Nicolaus Copernicus was a Renaissance-era mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe, in all likelihood independently of Aristarchus of Samos, who had formulated such a model some eighteen centuries earlier. The publication of Copernicus' model in his book De revolutionibus orbium coelestium, just before his death in 1543, was a major event in the history of science, triggering the Copernican Revolution and making a pioneering contribution to the Scientific Revolution. Copernicus was born and died in Royal Prussia, a region, part of the Kingdom of Poland since 1466. A polyglot and polymath, he obtained a doctorate in canon law and was a mathematician, physician, classics scholar, governor and economist. In 1517 he derived a quantity theory of money—a key concept in economics—and in 1519 he formulated an economic principle that came to be called Gresham's law. Nicolaus Copernicus was born on 19 February 1473 in the city of Thorn, in the province of Royal Prussia, in the Crown of the Kingdom of Poland.
His father was a merchant from Kraków and his mother was the daughter of a wealthy Toruń merchant. Nicolaus was the youngest of four children, his brother Andreas became an Augustinian canon at Frombork. His sister Barbara, named after her mother, became a Benedictine nun and, in her final years, prioress of a convent in Chełmno, his sister Katharina married the businessman and Toruń city councilor Barthel Gertner and left five children, whom Copernicus looked after to the end of his life. Copernicus never married and is not known to have had children, but from at least 1531 until 1539 his relations with Anna Schilling, a live-in housekeeper, were seen as scandalous by two bishops of Warmia who urged him over the years to break off relations with his "mistress". Copernicus' father's family can be traced to a village in Silesia near Nysa; the village's name has been variously spelled Kopernik, Copernic, Kopernic and today Koperniki. In the 14th century, members of the family began moving to various other Silesian cities, to the Polish capital, Kraków, to Toruń.
The father, Mikołaj the Elder the son of Jan, came from the Kraków line. Nicolaus was named after his father, who appears in records for the first time as a well-to-do merchant who dealt in copper, selling it in Danzig, he moved from Kraków to Toruń around 1458. Toruń, situated on the Vistula River, was at that time embroiled in the Thirteen Years' War, in which the Kingdom of Poland and the Prussian Confederation, an alliance of Prussian cities and clergy, fought the Teutonic Order over control of the region. In this war, Hanseatic cities like Danzig and Toruń, Nicolaus Copernicus's hometown, chose to support the Polish King, Casimir IV Jagiellon, who promised to respect the cities' traditional vast independence, which the Teutonic Order had challenged. Nicolaus' father was engaged in the politics of the day and supported Poland and the cities against the Teutonic Order. In 1454 he mediated negotiations between Poland's Cardinal Zbigniew Oleśnicki and the Prussian cities for repayment of war loans.
In the Second Peace of Thorn, the Teutonic Order formally relinquished all claims to its western province, which as Royal Prussia remained a region of the Crown of the Kingdom of Poland until the First and Second Partitions of Poland. Copernicus's father married Barbara Watzenrode, the astronomer's mother, between 1461 and 1464, he died about 1483. Nicolaus' mother, Barbara Watzenrode, was the daughter of a wealthy Toruń patrician and city councillor, Lucas Watzenrode the Elder, Katarzyna, mentioned in other sources as Katarzyna Rüdiger gente Modlibóg; the Modlibógs were a prominent Polish family, well known in Poland's history since 1271. The Watzenrode family, like the Kopernik family, had come from Silesia from near Świdnica, after 1360 had settled in Toruń, they soon became one of most influential patrician families. Through the Watzenrodes' extensive family relationships by marriage, Copernicus was related to wealthy families of Toruń, Gdańsk and Elbląg, to prominent Polish noble families of Prussia: the Czapskis, Działyńskis, Konopackis and Kościeleckis.
Lucas and Katherine had three children: Lucas Watzenrode the Younger, who would become Bishop of Warmia and Copernicus's patron. Lucas Watzenrode the Elder, a wealthy merchant and in 1439–62 president of the judicial bench, was a decided opponent of the Teutonic Knights. In 1453 he was the delegate from Toruń at the Grudziądz conference that planned the uprising against them. During the ensuing Thirteen Years' War, he supported the Prussian cities' war effort with substantial monetary subsidies, with political activity in Toruń and Danzig, by fighting in battles at Łasin and Malbork, he died in 1462. Lucas Watzenrode the Younger, the astronomer's maternal uncle and patron, was educated at the University of Kraków and at the universities of Cologne and Bologna, he was a bitter opponent of the Teutonic Order, its Grand Master once referred to him as "the devil incarn
Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics and chemistry in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, stars, nebulae and comets. More all phenomena that originate outside Earth's atmosphere are within the purview of astronomy. A related but distinct subject is physical cosmology, the study of the Universe as a whole. Astronomy is one of the oldest of the natural sciences; the early civilizations in recorded history, such as the Babylonians, Indians, Nubians, Chinese and many ancient indigenous peoples of the Americas, performed methodical observations of the night sky. Astronomy has included disciplines as diverse as astrometry, celestial navigation, observational astronomy, the making of calendars, but professional astronomy is now considered to be synonymous with astrophysics. Professional astronomy is split into theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, analyzed using basic principles of physics.
Theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain observational results and observations being used to confirm theoretical results. Astronomy is one of the few sciences in which amateurs still play an active role in the discovery and observation of transient events. Amateur astronomers have made and contributed to many important astronomical discoveries, such as finding new comets. Astronomy means "law of the stars". Astronomy should not be confused with astrology, the belief system which claims that human affairs are correlated with the positions of celestial objects. Although the two fields share a common origin, they are now distinct. Both of the terms "astronomy" and "astrophysics" may be used to refer to the same subject. Based on strict dictionary definitions, "astronomy" refers to "the study of objects and matter outside the Earth's atmosphere and of their physical and chemical properties," while "astrophysics" refers to the branch of astronomy dealing with "the behavior, physical properties, dynamic processes of celestial objects and phenomena."
In some cases, as in the introduction of the introductory textbook The Physical Universe by Frank Shu, "astronomy" may be used to describe the qualitative study of the subject, whereas "astrophysics" is used to describe the physics-oriented version of the subject. However, since most modern astronomical research deals with subjects related to physics, modern astronomy could be called astrophysics; some fields, such as astrometry, are purely astronomy rather than astrophysics. Various departments in which scientists carry out research on this subject may use "astronomy" and "astrophysics" depending on whether the department is affiliated with a physics department, many professional astronomers have physics rather than astronomy degrees; some titles of the leading scientific journals in this field include The Astronomical Journal, The Astrophysical Journal, Astronomy and Astrophysics. In early historic times, astronomy only consisted of the observation and predictions of the motions of objects visible to the naked eye.
In some locations, early cultures assembled massive artifacts that had some astronomical purpose. In addition to their ceremonial uses, these observatories could be employed to determine the seasons, an important factor in knowing when to plant crops and in understanding the length of the year. Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye; as civilizations developed, most notably in Mesopotamia, Persia, China and Central America, astronomical observatories were assembled and ideas on the nature of the Universe began to develop. Most early astronomy consisted of mapping the positions of the stars and planets, a science now referred to as astrometry. From these observations, early ideas about the motions of the planets were formed, the nature of the Sun and the Earth in the Universe were explored philosophically; the Earth was believed to be the center of the Universe with the Sun, the Moon and the stars rotating around it. This is known as the geocentric model of the Ptolemaic system, named after Ptolemy.
A important early development was the beginning of mathematical and scientific astronomy, which began among the Babylonians, who laid the foundations for the astronomical traditions that developed in many other civilizations. The Babylonians discovered. Following the Babylonians, significant advances in astronomy were made in ancient Greece and the Hellenistic world. Greek astronomy is characterized from the start by seeking a rational, physical explanation for celestial phenomena. In the 3rd century BC, Aristarchus of Samos estimated the size and distance of the Moon and Sun, he proposed a model of the Solar System where the Earth and planets rotated around the Sun, now called the heliocentric model. In the 2nd century BC, Hipparchus discovered precession, calculated the size and distance of the Moon and inven
Germany the Federal Republic of Germany, is a country in Central and Western Europe, lying between the Baltic and North Seas to the north, the Alps to the south. It borders Denmark to the north and the Czech Republic to the east and Switzerland to the south, France to the southwest, Luxembourg and the Netherlands to the west. Germany includes 16 constituent states, covers an area of 357,386 square kilometres, has a temperate seasonal climate. With 83 million inhabitants, it is the second most populous state of Europe after Russia, the most populous state lying in Europe, as well as the most populous member state of the European Union. Germany is a decentralized country, its capital and largest metropolis is Berlin, while Frankfurt serves as its financial capital and has the country's busiest airport. Germany's largest urban area is the Ruhr, with its main centres of Essen; the country's other major cities are Hamburg, Cologne, Stuttgart, Düsseldorf, Dresden, Bremen and Nuremberg. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity.
A region named Germania was documented before 100 AD. During the Migration Period, the Germanic tribes expanded southward. Beginning in the 10th century, German territories formed a central part of the Holy Roman Empire. During the 16th century, northern German regions became the centre of the Protestant Reformation. After the collapse of the Holy Roman Empire, the German Confederation was formed in 1815; the German revolutions of 1848–49 resulted in the Frankfurt Parliament establishing major democratic rights. In 1871, Germany became a nation state when most of the German states unified into the Prussian-dominated German Empire. After World War I and the revolution of 1918–19, the Empire was replaced by the parliamentary Weimar Republic; the Nazi seizure of power in 1933 led to the establishment of a dictatorship, the annexation of Austria, World War II, the Holocaust. After the end of World War II in Europe and a period of Allied occupation, Austria was re-established as an independent country and two new German states were founded: West Germany, formed from the American and French occupation zones, East Germany, formed from the Soviet occupation zone.
Following the Revolutions of 1989 that ended communist rule in Central and Eastern Europe, the country was reunified on 3 October 1990. Today, the sovereign state of Germany is a federal parliamentary republic led by a chancellor, it is a great power with a strong economy. As a global leader in several industrial and technological sectors, it is both the world's third-largest exporter and importer of goods; as a developed country with a high standard of living, it upholds a social security and universal health care system, environmental protection, a tuition-free university education. The Federal Republic of Germany was a founding member of the European Economic Community in 1957 and the European Union in 1993, it is part of the Schengen Area and became a co-founder of the Eurozone in 1999. Germany is a member of the United Nations, NATO, the G7, the G20, the OECD. Known for its rich cultural history, Germany has been continuously the home of influential and successful artists, musicians, film people, entrepreneurs, scientists and inventors.
Germany has a large number of World Heritage sites and is among the top tourism destinations in the world. The English word Germany derives from the Latin Germania, which came into use after Julius Caesar adopted it for the peoples east of the Rhine; the German term Deutschland diutisciu land is derived from deutsch, descended from Old High German diutisc "popular" used to distinguish the language of the common people from Latin and its Romance descendants. This in turn descends from Proto-Germanic *þiudiskaz "popular", derived from *þeudō, descended from Proto-Indo-European *tewtéh₂- "people", from which the word Teutons originates; the discovery of the Mauer 1 mandible shows that ancient humans were present in Germany at least 600,000 years ago. The oldest complete hunting weapons found anywhere in the world were discovered in a coal mine in Schöningen between 1994 and 1998 where eight 380,000-year-old wooden javelins of 1.82 to 2.25 m length were unearthed. The Neander Valley was the location where the first non-modern human fossil was discovered.
The Neanderthal 1 fossils are known to be 40,000 years old. Evidence of modern humans dated, has been found in caves in the Swabian Jura near Ulm; the finds included 42,000-year-old bird bone and mammoth ivory flutes which are the oldest musical instruments found, the 40,000-year-old Ice Age Lion Man, the oldest uncontested figurative art discovered, the 35,000-year-old Venus of Hohle Fels, the oldest uncontested human figurative art discovered. The Nebra sky disk is a bronze artefact created during the European Bronze Age attributed to a site near Nebra, Saxony-Anhalt, it is part of UNESCO's Memory of the World Programme. The Germanic tribes are thought to date from the Pre-Roman Iron Age. From southern Scandinavia and north Germany, they expanded south and west from the 1st century BC, coming into contact with the Celtic tribes of Gaul as well
A priest or priestess is a religious leader authorized to perform the sacred rituals of a religion as a mediatory agent between humans and one or more deities. They have the authority or power to administer religious rites, their office or position is the priesthood, a term which may apply to such persons collectively. According to the trifunctional hypothesis of prehistoric Proto-Indo-European society, priests have existed since the earliest of times and in the simplest societies, most as a result of agricultural surplus and consequent social stratification; the necessity to read sacred texts and keep temple or church records helped foster literacy in many early societies. Priests exist in many religions today, such as all or some branches of Judaism, Buddhism and Hinduism, they are regarded as having privileged contact with the deity or deities of the religion to which they subscribe interpreting the meaning of events and performing the rituals of the religion. There is no common definition of the duties of priesthood between faiths.
These include blessing worshipers with prayers of joy at marriages, after a birth, at consecrations, teaching the wisdom and dogma of the faith at any regular worship service, mediating and easing the experience of grief and death at funerals – maintaining a spiritual connection to the afterlife in faiths where such a concept exists. Administering religious building grounds and office affairs and papers, including any religious library or collection of sacred texts, is commonly a responsibility – for example, the modern term for clerical duties in a secular office refers to the duties of a cleric; the question of which religions have a "priest" depends on how the titles of leaders are used or translated into English. In some cases, leaders are more like those that other believers will turn to for advice on spiritual matters, less of a "person authorized to perform the sacred rituals." For example, clergy in Roman Catholicism and Eastern Orthodoxy are priests, but in Protestant Christianity they are minister and pastor.
The terms priest and priestess are sufficiently generic that they may be used in an anthropological sense to describe the religious mediators of an unknown or otherwise unspecified religion. In many religions, being a priest or priestess is a full-time position, ruling out any other career. Many Christian priests and pastors choose or are mandated to dedicate themselves to their churches and receive their living directly from their churches. In other cases it is a part-time role. For example, in the early history of Iceland the chieftains were titled goði, a word meaning "priest"; as seen in the saga of Hrafnkell Freysgoði, being a priest consisted of offering periodic sacrifices to the Norse gods and goddesses. In some religions, being a priest or priestess is by human election or human choice. In Judaism the priesthood is inherited in familial lines. In a theocracy, a society is governed by its priesthood; the word "priest", is derived from Greek via Latin presbyter, the term for "elder" elders of Jewish or Christian communities in late antiquity.
The Latin presbyter represents Greek πρεσβύτερος presbúteros, the regular Latin word for "priest" being sacerdos, corresponding to ἱερεύς hiereús. It is possible that the Latin word was loaned into Old English, only from Old English reached other Germanic languages via the Anglo-Saxon mission to the continent, giving Old Icelandic prestr, Old Swedish präster, Old High German priast. Old High German has the disyllabic priester, priestar derived from Latin independently via Old French presbtre. Αn alternative theory makes priest cognate with Old High German priast, from Vulgar Latin *prevost "one put over others", from Latin praepositus "person placed in charge". That English should have only the single term priest to translate presbyter and sacerdos came to be seen as a problem in English Bible translations; the presbyter is the minister who both presides and instructs a Christian congregation, while the sacerdos, offerer of sacrifices, or in a Christian context the eucharist, performs "mediatorial offices between God and man".
The feminine English noun, was coined in the 17th century, to refer to female priests of the pre-Christian religions of classical antiquity. In the 20th century, the word was used in controversies surrounding the women ordained in the Anglican communion, who are referred to as "priests", irrespective of gender, the term priestess is considered archaic in Christianity. In historical polytheism, a priest administers the sacrifice to a deity in elaborate ritual. In the Ancient Near East, the priesthood acted on behalf of the deities in managing their property. Priestesses in antiquity performed sacred prostitution, in Ancient Greece, some priestesses such as Pythia, priestess at Delphi, acted as oracles. Sumerian en were top-ranking priestesses who were distinguished with special ceremonial attire and held equal status to high priests, they owned property, transacted business, initiated the hieros gamos with priests and kings. Enheduanna was the first known holder of the title en. Nadītu served as priestesses in the temples of Inanna in the city of Uruk.
They were recruited from the highest families in the land and were supposed to remain childless, own
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work to solve mathematical problems. Mathematics is concerned with numbers, quantity, space and change. One of the earliest known mathematicians was Thales of Miletus, he is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number", it was the Pythagoreans who coined the term "mathematics", with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypatia of Alexandria, she succeeded her father as Librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells.
Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences; as these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was al-Khawarizmi. A notable feature of many scholars working under Muslim rule in medieval times is that they were polymaths. Examples include the work on optics and astronomy of Ibn al-Haytham; the Renaissance brought an increased emphasis on science to Europe.
During this period of transition from a feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli. As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists Robert Hooke and Robert Boyle, at Cambridge where Isaac Newton was Lucasian Professor of Mathematics & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag productive thinking.” In 1810, Humboldt convinced the King of Prussia to build a university in Berlin based on Friedrich Schleiermacher’s liberal ideas. Thus and laboratories started to evolve. British universities of this period adopted some approaches familiar to the Italian and German universities, but as they enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.
The Universities of Oxford and Cambridge emphasized the importance of research, arguably more authentically implementing Humboldt’s idea of a university than German universities, which were subject to state authority. Overall, science became the focus of universities in the 20th centuries. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge; the German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France. In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of “freedom of scientific research and study.” Mathematicians cover a breadth of topics within mathematics in their undergraduate education, proceed to specialize in topics of their own choice at the graduate level.
In some universities, a qualifying exam serves to test both the breadth and depth of a student's understanding of mathematics. Mathematicians involved with solving problems with applications in real life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their specialized knowledge and professional methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, localized constructs, applied mathematicians work in the study and formulation of mathematical models. Mathematicians and applied mathematicians are considered to be two of the STEM careers; the discipline of applied mathematics concerns
A comet is an icy, small Solar System body that, when passing close to the Sun and begins to release gases, a process called outgassing. This produces a visible atmosphere or coma, sometimes a tail; these phenomena are due to the effects of solar radiation and the solar wind acting upon the nucleus of the comet. Comet nuclei range from a few hundred metres to tens of kilometres across and are composed of loose collections of ice and small rocky particles; the coma may be up to 15 times the Earth's diameter, while the tail may stretch one astronomical unit. If sufficiently bright, a comet may be seen from the Earth without the aid of a telescope and may subtend an arc of 30° across the sky. Comets have been recorded since ancient times by many cultures. Comets have eccentric elliptical orbits, they have a wide range of orbital periods, ranging from several years to several millions of years. Short-period comets originate in the Kuiper belt or its associated scattered disc, which lie beyond the orbit of Neptune.
Long-period comets are thought to originate in the Oort cloud, a spherical cloud of icy bodies extending from outside the Kuiper belt to halfway to the nearest star. Long-period comets are set in motion towards the Sun from the Oort cloud by gravitational perturbations caused by passing stars and the galactic tide. Hyperbolic comets may pass once through the inner Solar System before being flung to interstellar space; the appearance of a comet is called an apparition. Comets are distinguished from asteroids by the presence of an extended, gravitationally unbound atmosphere surrounding their central nucleus; this atmosphere has parts termed the tail. However, extinct comets that have passed close to the Sun many times have lost nearly all of their volatile ices and dust and may come to resemble small asteroids. Asteroids are thought to have a different origin from comets, having formed inside the orbit of Jupiter rather than in the outer Solar System; the discovery of main-belt comets and active centaur minor planets has blurred the distinction between asteroids and comets.
In the early 21st century, the discovery of some minor bodies with long-period comet orbits, but characteristics of inner solar system asteroids, were called Manx comets. They are still classified as comets, such as C/2014 S3. 27 Manx comets were found from 2013 to 2017. As of July 2018 there are 6,339 known comets, a number, increasing as they are discovered. However, this represents only a tiny fraction of the total potential comet population, as the reservoir of comet-like bodies in the outer Solar System is estimated to be one trillion. One comet per year is visible to the naked eye, though many of those are faint and unspectacular. Bright examples are called "great comets". Comets have been visited by unmanned probes such as the European Space Agency's Rosetta, which became the first to land a robotic spacecraft on a comet, NASA's Deep Impact, which blasted a crater on Comet Tempel 1 to study its interior; the word comet comētēs. That, in turn, is a latinisation of the Greek κομήτης, the Oxford English Dictionary notes that the term κομήτης meant "long-haired star, comet" in Greek.
Κομήτης was derived from κομᾶν, itself derived from κόμη and was used to mean "the tail of a comet". The astronomical symbol for comets is ☄; the solid, core structure of a comet is known as the nucleus. Cometary nuclei are composed of an amalgamation of rock, water ice, frozen carbon dioxide, carbon monoxide and ammonia; as such, they are popularly described as "dirty snowballs" after Fred Whipple's model. However, some comets may have a higher dust content, leading them to be called "icy dirtballs". Research conducted in 2014 suggests that comets are like "deep fried ice cream", in that their surfaces are formed of dense crystalline ice mixed with organic compounds, while the interior ice is colder and less dense; the surface of the nucleus is dry, dusty or rocky, suggesting that the ices are hidden beneath a surface crust several metres thick. In addition to the gases mentioned, the nuclei contain a variety of organic compounds, which may include methanol, hydrogen cyanide, formaldehyde and ethane and more complex molecules such as long-chain hydrocarbons and amino acids.
In 2009, it was confirmed that the amino acid glycine had been found in the comet dust recovered by NASA's Stardust mission. In August 2011, a report, based on NASA studies of meteorites found on Earth, was published suggesting DNA and RNA components may have been formed on asteroids and comets; the outer surfaces of cometary nuclei have a low albedo, making them among the least reflective objects found in the Solar System. The Giotto space probe found that the nucleus of Halley's Comet reflects about four percent of the light that falls on it, Deep Space 1 discovered that Comet Borrelly's surface reflects less than 3.0%. The dark surface material of the nucleus may consist of complex organic compounds. Solar heating drives off lighter volatile compounds, leaving behind larger organic compounds that tend to be dark, like tar or crude oil; the low reflectivity of cometary surfaces causes them to absorb t
Johann Werner was a German mathematician. He was born in Nuremberg, where he became a parish priest, his primary work was in astronomy and geography, although he was considered a skilled instrument maker. His mathematical works were in the areas of spherical trigonometry, as well as conic sections, he published an original work on conic sections in 1522 and is one of several mathematicians sometimes credited with the invention of prosthaphaeresis, which simplifies tedious computations by the use of trigonometric formulas, sometimes called Werner's formulas. In 1500 he observed a comet, kept observations of its movements from June 1st until the 24th; this work further developed the suggestion of Regiomontanus that the occurrences of eclipses and cometary orbits could be used to find longitude, giving a practical approach for this method by means of the cross-staff. His trepidations method to describe precession of the equinoxes De motu octauæ Sphær was posthumously challenged in 1524 by Nicolaus Copernicus in The Letter against Werner.
He is most noted for his work, In Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei, written in 1514, a translation of the work Geographia, written by Ptolemy. He refined and promoted the Werner map projection, a cordiform projection map, developed by Johannes Stabius of Vienna around 1500. After its introduction by Werner in his 1514 book, Nova translatio primi libri geographiaae C. Ptolemaei, the Werner projection was used for world maps and some continental maps through the 16th century and into the 17th century, it was used by Mercator, Oronce Fine, Ortelius in the late 16th century for maps of Asia and Africa. By the 18th century, it was replaced by the Bonne projection for continental maps; the Werner projection is only used today as a novelty. Many consider Werner as a pioneer of modern weather forecasting. Between 1513 and 1520, Johann Werner made the first regular observations of the weather conditions in Germany. To determine longitude in navigation, Werner proposed determining time by measuring the position of the moon relative to the background stars.
He published this in In hoc opere haec continentur Nova translatio primi libri geographiae Cl' Ptolomaei.... The method was discussed in detail by Petrus Apianus in his Cosmographicus liber; this became known as the lunar distance method. In hoc opere haec continentur Nova translatio primi libri geographiae Cl. Ptolomaei: quae quidem translatio verbum: habet. Libellus de quattuor terrarum orbis in plano figurationibus.: In idem Georgii Amirucii opusculaum. Appendices, Nürnberg 1514 In hoc opere haec continentur. Libellvs Ioannis Verneri Nvrembergen. Svper Vigintidvobvs Elementis Conicis. Comentarius seu paraphrastica enarratio in vndecim modos conficiendi eius Problematis quod Cubi duplicatio dicitur. Eivsdem. Comentatio in Dionysodori problema, quo data sphæra plano sub data secat ratione, Alivs modus idem problema coficiendi ab eodem Ioanne Vernero nouissime copertus demostratusq. Summaria enarratio Theoricæ motus octau Sphæræ. Nürnberg, Petrejus 1522 De Triangulis sphaericis libri quatuor de meteoroscopiis libri sex, https://archive.org/details/ioannisvernerid00rhgoog Canones sicut breuissimi, ita etiam doctissimi, complectentes praecepta & obseruationes de mutatione aurae, 1546 Compendiosa institvtio in vniversam dialecticam, ex Aristot.
Riuio, aliisque auctoribus recentioribus collecta, nuperrime scholiis philosophicis illustrata The crater Werner on the Moon is named after him. Some of the trigonometric identities used in prosthaphaeresis, an early method for rapid computation of products, were named Werner formulas in honor of Werner's role in development of the algorithm. Werner Map Projection Bonne Map Projection Cordiform Map Projection Johann Werner