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Throughout his work, Habash compares the parameters calculated by Ptolemy for the motion of the different heavenly bodies with his own calculations and systematically modifies the composition of his tables accordingly for each one, without returning to the theoretical aspect of the geometrical models. But Habash’s most important theoretical innovation occurs in his study of the visibility of the crescent moon. This problem of the visibility of the crescent is not treated in the Greek tradition of astronomy, but some methods of calculation were elaborated in the Indian tradition.
4). Based on the reasoning in Euclid’s Elements he proves that the arcs of apparent motion observed on the ecliptic are such that G′F ′ < B ′K ′ < L ′M′ < H′I′, so that he can conclude precisely: When the motion of a heavenly body or of the centre of any orb is uniform on an eccentric, its slowest apparent motion, on the ecliptic, will be produced when the moving body is at the apogee of its eccentric, and its fastest apparent movement will occur when it is at its perigee. For the rest, apparent motion is slower when it occurs close to the apogee than when it occurs far away from it.
2. ABCD is the circle of the ecliptic, with centre E, the position of the observer; the circle MNPO, with centre G, is the eccentric orb around which the sun moves, A and C are the two equinoxes and B is the summer solstice. The figure is completed by the straight lines MQGP and NGXO parallel to DEB and AEC respectively, and the straight line EGH which intersects the eccentric orb at H, its apogee. By observing the moment at which the sun passes over A, B and C, one can obtain, by a simple calculation based on the mean movement of the sun, the value of the arcs IL, IK, KL, IN, PK, LO on the eccentric, and consequently calculate all the parameters.