Le “Commentaire” d'Hipparque II. Position de 78 étoiles
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The following paper is the second part of a study devoted to the only preserved work of Hipparchus, his Commentary to Aratus. The first part, published in 1984, was based on the hypothesis that Hipparchus wrote his treatise with the help of a mobile sphere and led us to the determination of some features of that instrument. The coordinates of 78 stars, which are given below, have been obtained on the basis of the same hypothesis and using results already published. The stars selected are those for which the text connects numerical data to at least two events out of rising, setting or culmination. An analysis of the positions shows that the stars have been located on the sphere in an equatorial frame slightly different from the rotation axis frame. Statistical data processing shows that the stars were plotted on the sphere as circles rather than as points: the celestial coordinates of the stars are then those of the center of the disc, whose radius was determined. The position of a few stars could be evaluated thanks to the determination of an approximate value of the cubit used by Hipparchus. Lastly, the time of the observations was confirmed to be −140±25 years.
The study confirms the basic hypothesis and throws light on the part played by the mobile sphere when the heavens are being described. It gives a better idea of the difficulties of constructing the instrument and of the ways of using it; a more detailed model of Hipparchus' mobile sphere will allow a more thorough investigation of all stars mentioned in the Commentary.
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