Johann(es) Werner ( la, Ioannes Vernerus; February 14, 1468 – May 1522) was a German

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He was born in

Nuremberg Nuremberg ( ; german: link=no, Nürnberg ; in the local East Franconian dialect: ''Nämberch'' ) is the second-largest city of the German state of Bavaria after its capital Munich, and its 518,370 (2019) inhabitants make it the 14th-largest ...

Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwee ...

, where he became a

parish A parish is a territorial entity in many Christian denominations, constituting a division within a diocese. A parish is under the pastoral care and clerical jurisdiction of a priest, often termed a parish priest, who might be assisted by one or ...

priest A priest is a religious leader authorized to perform the sacred rituals of a religion, especially as a mediatory agent between humans and one or more deities. They also have the authority or power to administer religious rites; in partic ...

. His primary work was in

astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...

mathematics 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 ...

, and

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, an ...

, although he was also considered a skilled instrument maker.

Mathematics

His mathematical works were in the areas of

spherical trigonometry Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are grea ...

, as well as

conic section In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a ...

s. 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.

Astronomy

In 1500 he observed a

comet A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena ...

, and kept observations of its movements from June 1 until the 24th. This work further developed the suggestion of

Regiomontanus Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus (), was a mathematician, astrologer and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg. His contributions were instrument ...

that the occurrences of

eclipse An eclipse is an astronomical event that occurs when an astronomical object or spacecraft is temporarily obscured, by passing into the shadow of another body or by having another body pass between it and the viewer. This alignment of three c ...

s and cometary orbits could be used to find

longitude Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek let ...

, giving a practical approach for this method by means of the cross-staff. (The approach did not actually solve the problem as the instrument was not sufficiently accurate.) His trepidations method to describe

precession of the equinoxes In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In the absence of precession, the astronomical body's orbit would show axial parallelism. In partic ...

' was posthumously challenged in 1524 by

Nicolaus 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 formulat ...

in ''The Letter against Werner''. Edward Rosen, ''Three Copernican Treatises: The

Commentariolus The ''Commentariolus'' (''Little Commentary'') is Nicolaus Copernicus's brief outline of an early version of his revolutionary heliocentric theory of the universe. After further long development of his theory, Copernicus published the mature ver ...

of Copernicus, The Letter against Werner, The

Narratio Prima ''De libris revolutionum Copernici narratio prima'', usually referred to as ''Narratio Prima'' ( la, First Account), is an abstract of Nicolaus Copernicus' heliocentric theory, written by Georg Joachim Rheticus in 1540. It is an introduction to ...

Rheticus Georg Joachim de Porris, also known as Rheticus ( /ˈrɛtɪkəs/; 16 February 1514 – 5 December 1576), was a mathematician, astronomer, cartographer, navigational-instrument maker, medical practitioner, and teacher. He is perhaps best known for ...

'', Columbia University Press, 1939

Geography

He is most noted for his work, ', published in

in 1514, a translation of

Claudius Ptolemy Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importa ...

's ''

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, an ...

''. In it, he refined and promoted the '' Werner map projection'', a cordiform (heart-shape) projection map that had been developed by Johannes Stabius (Stab) of

Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...

around 1500. This projection would be used for world maps and some continental maps through the 16th century and into the 17th century. It was used by

Mercator __NOTOC__ Mercator (Latin for "merchant") may refer to: People * Marius Mercator (c. 390–451), a Catholic ecclesiastical writer * Arnold Mercator, a 16th-century cartographer * Gerardus Mercator, a 16th-century cartographer ** Mercator 1569 ...

, Oronce Fine, and Ortelius in the late 16th century for maps of

Asia Asia (, ) is one of the world's most notable geographical regions, which is either considered a continent in its own right or a subcontinent of Eurasia, which shares the continental landmass of Afro-Eurasia with Africa. Asia covers an are ...

and

Africa Africa is the world's second-largest and second-most populous continent, after Asia in both cases. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 6% of Earth's total surface area ...

. By the 18th century, it was replaced by the ''

Bonne projection The Bonne projection is a pseudoconical equal-area map projection, sometimes called a dépôt de la guerre, modified Flamsteed, or a Sylvanus projection. Although named after Rigobert Bonne (1727–1795), the projection was in use prior to his ...

'' for continental maps. The ''Werner projection'' is only used today for instructional purposes and as a novelty. In this work, Werner also proposed an astronomical method to determine

, by measuring the position of the moon relative to the background stars. The idea was later discussed in detail by Petrus Apianus in his ' (Landshut 1524) and became known as the lunar distance method.

Meteorology

Many consider Werner as a pioneer of modern

meteorology Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did no ...

and weather forecasting. Between 1513 and 1520, Johann Werner made the first regular observations of the

weather Weather is the state of the atmosphere, describing for example the degree to which it is hot or cold, wet or dry, calm or stormy, clear or cloudy. On Earth, most weather phenomena occur in the lowest layer of the planet's atmosphere, the ...

conditions in Germany.

Notable publications

*', Nürnberg 1514 *', Nürnberg, Petrejus 1522 *', https://archive.org/details/ioannisvernerid00rhgoog *', 1546 *'

Honours

The crater Werner on 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 ...

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 In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

References

External links

Johann WernerWerner Map Projection
{{DEFAULTSORT:Werner, Johannes 1468 births 1528 deaths Scientists from Nuremberg German cartographers Medieval German mathematicians 15th-century German astronomers German scientific instrument makers 16th-century German mathematicians 16th-century German astronomers 16th-century cartographers 16th-century geographers 16th-century Latin-language writers 16th-century German writers 16th-century German male writers 15th-century German mathematicians