The core concept of Calculus is motivated by the dynamic examples of astronomy dealing with instantaneous velocities of planets. The first attempt at formalisation of these ideas was made during the periods of Bhāskarācārya and Mādhava and, Isaac Newton and G F Leibniz developing the entire Calculus, and later Cauchy laying the foundation for modern Calculus based on the rigorous treatment of the concept of limit. In this paper Bhāskarācārya's algorithm to deal with expressions involving multiples of zero (treated as infinitesimals) and zero-divisors (zero as divisors), is considered with a brief reference to the similarity it bears with the ideas of Newton and Leibniz. Bhāskarācārya says that this mathematics is of great use in Astronomy.1 Therefore, the infinitesimal concepts suggested in his Līlāvatī and implied in his geometric treatment of instantaneous sine-difference equivalent of the differential equation d sin θ = cos θ dθ, (in Leibniz′s notation) are considered in some detail as given in Ganẹśadaivajña's own commentary (Buddhiviāsinī) and his commentary (Vāsanābhāsỵa) of Siddhāntaśiromanị.

中文翻译：

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Lilavati和Siddhantasiromani中的Bhaskaracarya的无穷小思想

微积分的核心概念是由涉及行星瞬时速度的天文学的动态例子所激发的。这些想法的形式化的第一次尝试是在Bhāskarācārya和Mādhava时期，以及Isaac Newton和GF Leibniz时期开发了整个微积分，后来的Cauchy在严格处理极限概念的基础上奠定了现代微积分的基础。在本文中，Bhāskarācārya的算法处理涉及零（视为无穷小）和零除数（零作为除数）的倍数的表达式，并简短地参考了它与牛顿和莱布尼兹思想的相似性。Bhāskarācārya说，这种数学在天文学中有很大的用处。1因此，