The Klein disk ( K, in the picture ) is a gnomonic projection of the hyperboloid model ( Hy ) with as center the center of the hyperboloid ( O ) and the projection plane tangent to the nearest point of the hyperboloid.
22.
This gnomonic technique also provides a mathematical proof that the sum of the first " n " odd numbers is " n " 2; the figure illustrates 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64 = 8 2.
23.
The topics covered are computation of mean and true longitudes of planets, Earth and celestial spheres, fifteen problems relating to ascension, declination, longitude, etc ., determination of time, place, direction, etc ., from gnomonic shadow, eclipses, Vyatipata ( when the sun and moon have the same declination ), visibility correction for planets and phases of the moon.
