Of these topics it will be noted that the second was dealt with to some extent in the S'ulvasūtras; but a close examination seems to show that there is no real connection and that the writers of the third period were actually ignorant of the results achieved by Baudhāyana and Āpastamba.
12. Indeterminate Equations. The interesting names and dates connected with the early history of indeterminates in India are:
That we cannot fill up the gap between Diophantus and Āryabhata with more than the mere name of Hypatia is probably due to the fanatic ignorance and cruelty of the early Alexandrian Christians rather than the supposed destruction of the Alexandrian library by the Muhammadans. It would be pleasant to conceive that in the Indian works we have some record of the advances made by Hypatia, or of the contents of the lost books of Diophantus—but we are not justified in indulging in more than the mere fancy. The period is one of particular interest. The murder of Hypatia (A.D. 415), the imprisonment and execution of Boethius (A.D. 524), the closing of the Athenean schools in A.D. 530 and the fall of Alexandria in 640 are events full of suggestions to the historian of mathematics. It was during this period also that Damascius, Simplicius (mathematicians of some repute) and others of the schools of Athens, having heard that Plato's ideal form of government was actually realised under Chosroes I in Persia, emigrated thither (c. A.D.
