How the Ancient Indians Get the Measurements to Build Their Sacrificial Altars

The lives of ancient Indians were strictly bound to the religion. Sacrifices(yajña) were the main custom of them. To perform the sacrifices they wanted to makealtars which were built with appropriate measurements. Therefore, Brahmins havedeveloped some Mathematical rules and techniques which are in manuals called śulbasūtras and they have used a few equipments for it.Here, our attention is paid to examine how the Brahmins measured the width,length, area etc. of the altars accurately and what equipments were used by them for it.The main methodology is studying literary sources collecting the facts andverifying them in accordance with the theoretical knowledge of modern Mathematics.The ancient Indians have used only five measuring equipments to getmeasurements. They are a stake (śaṅ ku), cord (rajju), angular rod (sphya) and a peg(khīla) but, additionally, a special measuring rod which has been made according to thephysical measurements of the patron of the sacrifice for the particular sacrifice, too, isused. They have used them to find directions as well. In śulba sūtras, three main altarsand other various altars have been recommended. First, it guides us to form a right angletriangle. Based on it, there is much guidance in the śulba sūtras to form squares,rectangles, circles, trapeziums etc. In addition, including the Pythagorean Theorem, themathematical rules used to form a square or a rectangle or a circle etc. which is similarin area to two identical squares or two unequal squares, a rectangle, a circle etc. andvice versa, can be seen there. The Brahmins, indeed, have used the cord to bisect anangle and to divide a figure into equal shares. Comparing these methods with modernmathematical theories, it is worth to say that the ancient Indians were capable tomeasure accurately using a few equipments.Key words: Śulba sūtra, Vedic Mathematics, Altar, Sacrific

Sripati’s arithmetic in the Siddhantasekhara and Ganitatilakac

The literature on the exact sciences in Sanskrit in the second millennium is significant from a historical point of view because of the emergence of innovative ideas, systematization of the traditional knowledge, advanced technicality, creativity of the scientific writing style, and so on. Śrīpati, a mathematician-astronomer, is the first known writer of exact sciences in this era. He lived in the 11th century most probably in Maharashtra and he wrote in a vast range of subjects from astrology to astronomy. In spite of his prolific writings and influence in the early stages of the second millennium, Śrīpati has been understudied. Śrīpati is the first author who wrote a separate mathematical text while still retaining all the main mathematical rules in theoretical astronomical texts. It is Śrīpati who used different elegant metrical forms in versification of mathematical rules. Most importantly, he invented several rules in arithmetic and provided inspiration for successive mathematicians and astronomers especially Bhāskara II. In this thesis we provide a critical edition of the 13th chapter of Śrīpati’s Siddhāntaśekhara, an astronomical work, consulting the published edition and three manuscripts and his Gaṇitatilaka, his arithmetic text, based on the published edition. They are followed by the critical translation and the commentary where mathematical analysis of all the rules is given. These mathematical rules, procedures, and executions are compared with that of other preceding and succeeding mathematical authors mainly in identifying Śrīpati’s contribution and innovation. We attempt to understand Śrīpati’s role in the history of Indian mathematics, how he was influenced by his predecessors, his influence on succeeding mathematicians, and to contextualize the mathematical rules given in both texts. This research will also examine, wherever possible, the use of mathematical rules given in the texts in daily practices, similarity or differences of the same rule in different texts, the characteristics of the executions of rules, and the commentators’ approaches to the base texts

A Critical Edition of the Candrārkī of Dinakara

A set of tables devoted to solar and lunar phenomena entitled the Candrārkī  was prepared in Sanskrit by the sixteenth-century Indian astronomer Dinakara.  Along with the tables, Dinakara composed a short accompanying text which instructed the user how to extract and manipulate the tabular data to construct their own calendar for any desired year and geographical circumstances.  The work proved to be popular.  Based on a small fraction of the extant manuscripts, we present a critical edition of the text together with a discussion of the challenges raised while preparing the edition