Editing Pope Sylvester II (section)

===Armillary sphere and sighting tube===
Although lost to Europe since the terminus of the [[Greco-Roman]] era, Gerbert reintroduced the astronomical [[armillary sphere]] to Latin Europe via the Islamic civilization of Al-Andalus, which was at that time at the "cutting edge" of civilization.{{sfnp |Tester|1987| pp=130–131}}<ref>{{harvtxt|Darlington|1947|pp=467–472}}.</ref> The details of Gerbert's armillary sphere are revealed in letters from Gerbert to his former student and monk Remi of [[Trier|Trèves]] and to his colleague Constantine, the [[abbot]] of [[Micy Abbey|Micy]], as well as the accounts of his former student and French nobleman Richer, who served as a monk in [[Rheims]].<ref>{{harvtxt|Darlington|1947|pp=464, 467–472}}.</ref> Richer stated that Gerbert discovered that stars coursed in an oblique direction across the night sky.<ref name="darlington 467">{{harvtxt|Darlington|1947|p=467}}.</ref> Richer described Gerbert's use of the armillary sphere as a visual aid for teaching mathematics and astronomy in the classroom.

[[Image:Sandro Botticelli 052.jpg|thumb|right|upright|An [[armillary sphere]] in [[Saint Augustine in His Study (Botticelli, Ognissanti)|a painting]] by [[Sandro Botticelli]], {{Circa|1480}}]]

Historian Oscar G. Darlington asserts that Gerbert's division by 60 degrees instead of 360 allowed the lateral lines of his sphere to equal to six degrees.<ref name="darlington 468">{{harvtxt|Darlington|1947|p=468}}.</ref> By this account, the [[polar circle]] on Gerbert's sphere was located at 54 degrees,  several degrees off from the actual 66° 33'.<ref name="darlington 468"/> His positioning of the [[Tropic of Cancer]] at 24 degree was nearly exact, while his positioning of the [[equator]] was correct by definition.<ref name="darlington 468"/> Richer also revealed how Gerbert made the planets more easily observable in his armillary sphere:

{{Blockquote|He succeeded equally in showing the paths of the planets when they come near or withdraw from the earth. He fashioned first an armillary sphere. He joined the two circles called by the Greeks ''coluri'' and by the Latins ''incidentes'' because they fell upon each other, and at their extremities he placed the poles. He drew with great art and accuracy, across the ''colures'', five other circles called parallels, which, from one pole to the other, divided the half of the sphere into thirty parts. He put six of these thirty parts of the half-sphere between the pole and the first circle; five between the first and the second; from the second to the third, four; from the third to the fourth, four again; five from the fourth to the fifth; and from the fifth to the pole, six. On these five circles he placed obliquely the circles that the Greeks call ''loxos'' or ''zoe'', the Latins ''obliques'' or ''vitalis'' (the zodiac) because it contained the figures of the animals ascribed to the planets. On the inside of this oblique circle he figured with an extraordinary art the orbits traversed by the planets, whose paths and heights he demonstrated perfectly to his pupils, as well as their respective distances.{{sfnp |Darlington|1947| pp=468–469}}}}

Richer wrote about another of Gerbert's last armillary spheres, which had sighting tubes fixed on the axis of the hollow sphere that could observe the constellations, the forms of which he hung on iron and copper wires.<ref name="darlington 469">{{harvtxt|Darlington|1947|p=469}}.</ref> This armillary sphere was also described by Gerbert in a letter to his colleague Constantine.<ref name="darlington 469 470">{{harvtxt|Darlington|1947|pp=469–470}}.</ref> Gerbert instructed Constantine that, if doubtful of the position of the [[pole star]], he should fix the sighting tube of the armillary sphere into position to view the star he suspected was it, and if the star did not move out of sight, it was thus the pole star.<ref name="darlington 470">{{harvtxt|Darlington|1947|p=470}}.</ref> Furthermore, Gerbert instructed Constantine that the north pole could be measured with the upper and lower sighting tubes, the Arctic Circle through another tube, the Tropic of Cancer through another tube, the equator through another tube, and the [[Tropic of Capricorn]] through another tube.<ref name="darlington 470"/>