ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

36 ASTRONOMY IN ANCIENT NATIONS method may be adopted for Venus and the three outer planets, and Nasir ed-din promises to explain the new theory of Mercury in an appendix, but this appears to have been lost. Nasir ed-din also endeavours to improve on the machinery proposed by Ptolemy to illustrate the manner in which the epicy- cle remains parallel to the plane of the ecliptic. He mentions that the celebrated Ibn al Haitham (afterwards known in the west as Alhazen, author of a well-known book on optics) had written a chapter on this subject, adding to each epicycle two spheres to account for the inclination of the diameter perigee-apogee, and two additional ones for the inferior planets for the diameter at right angles thereto.¹ Nasir ed-din makes use of the same principle which guided him in his demonstration about the motion in longitude, and he shows how in this way we may by means of two spheres make the extremities of the diameter of the epicycle move backwards and forwards along an arc of a sphere.² He claims that this arrangement is superior to that of Ptolemy by not intro- ducing any error in longitude,³ but he acknowledges that he has not been able to get rid of the strong objection to Ptolemy's auxiliary circle, viz. that the irregular motion in longitude with regard to the centre of the deferent necessitates the introduction of a corresponding irregularity in the motion on the auxiliary circle by letting the motion be uniform with regard to an equant. It baffled Nasir ed-din's ingenuity to find an arrangement of spheres which could obviate the necessity of having recourse to this expedient. All the attempts at rebellion against the Ptolemaic system had thus turned out failures. And they deserved nothing else, since it was impossible to find anything better than what Ptolemy had produced, until it was perceived that where Ptolemy was wrong was not in his mathematical methods, which were perfect, but in the fundamantal idea of the Earth being at rest. The time

1. Ibn al Haitham said that by using discs instead of spheres one might com- plete the demonstration; but Nasir ed-din objects to the arrangement (about which he gives no details) that a non-spherical system is not in accordance with the principles of astronomy.
2. It is not quite clear whether this plan is his own or is the same as Ibn al Haitham's.
3. Due to disturbance of the position of the diameter from perigee to apogee, from which the anomaly is counted.