Johannes Werner

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Johannes Werner Iohannes Werner.jpg
Johannes Werner

Johann(es) Werner (Latin : Ioannis Vernerus; February 14, 1468 – May 1522) was a German mathematician. He was born in Nuremberg, Germany, where he became a parish priest. His primary work was in astronomy, mathematics, and geography, although he was also considered a skilled instrument maker.

Germany Federal parliamentary republic in central-western Europe

Germany, officially the Federal Republic of Germany, is a country in Central and Western Europe, lying between the Baltic and North Seas to the north and the Alps, Lake Constance and the High Rhine to the south. It borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, France to the southwest, and Luxembourg, Belgium and the Netherlands to the west.

Mathematician person with an extensive knowledge of mathematics

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

Nuremberg city in Bavaria, Germany

Nuremberg is the second-largest city of the German federal state of Bavaria after its capital Munich, and its 511,628 (2016) inhabitants make it the 14th largest city in Germany. On the Pegnitz River and the Rhine–Main–Danube Canal, it lies in the Bavarian administrative region of Middle Franconia, and is the largest city and the unofficial capital of Franconia. Nuremberg forms a continuous conurbation with the neighbouring cities of Fürth, Erlangen and Schwabach with a total population of 787,976 (2016), while the larger Nuremberg Metropolitan Region has approximately 3.5 million inhabitants. The city lies about 170 kilometres (110 mi) north of Munich. It is the largest city in the East Franconian dialect area.



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. [1]

Spherical trigonometry is the branch of spherical geometry that deals with the relationships between trigonometric functions of the sides and angles of the spherical polygons defined by a number of intersecting great circles on the sphere. Spherical trigonometry is of great importance for calculations in astronomy, geodesy and navigation.

Conic section Curve that can be obtained as the intersection of a cone with a plane

In mathematics, a conic section 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 special case of the ellipse, though historically it was sometimes called a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties.

Prosthaphaeresis was an algorithm used in the late 16th century and early 17th century for approximate multiplication and division using formulas from trigonometry. For the 25 years preceding the invention of the logarithm in 1614, it was the only known generally applicable way of approximating products quickly. Its name comes from the Greek prosthesis (πρόσθεσις) and aphaeresis (ἀφαίρεσις), meaning addition and subtraction, two steps in the process.


In 1500 he observed a comet, and kept observations of its movements from June 1st until the 24th.

Comet Icy small Solar System body

A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process called outgassing. This produces a visible atmosphere or coma, and sometimes also 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, dust, 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 observed and recorded since ancient times by many cultures.

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. (The approach did not actually solve the problem as the instrument was not sufficiently accurate.)

Regiomontanus German mathematician and astronomer

Johannes Müller von Königsberg, better known as Regiomontanus, was a mathematician and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg. His contributions were instrumental in the development of Copernican heliocentrism in the decades following his death.

Eclipse Astronomical event where one body is hidden by another

An eclipse is an astronomical event that occurs when an astronomical object is temporarily obscured, either by passing into the shadow of another body or by having another body pass between it and the viewer. This alignment of three celestial objects is known as a syzygy. Apart from syzygy, the term eclipse is also used when a spacecraft reaches a position where it can observe two celestial bodies so aligned. An eclipse is the result of either an occultation or a transit.

Longitude A geographic coordinate that specifies the east-west position of a point on the Earths surface

Longitude, is a geographic coordinate that specifies the east–west position of a point on the Earth's surface, or the surface of a celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek letter lambda (λ). Meridians connect points with the same longitude. By convention, one of these, the Prime Meridian, which passes through the Royal Observatory, Greenwich, England, was allocated the position of 0° longitude. The longitude of other places is measured as the angle east or west from the Prime Meridian, ranging from 0° at the Prime Meridian to +180° eastward and −180° westward. Specifically, it is the angle between a plane through the Prime Meridian and a plane through both poles and the location in question.

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. [2]

Nicolaus Copernicus Renaissanse-era mathematician and astronomer who formulated the heliocentric model of the Universe

Nicolaus Copernicus was a Renaissance-era mathematician and astronomer, who formulated a model of the universe that placed the Sun rather than 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.


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 (Ptolemy) , written by Ptolemy.

Ptolemy 2nd-century Greco-Egyptian writer and astronomer

Claudius Ptolemy was a mathematician, astronomer, geographer and astrologer. He lived in the city of Alexandria in the Roman province of Egypt, under the rule of the Roman Empire, had a Latin name, which several historians have taken to imply he was also a Roman citizen, cited Greek philosophers, and used Babylonian observations and Babylonian lunar theory. The 14th-century astronomer Theodore Meliteniotes gave his birthplace as the prominent Greek city Ptolemais Hermiou in the Thebaid. This attestation is quite late, however, and there is no other evidence to confirm or contradict it. He died in Alexandria around AD 168.

He refined and promoted the Werner map projection , a cordiform (heart-shape) projection map that had been developed by Johannes Stabius (Stab) of Vienna around 1500.

After its introduction by Werner in his 1514 book, Nova translatio primi libri geographiaae C. Ptolemaei, the Werner projection was commonly used for world maps and some continental maps through the 16th century and into the 17th century. It was used by Mercator, Oronce Fine, and 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 for instructional purposes and as a novelty.


Many consider Werner as a pioneer of modern meteorology and weather forecasting. Between 1513 and 1520, Johann Werner made the first regular observations of the weather conditions in Germany.

Problem of longitude

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... (Nürnberg 1514). The method was discussed in detail by Petrus Apianus in his Cosmographicus liber (Landshut 1524). This became known as the lunar distance method.

Notable publications


Werner Crater on the moon Werner crater 4101 h1.jpg
Werner Crater on the moon

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.

See also

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  1. Howard Eves, An Introduction to the History of Mathematics, Sixth Edition, p. 309, Thompson, 1990, ISBN   978-0-03-029558-4.
  2. Edward Rosen, Three Copernican Treatises: The Commentariolus of Copernicus, The Letter against Werner, The Narratio Prima of Rheticus , Columbia University Press, 1939