Mathematics in Ancient and Medieval India c9.2

c9.2

The infinitesimal calculus may be described as a mathematical method of calculating results produced by non-uniform continuous changes as occur in nature. The idea of such method first appeard in the works of Greek scholars like Antiphon ( 430 B. C. ), Eudoxus ( 370 B. C. ), Eudemus (335 B. C) and others. Nearest approach to infinitesimal calculus is first found in the work of Archimedes ( 225 B. C. ). A similar approach to calculus in the middle ages relating to idea of infinitesimal appears in the Indian works, *Siddhānta-śiromaṇi* of Bhāskara II ( 1150 A. D. ) and *Yuktibhāṣā* ( *c.* 1500 A. D. ). In Europe in the 17th century A.D. Kepler ( 1604 A. D. ) used the method in a rather primitive form and later in 1629 A.D. Cavaliery made a more clear statement of the idea while describing a method for the calculation of the area of a triangle. In the 17th century A. D., the Japanese scholar Seki Kowa ( 1642-1708 A. D.) deve'oped a form of calculus known as *Yenri* meaning ‘circle principle’ to calculate the area of a circle. The subject was finally developed in the modern form by Newton ( 1664 A. D. ) and Leibniz ( 1676 A. D. ).