The present study aims to evaluate the accuracy of the values obtained in the medieval Islamic astronomy for the Venus’ eccentricity. With transforming the heliocentric orbital elements of the planet to its geocentric ones, the below polynomials as a function of the time (counted in Julian days) remained to or elapsed from 1 January 2000 are produced for the geocentric eccentricities of the deferent e₁ and of the equant e₂, and the longitude A of the apogee (the radius of orbit R = 1):

e₁ = 0.01263567028 – 0.0003177437352 · t – 0.000003472804123 · t²

e₂ = 0.01641895960 – 0.0003272424646 · t – 0.00002041205570 · t²

A = 92.25290697 + 18.78218517 · t + 0.05501188560 · t² – 0.00007412766659 · t³.

Since the eccentricity of the Earth/Sun remains more than two times as large as the Venus’ heliocentric eccentricity, e₁ and e₂ are both much related to the first. Due to the smallness of the Venus’ heliocentric eccentricity, the geocentric apsidal line of the Venus remains closer to the Earth’s apsidal line than that of any other planet: the angle between them changes from 13.8° in AD 0 to 10.7° in AD 2000. e₁ and e2 decrease with the passage of time. Nevertheless, since the rate of decrease is negligible (≈ 3·10⁻⁴ in a millennium or about 0;1 in a millennium with the Ptolemaic norm R = 60), the ratio e₁/e₂ remains nearly constant, ~0.8, during the two millennia.

Ptolemy found out e = e₁ = e₂ = 1;15 (the orbit’s radius R = 60) and the Venus’ apogee remains behind the solar apogee. The early Islamic astronomers believed that Venus’ apsidal line coincides with that of the sun/Earth, and their maximum equations of centre (namely, their eccentricities) are identical. The idea roots in Indian astronomy and penetrated into Islamic astronomy through pre-Islamic Persian astronomy. Since the geocentric apsidal line of Venus is very close to the solar/Earth’s apsidal line, it is imaginable that somewhere (either in Indian astronomy or its Greek antecedents) the careless observations would have resulted that the two coincide with each other (perhaps, to distinguish between the directions of the two may be counted as another contribution of Ptolemy to the planetary astronomy). The idea was rendered obsolete in Islamic astronomy after the 11th century.

Whether or not the values adopted for the Venus’ eccentricity in the Islamic astronomical tables are equal to half the solar eccentricity, they are between 1;2 and 1;3, and remain very close to the solar/Earth’s eccentricity at the time. The only exception is Ulugh Beg’s remarkable value 0;52 which is close to the average of the values of e₁ and e₂ at the time. Nevertheless, to hold the opinion of the Venus’ eccentricity being lesser than the Sun’s may be considered as an achievement of the late Islamic astronomy.