Johannes Werner (cartographer)

from Wikipedia, the free encyclopedia
Johannes Werner

Johannes Werner or Johann Werner ( Latin Ioannes Vernerus ; born February 14, 1468 in Nuremberg ; † May 1522 ibid) was a German pastor, mathematician , astronomer , astrologer , geographer and cartographer .

Werner studied theology and mathematics in Ingolstadt from 1484 . In 1490 he became a chaplain in Herzogenaurach . From 1493 to 1497 he stayed in Rome . In 1503 he was appointed vicar at the church in Nuremberg's suburb Wöhrd . He then became a pastor at the Johanniskirche in Nuremberg, a position he held until his death. Emperor Maximilian I appointed him imperial chaplain. The IAU honored him with the lunar crater Werner and the UK Antarctic Place-Names Committee with the naming of Werner Peak .

Astronomer / astrologer, mathematician

Inspired by Regiomontanus , Johann Werner dealt with observational astronomy. He continued the systematic observations of the planets that Regiomontanus and Bernard Walther had begun. He discovered a comet on June 1, 1500, which he followed until the 24th of the month. His trepidation theory to describe the precession of the equinoxes in De motu octauæ Sphæræ was attacked by Nicolaus Copernicus , in his " Letter to Werner ". In addition, he was a skilled instrument maker. He further developed the Jacob's staff introduced into astronomy by Regiomontanus and invented an instrument for solving problems of spherical trigonometry, the meteoroscope, about which he left a manuscript.

Werner was also active as astrology. He provided horoscopes for many Nuremberg citizens. His weather observations, which were carefully carried out over many years and published by Johannes Schöner in 1546 , are also entirely in the tradition of astrology.

In mathematics, he dealt with spherical trigonometry and conic sections . On behalf of the bell founder Sebald Behaim, he had written a (not preserved) translation of the elements of Euclid from the Greek original into German, in which a practical example was added to each proposition. Werner and Willibald Pirckheimer advised their friend Albrecht Dürer on theoretical as well as practical problems in mathematics.

The prostaphairetic method

Werner discovered that the formula

can be used to simplify the multiplication. This so-called prostaphairetic method was often used until the invention of the logarithms , among others by Rheticus and Brahe . In English these algorithms are called Werner Formulas .

First, the two factors are represented as sine values ​​by multiplication or division with suitable powers of ten, and the corresponding angles are looked up in a trigonometric table . Then you determine the sum and the difference of the two angles, look up the cosine values, calculate the difference between these values ​​and divide the result by two. Finally, the original multiplication or division by the powers of ten is reversed.

Length problem

To solve the longitude problem in navigation , it was proposed to use the distance from stars to the moon . This method was first mentioned by Werner in his translation of the first book of Ptolemaic Geography (Nuremberg 1514), but only gained attention when Peter Apian discussed it in more detail in his Cosmographicus liber… (Landshut 1524).

cartographer

The earth represented by means of the Stab-Werner projection

However, he achieved his most important achievement together with Johannes Stabius in the field of cartography with the first true-to-area representation of the globe. This so-called Stab-Werner heart-shaped projection was not published in print until 1514, but was already used by Martin Waldseemüller for his world map from 1507. This projection was widely used in the first half of the 16th century, but was then replaced by the Mercator projection .

The calculation of sundials is based on a similar projection task. Together with Johannes Stabius , he calculated the sundial on the east choir of the Lorenz Church in Nuremberg.

Fonts

  • Nova translatio primi libri geographiae Cl. Ptolomaei: quae quidem translatio verbum: habet e verbo fideliter expressum.
  • Libellus de quattuor terrarum orbis in plano figurationibus. Nuremberg 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. Petrejus, Nuremberg 1522. ( online )
  • In hoc opere haec continentur Libellus Ioannis Verneri Nurembergen. super viginti duobus elementis conicis: Eiusd. comment. in 11 modos conficiendi cubi. Eiusd. comment. in Dionysodori problema. Alius modus idem problema conficiendi Eiusd. Ionnnis Verneri de motu octavae sphaerae tractatus duo. Eiusd. summaria enarratio theoricae motus octavae sphaerae. Peypus Publishing House, 1522.
  • De Triangulis sphaericis libri quatuor de meteoroscopiis libri sex ( online ).
  • 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.
  • Ioannis Vernereti Animadversiones in Michael Poletum, 1575 ( online in the Google book search).
  • Ichneumon, 1602 ( online in Google book search).

expenditure

  • Ioannis Verneri de triangulis sphaericis libri quatuor, de meteoroscopiis libri sex. Teubner, Leipzig 1907–1913 (critical edition)

literature

Web links

Commons : Johannes Werner  - Collection of images, videos and audio files

Individual evidence

  1. ↑ See for example: Hans Kaiser, Wilfried Nöbauer: Geschichte der Mathematik, Vienna 1998, p. 93.
personal data
SURNAME Werner, Johannes
ALTERNATIVE NAMES Vernerus, Ioannes
BRIEF DESCRIPTION German pastor, mathematician, astronomer, astrologer, geographer and cartographer
DATE OF BIRTH February 14, 1468
PLACE OF BIRTH Nuremberg
DATE OF DEATH May 1522
Place of death Nuremberg