The tittle of this blog post is a play on the names of a father and son duo of influential sixteenth century Renaissance mathematici. The father was Peter Bienewitz born 16 April 1495 in Leisnig in Saxony just south of Leipzig. His father was a well off shoemaker and Peter was educated at the Latin school in Rochlitz and then from 1516 to 1519 at the University of Liepzig. It was here that he acquired the humanist name Apianus from Apis the Latin for a bee, a direct translation of the German Biene. From now on he became Petrus Apianus or simply Peter Apian.
In 1519 he went south to the University of Vienna to study under Georg Tannstetter a leading cosmographer of the period.
Tannstetter was a physician, mathematician astronomer and cartographer, who studied mathematics at the University of Ingolstadt under Andreas Stiborius and followed Conrad Celtis and Stiborius to Vienna in 1503 to teach at Celtis’ Collegium poetarum et mathematicorum. The relationship between teacher and student was a very close one. Tannstetter edited a map of Hungary that was later printed by Apian and the two of them produced the first printed edition of Witelo’s Perspectiva, which was printed and published by Petreius in Nürnberg in 1535. This was one of the books that Rheticus took with him to Frombork as a gift for Copernicus.
In 1520 Apian published a smaller updated version of the Waldseemüller/ Ringmann world map, which like the original from 1507 named the newly discovered fourth continent, America. Waldseemüller and Ringmann had realised their original error and on their 1513 Carte Marina dropped the name America, However, the use by Apian and by Johannes Schöner on his 1515 terrestrial globe meant that the name became established.
Apian graduated BA in 1521 and moved first to Regensburg then Landshut. In 1524 he printed and published his Cosmographicus liber, a book covering the full spectrum of cosmography – astronomy, cartography, navigation, surveying etc. The book became a sixteenth century best seller going through 30 expanded editions in 14 languages but after the first edition all subsequent editions were written by Gemma Frisius.
In 1527 Apian was called to the University of Ingolstadt to set up a university printing shop and to become Lektor for mathematics. He maintained both positions until his death in 1552.
In 1528 he printed Tannstetter’s Tabula Hungariaethe earliest surviving printed map of Hungary. In the same year Apian dedicated his edition of Georg von Peuerbach’s New Planetary Theory to his “famous teacher and professor for mathematics” Tannstetter.
One year earlier he published a book on commercial arithmetic, Ein newe und wolgegründete underweisung aller Kauffmanns Rechnung in dreyen Büchern, mit schönen Regeln und fragstücken begriffen(A new and well-founded instruction in all Merchants Reckoning in three books, understood with fine rules and exercises). It was the first European book to include (on the cover), what is know as Pascal’s triangle, which was known earlier to both Chinese and Muslim mathematicians.
This is one of the volumes lying on the shelf in Holbein’s painting The Ambassadors. Like his Cosmographicusit was a bestseller.
In the 1530s Apian was one of a group of European astronomers, which included Schöner, Copernicus, Fracastoro and Pena, who closely observed the comets of that decade and began to question the Aristotelian theory that comets are sublunar meteorological phenomena. He was the first European to observe and publish that the comet’s tail always points away from the sun, a fact already known to Chinese astronomers. Fracastoro made the same observation, which led him and Pena to hypothesise that the comet’s tail was an optical phenomenon, sunlight focused through the lens like translucent body of the comet. These observations in the 1530s led to an increased interest in cometary observation and the determination in the 1570s by Mästlin, Tycho and others that comets are in fact supralunar objects.
Through the Cosmographicus he became a favourite of Karl V, the Holy Roman Emperor, and Apian became the Emperor’s astronomy tutor. Karl granted him the right to display a coat of arms in 1535 and knighted him in 1541. In 1544 Karl even appointed him Hofpfalzgraf (Imperial Count Palatine), a high ranking court official.
Apian’s association with Karl led to his most spectacular printing project, one of the most complicated and most beautiful books published in the sixteenth century, his Astronomicum Caesareum (1540). This extraordinary book is a presentation of the then Standard Ptolemaic astronomy in the form of a series of highly complex and beautifully designed volvelles. A vovelle or wheel chart is a form of paper analogue computer. A series of rotating paper discs mounted on a central axis or pin that can be used to calculate various mathematical functions such as the orbital positions of planets.
The Astronomicum Caesareumcontains two volvelles for each planet, one to calculate its longitude for a given time and one to calculate its latitude.
There is also a calendar disc to determine the days of the week for a given year.
Finally there are vovelles to determine the lunar phases as well as lunar and solar eclipse.
Johannes Kepler was very rude about the Astronomicum Caesareum, calling it a thing of string and paper. Some have interpreted this as meaning that it had little impact. However, I think the reverse is true. Kepler was trying to diminish the status of a serious rival to his endeavours to promote the heliocentric system. Owen Gingerich carried out a census of 111 of the approximately 130 surviving copies of the book and thinks that these represent almost the whole print run. This book is so spectacular and so expensive that the copies rarely got seriously damaged of thrown away.
Like other contemporary mathematici Apian designed sundials and astronomical instruments as well as marketing diverse volvelles for calculation purposes. Apian died in 1552 and was succeeded on his chair for mathematics by his son Philipp, the second of the bees from Ingolstadt.
Philipp Apian was born 14 September 1531, as the fourth of fourteen children (nine sons and five daughters) to Peter Apian and his wife Katharina Mesner.
He started receiving tuition at the age of seven together with Prince Albrecht the future Duke of Bavaria, who would become his most important patron.
He entered the University of Ingolstadt at the age of fourteen and studied under his father until he was eighteen. He completed his studies in Burgundy, Paris and Bourges. In 1552 aged just 21 he inherited his fathers printing business and his chair for mathematics on the University of Ingolstadt. As well as teaching mathematics at the university, which he had started before his father died, Philipp studied medicine. He graduated in medicine several years later during a journey to Italy, where he visited the universities of Padua, Ferrara and Bolgna.
In 1554 his former childhood friend Albrecht, now Duke of Bavaria, commissioned him to produce a new map of Bavaria. During the summers of the next seven years he surveyed the land and spent the following two years drawing the map. The 5 metres by 6 metres map at the scale of 1:45,000, hand coloured by Bartel Refinger was hung in the library of the Bavarian palace.
In 1566 Jost Amman produced 24 woodblocks at the smaller scale of 1:144,000, which Apian printed in his own print shop. Editions of this smaller version of the map continued to be issued up to the nineteenth century.
In 1576 he also produced a terrestrial globe for Albrecht. Map, woodblocks, woodblock prints and globe are all still extant.
In 1568 Phillip converted to Protestantism and in the following year was forced by the Jesuit, who controlled the University of Ingolstadt to resign his post. In the same year, he was appointed professor for mathematics at the Protestant University of Tübingen. In Tübingen his most famous pupil was Michael Mästlin, who succeeded him as professor for mathematics at the university and would become Johannes Kepler’s teacher. An irony of history is that Philipp was forced to resign in Tübingen in 1583 for refusing to sign the Formal of Concord, a commitment to Lutheran Protestantism against Calvinism. He continued to work as a cartographer until his death in 1589.
There is a genealogy of significant Southern German Renaissance mathematici: Andreas Stiborius (1464–1515) taught Georg Tannstetter (1482–1535), who taught Peter Apian (1495–1552), who taught Philipp Apian (1531–1589), who taught Michael Mästlin (1550–1631), who taught Johannes Kepler (1571–1630)