This task was undertaken by Barretier with great ardour, and prosecuted by him with suitable application, for he not only drew up a formal confutation of Artemonius, but made large collections from the earliest writers, relating to the history of heresies, which he proposed at first to have published as preliminaries to his book, but, finding the introduction grew at last to a greater bulk than the book itself, he determined to publish it apart.

While he was engrossed by these inquiries, accident threw a pair of globes into his hands, in October, 1734, by which his curiosity was so much exalted, that he laid aside his Artemonius, and applied himself to geography and astronomy.  In ten days he was able to solve all the problems in the doctrine of the globes, and had attained ideas so clear and strong of all the systems, as well ancient as modern, that he began to think of making new discoveries; and for that purpose, laying aside, for a time, all searches into antiquity, he employed his utmost interest to procure books of astronomy and of mathematicks, and made such a progress in three or four months, that he seemed to have spent his whole life upon that study; for he not only made an astrolabe, and drew up astronomical tables, but invented new methods of calculation, or such at least as appeared new to him, because they were not mentioned in the books which he had then an opportunity of reading; and it is a sufficient proof, both of the rapidity of his progress, and the extent of his views, that in three months after his first sight of a pair of globes, he formed schemes for finding the longitude, which he sent, in January, 1735, to the Royal society at London.

His scheme, being recommended to the society by the queen, was considered by them with a degree of attention which, perhaps, would not have been bestowed upon the attempt of a mathematician so young, had he not been dignified with so illustrious a patronage.  But it was soon found, that, for want of books, he had imagined himself the inventor of methods already in common use, and that he proposed no means of discovering the longitude, but such as had been already tried and found insufficient.  Such will be very frequently the fate of those, whose fortune either condemns them to study without the necessary assistance from libraries, or who, in too much haste, publish their discoveries.

This attempt exhibited, however, such a specimen of his capacity for mathematical learning, and such a proof of an early proficiency, that the Royal society of Berlin admitted him as one of their members in 1735.

P. 381. Princes, who are commonly the last.

Barretier, had been distinguished much more early by the margravin of Anspach, who, in 1726, sent for his father and mother to the court, where their son, whom they carried with them, presented her with a letter in French, and addressed another in Latin to the young prince; who afterwards, in 1734, granted him the privilege of borrowing books from the libraries of Anspach, together with an annual pension of fifty florins, which he enjoyed for four years.