**Johann Werner**was born in Nuremberg, Bavaria, three years before the painter and mathematician Albrecht Dürer was born in the same city. (In fact in later life Dürer consulted Werner on mathematical matters.) Werner, in later life writing about his upbringing, said that, from early childhood, he knew he would be a mathematician.

On 21 September 1484 he entered the university at Ingolstadt, also in Bavaria. The university had been founded just four years after Werner's birth; in fact this university moved to Landshut in 1800 and then to Munich in 1826 becoming the present University of Munich. After studying in Ingolstadt, Werner was appointed chaplain in Herzogenaurach in 1490. He moved to Rome in 1493 where he was ordained a priest. He returned to Nuremberg in 1497 and celebrated his first mass in the church of St Sebald on 29 April 1498. He became the parish priest at a small church in Wöhrd, just outside the city, in 1503 but by 1508 he was the priest at the Church of St John (St Johannis) in the city of Nuremberg. He continued as a priest at this church until his death in 1522. Folkerts writes [1]:-

Werner's main scientific work was on astronomy, mathematics and geography. In astronomy he followed Regiomontanus, having access to all his writings which he studied carefully, while on the practical side was a skilled maker of instruments. His instruments include astrolabes, clocks, sundials, improved versions of Jacob's staff, and instruments to solve theoretical problems in spherical astronomy. He gave a description of a cross-staff with an angular scale on the staff from which degrees could be read off. Also a skilled observer with instruments of his own and those made by others, he recorded a comet on 1 June 1500 and kept a record of observations until 24 June 1500.Werner was reputed to have been "very diligent" in carrying out all official responsibilities. Since his pastoral duties were rather limited, he devoted much time to scientific study.

Werner's most famous work on astronomy and geography is *In Hoc Opere Haec Continentur Nova Translatio Primi Libri Geographicae Cl Ptolomaei* Ⓣ written in 1514. This book contains a translation of the Ptolemy's *Geography* with a commentary by Werner himself. He gives a method to determine longitude based on eclipses of the Moon (which had been suggested earlier by Regiomontanus). In addition, Werner suggested using the position of the Moon between the stars or the distance of the Moon from the Sun to allow an absolute time to be calculated. Then a calculation of local time would give the longitude. Later Peter Apianus and Gemma Frisius adopted Werner's ideas on determining longitude but when Werner suggested these ideas they were not really practical as sufficiently precise ephemeres could not be prepared. Werner suggested using for these measurements a cross-staff of the type which sailors already used for determining the latitude of a ship at sea by measuring the height of the pole star. Werner wrote:-

In mathematics Werner worked on spherical trigonometry and conic sections. A work on spherical triangles was not published during his lifetime but was published in 1907 around 400 years after it was written. He was the first to use the formulaOur aim is to find the distance in longitude between two distant places. The geographer will be in one of these places and will measure with a cross-staff the distance of the Moon from a star on the Ecliptic. If then we divide this distance by the velocity of the Moon per hour, we will know at what time in the future the Moon will be in conjunction with this body.

2sin(as an aid to calculation. This was used by Rheticus and Brahe and others up to the invention of logarithms.a)sin(b) = cos(a-b) - cos(a+b)

Some historians have suggested that Werner was the last writer in the medieval tradition of conic sections to produce anything original. He seems to have based his ideas on work by Giorgio Valla, on the *Speculi almukefi compositio* (in Regiomontanus's version), as well as on the short but influential anonymous work *De duabus lineis* Ⓣ whch had been translated by Johannes of Palermo, a member of Frederick II's court along with Fibonacci in the early thirteenth century. Werner's selection of the particular parts of the material to be included in his own work was largely based on what he needed for those parts of his omnibus volume of 1522 on the duplication of the cube and the section of the sphere. Werner's work was not much cited at the time but this is most likely because a translation of the *Conics* of Apollonius soon led to it being superfluous. His work on the duplication of the cube was not original but simply collected eleven methods which were known to the ancient Greeks. Perhaps of more interest is a series of twelve supplementary notes to this work. In one of these he shows that light is focused by a parabolic mirror.

Werner studied several other topics and we mention one, namely weather forecasting. Between 1513 and 1520, he made the first regular observations of the weather conditions in Germany. *Regula aurea de aeris dispositione diiudicanda singulis diebus*, one of several works which were published after his death, appeared in manuscript in 1546 and has never been printed. It contained:-

Many consider Werner as a pioneer of modern meteorology and weather forecasting.... guidelines that explain the principles and observations of the changes in the atmosphere.

**Article by:** *J J O'Connor* and *E F Robertson*

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