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

ARABIAN ASTRONOMERS AND PTOLEMAIC SYSTEM 39 (cerco del levador¹), as in Ptolemy's theory of Mercury, which the authors would seem to have extended to the planets, omitting the motion of the centre of the deferent on a small circle; this, they have, however, correctly given in the case of Mercury.² There is a very curious figure³ of the deferent of Mercury in the form of an ellipse (the axes being as 6 to 5 nearly), with what looks like the Sun in the centre. This curve has been construc- ted from a number of small circular arcs,⁴ and it is obviously nothing but the curve described by the centre of the epicycle of Mercury in Ptolemy's theory. For according to the latter the centre of the deferent describes a small circle with radius = 1/21 of that of the deferent, in direction from east to west, in the same time which the centre of the epicycle takes to pass round the cir- cumference of the deferent from west to east. This makes the cen- tre of the epicycle describe a closed curve resembling an ellipse, the axes of which are in the ratio 11: 10, almost exactly the same as in the Spanish diagram, and there is therefore in the latter no antici- pation whatever of Kepler's great discovery, since in the case of the inferior planets it is the epicycle which is the real orbit.⁵ The small sun-like object in the centre of the ellipse represents the centre of Ptolemy's small circle, and it has either been inser- ted in the manuscript centuries after the essay had been written, or, more likely, it has been caused by a small blot on the place in the parchment where the stationary leg of the draughtsman's compasses had made a small hole. An oval deferent of Mercury occurs in several books published in the sixteenth and seven- teenth centuries.⁶

1. Vol. III. pp. 246—253.
2. Vol. III, pp. 253 and 278. In the the latter place the radius of the small circle is 1/21, as in the "Hypotheses" of Ptolemy.
3. Vol. III. p. 282.
4. See the lengthy description on pp, 278—280.
5. The editor, Don Manuel Rice y Sinobas, on p. xxxiii, of his preface, even goes so far as to suggest that Kepler may have known of this great discovery of Alfonso's or rather of Arzachel's, as the text attributes the construction to him. This and other similar diagrams were intended to be used instead of planetary tables in the manner afterwards adopted by Apianus.
6. First (about 1460) in Purbach's Theoricae novae Planetarum (ed. of Basle, 1573, p. 82) : "Ex dictis apparet manifeste, centrum epicycle Mercurij, (Continued on next page)