The view that the stereographic projection was invented by Petrus
Apianus might be challenged.
Perhaps Lorch's "Ptolemy and Maslama on the Transformation of Circles
into Circles in Stereographic Projection", AHES 49 (1995) 3, 271-284,
could shed light on this matter. Besides, the dates given above for
Apian seem to be incorrect. According to several authoritative sources,
Petrus Apianus died at Ingolstadt on April 21, 1552.
<quote>
Petrus Apianus (also known as Peter Apian, Peter Bennewitz, Peter
Bienewitz) was born in Leisnig, Saxony in 1495. He first studied
mathematics, astronomy and the other branches of cosmography at
Leipzig and then Vienna. Prior to Cosmographia (1524), Apianus
published two cosmographical works, a compiled world map (Typus orbis
universalis) and an accompanying geographical commentary. In 1527,
Apianus was appointed Professor of Mathematics at the University
of Ingolstadt. Perhaps his most celebrated work, the Astronomicon
Caesareum, was presented to the Emperor Charles V in 1540. This
sumptuous book provided a cosmographical introduction similar to
that in the Cosmographia but in a more elaborate and elegant way.
Apianus' relationship with Charles V dated to least the early 1530's
when Apianus was granted an imperial privilege. However, it has been
suggested the young emperor may have studied cosmography under
Apianus even earlier still. Following the publication of the
Astronomicon Caesareum, Apianus was appointed court mathematician to
Charles V, and was knighted along with his three brothers. In the
following years, the success of Apianus' books and his favor with
the emperor brought him a substantial degree of wealth, prestige and
power. In 1544, he was granted special legal privileges, including
the authority to legitimize illegitimate children and to grant higher
degrees. Throughout his life, Apianus was involved in mathematical
publishing, cartography and instrument making. His instrument designs
included a new type of surveying quadrant and armillary spheres.
Apianus died in Ingolstadt at the age of 57 in 1552.
</quote>
Reference:
http://www.mhs.ox.ac.uk/students/98to99/Intro/Intropgs/Bios.html
Alfred Ross