[Pramāṇa](https://indike.org/pramana/) › [Studies](https://indike.org/pramana/ins) › [Science, technology and education](https://indike.org/pramana/ins.science) › [Jyotihshastra: Astral and Mathematical Literature](https://indike.org/pramana/ins.science.pingree-1981) › c5.s1.4 # Jyotihshastra: Astral and Mathematical Literature c5.s1.4 Jyotiḥśāstra: Astral and Mathematical Literature c5.s1.4 - **Language:** English ### [c5.s1.4](https://indike.org/pramana/ins.science.pingree-1981.c5.s1.4) shadow-problems; intersecting circles; sums of various series;⁴ solutions to quadratic equations; proportions; and the solution of indeterminate equations of the first degree.⁵ Thus he includes in this chapter on \*gaṇita\* not only arithmetic, geometry, and algebra, but several topics of primary interest to astronomers—i.e., trigonometry, intersecting circles (for eclipse calculations), and indeterminate equations (for deriving the numbers of rotations of the planets in a Mahāyuga). The solution to the indeterminate equations utilizes continued fractions; continued fractions had been investigated by Euclid, though not applied to the problem of indeterminate equations, so far as we know, by the Greeks. Many useful illustrations to Āryabhaṭa’s rules were given by his early commentator, Bhāskara.⁶ - [Previous: c5.s1.3](https://indike.org/pramana/ins.science.pingree-1981.c5.s1.3) - [Next: c5.s1.5](https://indike.org/pramana/ins.science.pingree-1981.c5.s1.5) - [Up: c5.s1](https://indike.org/pramana/ins.science.pingree-1981.c5.s1) --- Source: [https://indike.org/pramana/ins.science.pingree-1981.c5.s1.4](https://indike.org/pramana/ins.science.pingree-1981.c5.s1.4) · Pramāṇa