At the beginning of the XVIIIth century, Jai Singh II, a Rajput king vassal of the great Mughal emperor Muhammad Shah, was a passionate astronomer. After founding his new capital city, Jaipur, he began to erect there a large observatory and was charged by Muhammad Shah to build another observatory in Delhi. These celestial laboratories were aimed at improving the precision of the observations, in order to compare them with the results of the calculations made with the help of the algorithms given in the classical Indian astronomical treatises, the siddhāntas.
Already before 1720, Jai Singh II had been informed about other astronomico-mathematical traditions and had at his disposal the translations into Sanskrit of the Arabic versions, made by Naşīr ad-dīn at-Ţūsī, of Euclid's Elements and Ptolemy's Megalè Syntaxis (Almagest in Arabic) under the titles of Rekhagaņita et Siddhāntasamrāţ.
Around the end of the same decade, thanks to his encounter with Manuel de Figueiredo, Rector of the Agra Jesuit mission, Jai Singh learned about European astronomy. After sending the same Jesuit to Lisbon, to find treatises, instruments and informations in order to check his methods against those of the Portuguese King João V's court, Jai Singh wanted to complete his astronomical staff by a European astronomer. Unhappily, this was achieved only in 1740, three years before Jai Singh's death.
We will follow the eventful moments of Jai Singh's astronomical evolution, from his initiation to the siddhāntas until the arrival of a European astronomer in Jaipur, in various documents, of which many are still unedited : letters in Latin, Portuguese, French and German; Persian and Sanskrit manuscripts, that we had the opportunity to consult in Lisbon, in the Goa archives or in the Library of the Man Singh II Museum of Jaipur.