computer software created prior to 1974. Other works are dedicated by their authors to the public domain; the term public domain is not applied to situations where the creator of a work retains residual rights, in which case use of the work is referred to as "under license" or "with permission". As rights vary by country and jurisdiction, a work may be subject to rights in one country and be in the public domain in another; some rights depend on registrations on a country-by-country basis, the absence of registration in a particular country, if required, gives rise to public-domain status for a work in that country.
The term public domain may be interchangeably used with other imprecise or undefined terms such as the "public sphere" or "commons", including concepts such as the "commons of the mind", the "intellectual commons", the "information commons". Although the term "domain" did not come into use until the mid-18th century, the concept "can be traced back to the ancient Roman Law, as a preset system included in the property right system." The Romans had a large proprietary rights system where they defined "many things that cannot be owned" as res nullius, res communes, res publicae and res universitatis. The term res nullius was defined as things not yet appropriated; the term res communes was defined as "things that could be enjoyed by mankind, such as air and ocean." The term res publicae referred to things that were shared by all citizens, the term res universitatis meant things that were owned by the municipalities of Rome. When looking at it from a historical perspective, one could say the construction of the idea of "public domain" sprouted from the concepts of res communes, res publicae, res universitatis in early Roman law.
When the first early copyright law was first established in Britain with the Statute of Anne in 1710, public domain did not appear. However, similar concepts were developed by French jurists in the 18th century. Instead of "public domain", they used terms such as publici juris or propriété publique to describe works that were not covered by copyright law; the phrase "fall in the public domain" can be traced to mid-19th century France to describe the end of copyright term. The French poet Alfred de Vigny equated the expiration of copyright with a work falling "into the sink hole of public domain" and if the public domain receives any attention from intellectual property lawyers it is still treated as little more than that, left when intellectual property rights, such as copyright and trademarks, expire or are abandoned. In this historical context Paul Torremans describes copyright as a, "little coral reef of private right jutting up from the ocean of the public domain." Copyright law differs by country, the American legal scholar Pamela Samuelson has described the public domain as being "different sizes at different times in different countries".
Definitions of the boundaries of the public domain in relation to copyright, or intellectual property more regard the public domain as a negative space. According to James Boyle this definition underlines common usage of the term public domain and equates the public domain to public property and works in copyright to private property. However, the usage of the term public domain can be more granular, including for example uses of works in copyright permitted by copyright exceptions; such a definition regards work in copyright as private property subject to fair-use rights and limitation on ownership. A conceptual definition comes from Lange, who focused on what the public domain should be: "it should be a place of sanctuary for individual creative expression, a sanctuary conferring affirmative protection against the forces of private appropriation that threatened such expression". Patterson and Lindberg described the public domain not as a "territory", but rather as a concept: "here are certain materials – the air we breathe, rain, life, thoughts, ideas, numbers – not subject to private ownership.
The materials that compose our cultural heritage must be free for all living to use no less than matter necessary for biological survival." The term public domain may be interchangeably used with other imprecise or undefined terms such as the "public sphere" or "commons", including concepts such as the "commons of the mind", the "intellectual commons", the "information commons". A public-domain book is a book with no copyright, a book, created without a license, or a book where its copyrights expired or have been forfeited. In most countries the term of protection of copyright lasts until January first, 70 years after the death of the latest living author; the longest copyright term is in Mexico, which has life plus 100 years for all deaths since July 1928. A notable exception is the United States, where every book and tale published prior to 1924 is in the public domain.
Geometry is a branch of mathematics concerned with questions of shape, relative position of figures, the properties of space. A mathematician who works in the field of geometry is called a geometer. Geometry arose independently in a number of early cultures as a practical way for dealing with lengths and volumes. Geometry began to see elements of formal mathematical science emerging in the West as early as the 6th century BC. By the 3rd century BC, geometry was put into an axiomatic form by Euclid, whose treatment, Euclid's Elements, set a standard for many centuries to follow. Geometry arose independently in India, with texts providing rules for geometric constructions appearing as early as the 3rd century BC. Islamic scientists expanded on them during the Middle Ages. By the early 17th century, geometry had been put on a solid analytic footing by mathematicians such as René Descartes and Pierre de Fermat. Since and into modern times, geometry has expanded into non-Euclidean geometry and manifolds, describing spaces that lie beyond the normal range of human experience.
While geometry has evolved throughout the years, there are some general concepts that are more or less fundamental to geometry. These include the concepts of points, planes, surfaces and curves, as well as the more advanced notions of manifolds and topology or metric. Geometry has applications to many fields, including art, physics, as well as to other branches of mathematics. Contemporary geometry has many subfields: Euclidean geometry is geometry in its classical sense; the mandatory educational curriculum of the majority of nations includes the study of points, planes, triangles, similarity, solid figures and analytic geometry. Euclidean geometry has applications in computer science and various branches of modern mathematics. Differential geometry uses techniques of linear algebra to study problems in geometry, it has applications in physics, including in general relativity. Topology is the field concerned with the properties of geometric objects that are unchanged by continuous mappings. In practice, this means dealing with large-scale properties of spaces, such as connectedness and compactness.
Convex geometry investigates convex shapes in the Euclidean space and its more abstract analogues using techniques of real analysis. It has close connections to convex analysis and functional analysis and important applications in number theory. Algebraic geometry studies geometry through the use of multivariate polynomials and other algebraic techniques, it has applications including cryptography and string theory. Discrete geometry is concerned with questions of relative position of simple geometric objects, such as points and circles, it shares many principles with combinatorics. Computational geometry deals with algorithms and their implementations for manipulating geometrical objects. Although being a young area of geometry, it has many applications in computer vision, image processing, computer-aided design, medical imaging, etc; the earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles and volumes, which were developed to meet some practical need in surveying, construction and various crafts.
The earliest known texts on geometry are the Egyptian Rhind Papyrus and Moscow Papyrus, the Babylonian clay tablets such as Plimpton 322. For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, or frustum. Clay tablets demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiter's position and motion within time-velocity space; these geometric procedures anticipated the Oxford Calculators, including the mean speed theorem, by 14 centuries. South of Egypt the ancient Nubians established a system of geometry including early versions of sun clocks. In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. Pythagoras established the Pythagorean School, credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history.
Eudoxus developed the method of exhaustion, which allowed the calculation of areas and volumes of curvilinear figures, as well as a theory of ratios that avoided the problem of incommensurable magnitudes, which enabled subsequent geometers to make significant advances. Around 300 BC, geometry was revolutionized by Euclid, whose Elements considered the most successful and influential textbook of all time, introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom and proof. Although most of the contents of the Elements were known, Euclid arranged them into a single, coherent logical framework; the Elements was known to all educated people in the West until the middle of the 20th century and its contents are still taught in geometry classes today. Archimedes of Syracuse used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, gave remarkably accurate approximations of Pi.
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Robert Chambers (publisher, born 1802)
Robert Chambers was a Scottish publisher, evolutionary thinker and journal editor who, like his elder brother and business partner William Chambers, was influential in mid-19th century scientific and political circles. Chambers was an early phrenologist and was the anonymous author of Vestiges of the Natural History of Creation, so controversial that his authorship was not acknowledged until after his death. Chambers was born in Peebles in the Scottish borders 10 July 1802 to Jean Gibson and James Chambers, a cotton manufacturer, he was their second son of six children. The town had changed little in centuries; the town had new parts, each consisting of little more than a single street. Peebles was inhabited by weavers and labourers living in thatched cottages, his father, James Chambers, made his living as a cotton manufacturer. Their slate-roofed house was built by James Chambers' father as a wedding gift for his son, the ground floor served as the family workshop. A small circulating library in the town, run by Alexander Elder, introduced Robert to books and developed his literary interests when he was young.
His father would buy books for the family library, one day Robert found a complete set of the fourth edition of the Encyclopædia Britannica hidden away in a chest in the attic. He eagerly read this for many years. Near the end of his life, Chambers remembered feeling "a profound thankfulness that such a convenient collection of human knowledge existed, that here it was spread out like a well-plenished table before me." William recalled that for Robert, "the acquisition of knowledge was with him the highest of earthly enjoyments."Robert was sent to local schools and showed unusual literary taste and ability, though he found his schooling to be uninspiring. His education was typical for the day; the country school, directed by James Gray, taught the boys reading, and, for an additional charge, arithmetic. In grammar school it was the classics -- Ancient Greek, with some English composition. Boys bullied one another and the teacher administered corporal punishment in the classroom for unruly behaviour.
Although uninspired by the school, Robert made up for this at the bookseller. Both Robert and William were born with six fingers on six toes on each foot, their parents attempted to correct this abnormality through operations, while William's was successful Robert was left lame. So while other boys roughed it outside, Robert was content to study his books. Robert surpassed his elder brother in his education, which he continued for several years beyond William's. Robert had been destined for the ministry, but at the age of fifteen he dropped this intended career; the arrival of the power loom threatened James Chambers' cotton business, forcing him to close it down and become a draper. During this time, James began to socialise with a number of French prisoners-of-war on parole who were stationed in Peebles. James Chambers lent these exiles a large amount of credit, when they were abruptly transferred away he was forced to declare bankruptcy; the family moved to Edinburgh in 1813. Robert continued his education at the High School, William became a bookseller's apprentice.
In 1818 Robert, at 16 years old, began his own business as a bookstall-keeper on Leith Walk. At first, his entire stock consisted of some old books belonging to his father, amounting to thirteen feet of shelf space and worth no more than a few pounds. By the end of the first year the value of his stock went up to twelve pounds, modest success came gradually. While Robert built up a business, his brother William expanded his own by purchasing a home-made printing press and publishing pamphlets as well as creating his own type. Soon afterwards and William decided to join forces – with Robert writing and William printing, their first joint venture was a magazine series called The Kaleidoscope, or Edinburgh Literary Amusement, sold for threepence. This was issued every two weeks between 6 October 1821 and 12 January 1822, it was followed by Illustrations of the Author of Waverley, which offered sketches of individuals believed to have been the inspirations for some of the characters in Walter Scott's works of fiction.
The last book to be printed on William's old press was Traditions of Edinburgh, derived from Robert's enthusiastic interest in the history and antiquities of Edinburgh. He followed this with Walks in Edinburgh, these books gained him the approval and personal friendship of Walter Scott. After Scott's death, Robert paid tribute to him by writing a Life of Sir Walter Scott. Robert wrote a History of the Rebellions in Scotland from 1638 to 1745 and numerous other works on Scotland and Scottish traditions. On 7 December 1829 Robert married Anne Kirkwood, the only child of Jane and John Kirkwood. Together they had 14 children. Excluding these three, their children were Robert, Mary, Janet, Amelia, William and Alice. At the beginning of 1832 Robert's brother William Chambers started a weekly publication entitled Chambers's Edinburgh Journal, which speedily gained a large circulation. Robert was at first only a contributor, but after 14 volumes had appeared, he became joint editor with his brother, his collaboration contributed more than anything else to the success of the Journal.
François Viète, Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations. He was a lawyer by trade, served as a privy councillor to both Henry III and Henry IV of France. Viète was born at Fontenay-le-Comte in present-day Vendée, his grandfather was a merchant from La Rochelle. His father, Etienne Viète, was a notary in Le Busseau, his mother was the aunt of Barnabé Brisson, a magistrate and the first president of parliament during the ascendancy of the Catholic League of France. Viète went to a Franciscan school and in 1558 studied law at Poitiers, graduating as a Bachelor of Laws in 1559. A year he began his career as an attorney in his native town. From the outset, he was entrusted with some major cases, including the settlement of rent in Poitou for the widow of King Francis I of France and looking after the interests of Mary, Queen of Scots. In 1564, Viète entered the service of Antoinette d’Aubeterre, Lady Soubise, wife of Jean V de Parthenay-Soubise, one of the main Huguenot military leaders and accompanied him to Lyon to collect documents about his heroic defence of that city against the troops of Jacques of Savoy, 2nd Duke of Nemours just the year before.
The same year, at Parc-Soubise, in the commune of Mouchamps in present-day Vendée, Viète became the tutor of Catherine de Parthenay, Soubise's twelve-year-old daughter. He taught her science and mathematics and wrote for her numerous treatises on astronomy and trigonometry, some of which have survived. In these treatises, Viète used decimal numbers and he noted the elliptic orbit of the planets, forty years before Kepler and twenty years before Giordano Bruno's death. John V de Parthenay presented him to King Charles IX of France. Viète wrote a genealogy of the Parthenay family and following the death of Jean V de Parthenay-Soubise in 1566, his biography. In 1568, Lady Soubise, married her daughter Catherine to Baron Charles de Quellenec and Viète went with Lady Soubise to La Rochelle, where he mixed with the highest Calvinist aristocracy, leaders like Coligny and Condé and Queen Jeanne d’Albret of Navarre and her son, Henry of Navarre, the future Henry IV of France. In 1570, he refused to represent the Soubise ladies in their infamous lawsuit against the Baron De Quellenec, where they claimed the Baron was unable to provide an heir.
In 1571, he enrolled as an attorney in Paris, continued to visit his student Catherine. He lived in Fontenay-le-Comte, where he took on some municipal functions, he began publishing his Universalium inspectionum ad canonem mathematicum liber singularis and wrote new mathematical research by night or during periods of leisure. He was known to dwell on any one question for up to three days, his elbow on the desk, feeding himself without changing position. In 1572, Viète was in Paris during the St. Bartholomew's Day massacre; that night, Baron De Quellenec was killed after having tried to save Admiral Coligny the previous night. The same year, Viète met Françoise de Rohan, Lady of Garnache, became her adviser against Jacques, Duke of Nemours. In 1573, he became a councillor of the Parliament of Brittany, at Rennes, two years he obtained the agreement of Antoinette d'Aubeterre for the marriage of Catherine of Parthenay to Duke René de Rohan, Françoise's brother. In 1576, duc de Rohan took him under his special protection, recommending him in 1580 as "maître des requêtes".
In 1579, Viète printed his canonem mathematicum. A year he was appointed maître des requêtes to the parliament of Paris, committed to serving the king; that same year, his success in the trial between the Duke of Nemours and Françoise de Rohan, to the benefit of the latter, earned him the resentment of the tenacious Catholic League. Between 1583 and 1585, the League persuaded Henry III to release Viète, Viète having been accused of sympathy with the Protestant cause. Henry of Navarre, at Rohan's instigation, addressed two letters to King Henry III of France on March 3 and April 26, 1585, in an attempt to obtain Viète's restoration to his former office, but he failed. Vieta retired with François de Rohan, he spent four years devoted to mathematics. In 1589, Henry III took refuge in Blois, he commanded the royal officials to be at Tours before 15 April 1589. Viète was one of the first, he deciphered other enemies of the king. He had arguments with the classical scholar Joseph Juste Scaliger. Viète triumphed against him in 1590.
After the death of Henry III, Vieta became a Privy Councillor to Henry of Navarre, now Henry IV. He was appreciated by the king. Viète was given the position of councillor of the parlement at Tours. In 1590, Viète discovered the key to a Spanish cipher, consisting of more than 500 characters, this meant that all dispatches in that language which fell into the hands of the French could be read. Henry IV published a letter from Commander Moreo to the king of Spain; the contents of this letter, read by Viète, revealed that the head of the League in France, the Duke of Mayenne, planned to become king in place of Henry IV. This publication led to the settlement of the Wars of Religion; the king of Spain accused Viète of having used magical powers. In 1593, Viète published his arguments against Scaliger. Beginning in 1594, he was appointed deciphering the enemy's secret codes. In 1582, Pope Gregory X
Algebra is one of the broad parts of mathematics, together with number theory and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols, it includes everything from elementary equation solving to the study of abstractions such as groups and fields. The more basic parts of algebra are called elementary algebra. Elementary algebra is considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied by professional mathematicians. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values. For example, in x + 2 = 5 the letter x is unknown, but the law of inverses can be used to discover its value: x = 3. In E = mc2, the letters E and m are variables, the letter c is a constant, the speed of light in a vacuum.
Algebra gives methods for writing formulas and solving equations that are much clearer and easier than the older method of writing everything out in words. The word algebra is used in certain specialized ways. A special kind of mathematical object in abstract algebra is called an "algebra", the word is used, for example, in the phrases linear algebra and algebraic topology. A mathematician who does research in algebra is called an algebraist; the word algebra comes from the Arabic الجبر from the title of the book Ilm al-jabr wa'l-muḳābala by the Persian mathematician and astronomer al-Khwarizmi. The word entered the English language during the fifteenth century, from either Spanish, Italian, or Medieval Latin, it referred to the surgical procedure of setting broken or dislocated bones. The mathematical meaning was first recorded in the sixteenth century; the word "algebra" has several related meanings as a single word or with qualifiers. As a single word without an article, "algebra" names a broad part of mathematics.
As a single word with an article or in plural, "an algebra" or "algebras" denotes a specific mathematical structure, whose precise definition depends on the author. The structure has an addition, a scalar multiplication; when some authors use the term "algebra", they make a subset of the following additional assumptions: associative, unital, and/or finite-dimensional. In universal algebra, the word "algebra" refers to a generalization of the above concept, which allows for n-ary operations. With a qualifier, there is the same distinction: Without an article, it means a part of algebra, such as linear algebra, elementary algebra, or abstract algebra. With an article, it means an instance of some abstract structure, like a Lie algebra, an associative algebra, or a vertex operator algebra. Sometimes both meanings exist for the same qualifier, as in the sentence: Commutative algebra is the study of commutative rings, which are commutative algebras over the integers. Algebra began with letters standing for numbers.
This allowed proofs of properties. For example, in the quadratic equation a x 2 + b x + c = 0, a, b, c can be any numbers whatsoever, the quadratic formula can be used to and find the values of the unknown quantity x which satisfy the equation; that is to say. And in current teaching, the study of algebra starts with the solving of equations such as the quadratic equation above. More general questions, such as "does an equation have a solution?", "how many solutions does an equation have?", "what can be said about the nature of the solutions?" are considered. These questions led extending algebra to non-numerical objects, such as permutations, vectors and polynomials; the structural properties of these non-numerical objects were abstracted into algebraic structures such as groups and fields. Before the 16th century, mathematics was divided into only two subfields and geometry. Though some methods, developed much earlier, may be considered nowadays as algebra, the emergence of algebra and, soon thereafter, of infinitesimal calculus as subfields of mathematics only dates from the 16th or 17th century.
From the second half of 19th century on, many new fields of mathematics appeared, most of which made use of both arithmetic and geometry, all of which used algebra. Today, algebra has grown until it includes many branches of mathematics, as can be seen in the Mathematics Subject Classification where none of the first level areas is called algebra. Today algebra in
Marino Ghetaldi was a Ragusan scientist. A mathematician and physicist who studied in Italy and Belgium, his best results are in physics optics, mathematics, he was one of the few students of François Viète. Born into the Ghetaldi noble family, he was one of six children, he was known for the application of algebra in geometry and his research in the field of geometrical optics on which he wrote 7 works including the Promotus Archimedus and the De resolutione et compositione mathematica. He produced a leaflet with the solutions of 42 geometrical problems, Variorum problematum colletio, in 1607 and set grounds of algebraization of geometry, his contributions to geometry had been cited by Dutch physicist Christiaan Huygens and Edmond Halley, who calculated the orbit of what is known as Halley's comet, in England. Ghetaldi was the constructor of the parabolic mirror, kept today at the National Maritime Museum in London, he was a pioneer in making conic lenses. During his sejourn in Padua he met Galileo Galilei.
He was a good friend to the French mathematician François Viète. He was offered the post of professor of mathematics in Old University of Leuven in Belgium, at the time one of the most prestigious university centers in Europe, he was engaged in politics and was the envoy of the Republic of Ragusa in Constantinople in 1606 as well as the member of the Great and Small Council, the political bodies of the Republic. He was married to Marija Sorkočević. Two notable localities in Dubrovnik are associated with the name of Getaldić: Bete's Cave, named after Marino's nickname, where he conducted experiments with igniting mirrors. House of Getaldić List of notable Ragusans Vujić, Marko. "Marin Getaldić - Život i djelo". SVEUČILIŠTE JOSIPA JURJA STROSSMAYERA U OSIJEKU ODJEL ZA FIZIKU. A. Favaro, "Marino Ghetaldi," Amici e corrisponsdenti di Galileo, 3 vols. 2, 911-34. H. Wieleitner, "Marino Ghetaldi und die Anfänge der Koordinatengeometrie," Bibliotheca mathematica, 3rd ser. 13, pp. 242–247. G. Barbieri, "Marino Ghetaldi," in Pietro F. Martecchini, Galleria di Ragusei illustri.
O'Connor, John J.. "Ghetaldi, Marino". The Galileo Project. Works by Marino Ghetaldi at Open Library