Johannes Werner
Encyclopedia
Nuremberg
Nuremberg[p] is a city in the German state of Bavaria, in the administrative region of Middle Franconia. Situated on the Pegnitz river and the Rhine–Main–Danube Canal, it is located about north of Munich and is Franconia's largest city. The population is 505,664...
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
– May 1522) (also Ioannis Vernerus) was a German
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
parish
Parish
A parish is a territorial unit historically under the pastoral care and clerical jurisdiction of one parish priest, who might be assisted in his pastoral duties by a curate or curates - also priests but not the parish priest - from a more or less central parish church with its associated organization...
priest
Priest
A priest is a person authorized to perform the sacred rites of a religion, especially as a mediatory agent between humans and deities. They also have the authority or power to administer religious rites; in particular, rites of sacrifice to, and propitiation of, a deity or deities...
in Nuremberg
Nuremberg
Nuremberg[p] is a city in the German state of Bavaria, in the administrative region of Middle Franconia. Situated on the Pegnitz river and the Rhine–Main–Danube Canal, it is located about north of Munich and is Franconia's largest city. The population is 505,664...
and a mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. His primary work was in astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, and geography
Geography
Geography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...
, although he was also considered a skilled instrument maker
Tool
A tool is a device that can be used to produce an item or achieve a task, but that is not consumed in the process. Informally the word is also used to describe a procedure or process with a specific purpose. Tools that are used in particular fields or activities may have different designations such...
.
Mathematics
His mathematical works were in the areas of spherical trigonometryTrigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
, as well as conic section
Conic section
In mathematics, a conic section is a curve obtained by intersecting a cone with a plane. In analytic geometry, a conic may be defined as a plane algebraic curve of degree 2...
s. He published an original work on conic sections in 1522 and is one of several mathematicians sometimes credited with the invention of prosthaphaeresis
Prosthaphaeresis
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...
, which simplifies tedious computations by the use of trigonometric formulas, sometimes called Werner's formulas.
Astronomy
In 1500 he observed a cometComet
A comet is an icy small Solar System body that, when close enough to the Sun, displays a visible coma and sometimes also a tail. These phenomena are both due to the effects of solar radiation and the solar wind upon the nucleus of the comet...
, and kept observations of its movements from June 1 until the 24th.
This work further developed the suggestion of Regiomontanus
Regiomontanus
Johannes Müller von Königsberg , today best known by his Latin toponym Regiomontanus, was a German mathematician, astronomer, astrologer, translator and instrument maker....
that the occurrences of eclipse
Eclipse
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...
s and cometary orbits could be used to find longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
, 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
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 particular, it refers to the gradual shift in the orientation of Earth's axis of rotation, which, like a wobbling top, traces out a pair of cones joined...
De motu octauæ Sphær was posthumously challenged in 1524 by Nicolaus Copernicus
Nicolaus Copernicus
Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....
in The Letter against Werner.
Geography
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)Geographia (Ptolemy)
The Geography is Ptolemy's main work besides the Almagest...
, written by Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
.
He refined and promoted the Werner map projection, a cordiform (heart-shape) projection map that had been developed by Johannes Stabius
Johannes Stabius
Johannes Stabius was an Austrian cartographer of Vienna who developed, around 1500, the heart-shape projection map later developed further by Johannes Werner. It is called the Werner map projection, but also the Stabius-Werner or the Stab-Werner projection...
(Stab) of Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...
around 1500.
After its introduction by Werner in his 1514 book, Nova translatio primi libri geographiaae C. Ptolemaei, the Werner projection
Werner projection
The Werner projection is a pseudoconic equal-area map projection sometimes called the Stab-Werner or Stabius-Werner projection. Like other heart-shaped projections, it is also categorized as cordiform...
was commonly used for world map
Map
A map is a visual representation of an area—a symbolic depiction highlighting relationships between elements of that space such as objects, regions, and themes....
s and some continental maps through the 16th century and into the 17th century. It was used by Mercator
Gerardus Mercator
thumb|right|200px|Gerardus MercatorGerardus Mercator was a cartographer, born in Rupelmonde in the Hapsburg County of Flanders, part of the Holy Roman Empire. He is remembered for the Mercator projection world map, which is named after him...
, Oronce Fine
Oronce Finé
Oronce Fine was a French mathematician and cartographer.-Life:...
, and Ortelius in the late 16th century for maps of Asia
Asia
Asia is the world's largest and most populous continent, located primarily in the eastern and northern hemispheres. It covers 8.7% of the Earth's total surface area and with approximately 3.879 billion people, it hosts 60% of the world's current human population...
and Africa
Africa
Africa is the world's second largest and second most populous continent, after Asia. At about 30.2 million km² including adjacent islands, it covers 6% of the Earth's total surface area and 20.4% of the total land area...
. By the 18th century, it was replaced by the Bonne projection
Bonne projection
A Bonne projection is a pseudoconical equal-area map projection, sometimes called a dépôt de la guerre or a Sylvanus projection. Although named after Rigobert Bonne , the projection was in use prior to his birth, in 1511 by Sylvano, Honter in 1561, De l'Isle before 1700 and Coronelli in 1696.The...
for continental maps. The Werner projection is only used today for instructional purposes and as a novelty.
Meteorology
Many consider Werner as a pioneer of modern meteorologyMeteorology
Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...
and weather forecasting.
Between 1513 and 1520, Johann Werner made the first regular observations of the weather
Weather
Weather is the state of the atmosphere, to the degree that it is hot or cold, wet or dry, calm or stormy, clear or cloudy. Most weather phenomena occur in the troposphere, just below the stratosphere. Weather refers, generally, to day-to-day temperature and precipitation activity, whereas climate...
conditions in Germany.
Problem of longitude
To determine longitudeLongitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
in navigation
Navigation
Navigation is the process of monitoring and controlling the movement of a craft or vehicle from one place to another. It is also the term of art used for the specialized knowledge used by navigators to perform navigation tasks...
, 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
Petrus Apianus
Petrus Apianus , also known as Peter Apian, was a German humanist, known for his works in mathematics, astronomy and cartography.The lunar crater Apianus and minor planet 19139 Apian are named in his honour....
in his Cosmographicus liber (Landshut 1524). This became known as the lunar distance method.
Notable publications
- In hoc opere haec continentur Nova translatio primi libri geographiae Cl. Ptolomaei: quae quidem translatio verbum: habet e verbo fideliter expressum. 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; de motu octauæ Sphæræ, Tractatus duo. Summaria enarratio Theoricæ motus octau Sphæræ., Nürnberg, Petrejus 1522
- De Triangulis sphaericis libri quatuor de meteoroscopiis libri sex, http://www.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
Honours
The crater WernerWerner (crater)
Werner is a prominent lunar impact crater that lies in the rugged south-central highlands of the Moon. It is almost joined with the crater Aliacensis to the southeast, and the pair form a rugged valley in the intervening gap. Due west of Werner is the distorted Regiomontanus, and to the north is...
on the Moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
is named after him.
Some of the trigonometric identities used in prosthaphaeresis
Prosthaphaeresis
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...
, an early method for rapid computation of products, were named Werner formulas in honor of Werner's role in development of the algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
.