From Riemann Manifolds to Riemann Manifolds - Map Projections: Cartographic Information Systems - page 82

According to the documents of Synesius (378-430), bishop
of Ptolemaios, as well as of Prokius Diadochus (412-485),
a philosopher in Athens, the stereographic projection origi-
nates from Hipparch (180-125 B. C.), astronomer in Nicaea
(Bythinia). His planisphere shows the celestial sphere in a
polar stereographic projection. For the use of terrestrial
charts the stereographic projection has been used for the
first time by Walter Lude (1507), canonicus in Lothrin-
gen. While his choice was polar projection, J. Stab and J.
Werner (1514), respectively, used an arbitrary placement of
the projection plane, finally Gemma Frisius (1540) its equa-
torial placement. The particular properties of the stereo-
graphic projection, namely conformality and the circular
map of parallel circles of the sphere, has been recognized
only later: Jordanius Nemorarius (1507) mentioned the cir-
cularity of transformal parallel circles. Gerhard Mercator
(1587) invented conformality in his Duisburg map of the
eastern and western half spheres in stereographic projec-
tion. At the bottom line of his map he writes: “. . . Etsi
enim gradus a centro versus circumferentiam crescant, uti
in gradibus aeqhimoctialibus vides, tamem latitudinis lon-
gitudinisque gradus in eadem a centro distantia eandem ad
invicem proportionem servant quam in sphaera et quad-
ranguli inter duos proximos parallelos dusque meridianos
rectangulam figuram habent quemadmodum in sphaera, ita
ut regiones undiquaque omnes motivam figuram obtineant
sine omni tortuosa distractione.” (Indeed though the dis-
tances grow from the center to the periphery as to be
seen from the lines of constant aequinoctium, they pre-
serve the lengths of longitude and latitude arcs in rela-
tive proportion with respect to the sphere. Quadrangles
between to nearly parallels and two meridians are repre-
sented by a rectangular figure like on the sphere such that
all areas keep their natural figure without distortions.) The
name stereographic projection originates from the mathe-
matician Aguilonius(1566-1617) of Belgium. Compare with
Fig. 1.28 , which gives an impression of a typical ancient
map.