propinquity:

nearness in place; proximity.

 

overrunnings of the frame (from 1500): * see EndNote <A>

reference to the development of perspective by Faustian artists, beyond linear & aerial perspective, in particular to Caravaggio.

 

Polygnotus:

see Chapter III page 112, Chapter VII page 243 

 

Hipparchus (fixed celestial sphere):

greatest of the Greek astronomers, his quantitative & accurate models for the motion of the Sun & Moon have survived.  He was able to predict solar eclipses; he possibly invented the astrolabe & the armillary sphere (used for his star catalogue).  His geocentric model was based in observation not philosophical aesthetics.  He compiled a star catalogue recording the position & brightness of the stars.  He also discovered the Precession of the Equinoxes (the slow motion of the place of the equinoxes through the zodiac, caused by the shifting of the Earth's axis).  Hipparchus believed this was caused by the motion of the sphere of fixed stars.

see Chapter I, page 9

Copernicus:

see Chapter II, page 68

 

Copernicus ( and Pythagoras):

Spengler sets Pythagoras (569-475 BC) in the Summer period of the Apollonian Culture.  Likewise he attributes Copernicus (1473-1543), the astronomer who formulated the heliocentric  model of the universe, to the Faustian Summer.

 

Kepler (laws of planetary orbits as revelation):

1571-1630; key figure in the scientific revolution, famous for the discovery of planetary motion.  This consists of 3 scientific laws describing the motion of planets around the Sun (published 1609 to 1619).  They improve the heliocentric theory of Copernicus by replacing circular orbits & epicycles with elliptical trajectories; he also explained how planetary velocities vary.  Kepler incorporated religious arguments into his work, motivated by the religious conviction & belief that God created the world according to an intelligible plan accessible through the natural light of reason.  In his religious view of the cosmos, the Sun (a symbol of God the Father) was the source of motive force in the Solar System.  He purportedly said: "I am merely thinking God's thoughts after Him"

and see Chapter II, page 71, Chapter IV, page 147

 

Viking (infinity-wistfulness): * see EdnNote<B>

possible reference to Viking exploration or Viking myths (the Nibelungenlied) with a somewhat melancholic & tragic slant (the murder of the hero & queen, and end & destruction of the kingdom/world).  Viking sailors & traders are famous for their exploration, long before Columbus.  The Vikings enjoyed several technological innovations, notably developments in sailing technology (use of larger sails, tacking practices, and 24-hour sailing) allowed Viking sailors to travel much further.

 

telescope (discovery):

the earliest known telescope appeared in 1608 in the Netherlands, when a patent was submitted by Hans Lippershey (an eyeglass maker).  News of the invention spread across Europe.  The design of these early refracting telescopes consisted of a convex objective lens & a concave eyepiece.  Galileo improved on this design in 1609 & applied it to astronomy.  In 1611, Kepler described how a far more useful telescope could be made with a convex objective lens and a convex eyepiece lens. By 1655, astronomers such as Christiaan Huygens were building powerful but unwieldy Keplerian telescopes with compound eyepieces.

 

“vault" of heaven:

the apparent surface of the imaginary sphere on which celestial bodies appear to be projected; the celestial spheres were the fundamental entities of the cosmological models (as developed by Plato, Eudoxus, Aristotle, Ptolemy); Aristotle, drawing on Eudoxus, proposed that the universe was made of a complex system of concentric spheres, whose circular motions combined to carry the planets around the earth; the apparent motions of the fixed stars & planets was accounted for by treating them as embedded in rotating spheres made of an ethereal (a transparent 5th element, quintessence).  As the fixed stars did not change their positions relative to one another they must be on the surface of a single starry sphere (or vault)