the accuracy of the solar eccentricities measured during islamic medieval period

introducing three principal methods of determining the solar orbital eccentricity in the ancient and medieval astronomy (i.e., the method of seasons, of mid-signs, of three–points), the accuracy of the results obtained from each is being investigated. in doing so, two main goals have been targeted: (1) to determine the accuracy and the intrinsic limitation of each method with regard to their structural sensitivities to the input data; (2) to determine the accuracy of the historical magnitudes measured by each method for the solar eccentricity during the islamic medieval period. for the first, it has quantitatively been resulted that the method of three–points is the most accurate, while the method of seasons is the most sensitive. being aware of this fact, the medieval astronomers attempted, with the passage of time, to substitute the more accurate method for the less accurate one. as a result, the method of three–points became the standard method of determining the solar eccentricity. for the latter, comparing the historical values for the solar eccentricity with the true ones, it may be seen, as desired, that the mean errors and the divergences of the values resulted from the method of seasons are much more, while two other methods keep the results convergent and congruent. nevertheless, the method of three points is of high accuracy, but, surprisingly, the most accurate recorded value for the solar eccentricity during islamic period, measured by abū rayhān al-bīrūnī in the year 385 yazdigird 1016 a.d., comes from the method of season. the values attributed to marwarūdhī and nayrīzī, and that mentioned by khāzinī are of less accuracy. the more accurate value adopted in the islamic astronomical tables (zīj literature) is of ulugh beg’s sultānī zīj. nevertheless, the majority of the solar eccentricity measurements by the medieval astronomers are more accurate than that of copernicus in the sixteenth century.