# ACADÉMIE ROYALE DES SCIENCES || FANTET DE LAGNY, Thomas. Analyse générale ou méthodes nouvelles pour résoudre les problèmes de tous les genres et de tous les degrez à l'infini.
Mémoires de l'Académie Royale des Sciences. Depuis 1666 jusqu'à 1699. Tome XI. 1733.

## ACADÉMIE ROYALE DES SCIENCES || FANTET DE LAGNY, Thomas.

## Analyse générale ou méthodes nouvelles pour résoudre les problèmes de tous les genres et de tous les degrez à l'infini.

Mémoires de l'Académie Royale des Sciences. Depuis 1666 jusqu'à 1699. Tome XI.

Paris, Compagnie des Libraires, 1733.

4to (256x188 mm), (2)-xxii-612-(12) pages. binding : Contemporary full mottled calf, spine gilt in six compartments, title in gilt on lettering-piece, red edges. Upper margin cut on 1 cm. Some leaves browned.

#### This volume contains the first edition of the treatise of Lagny.

There is an other issue with a different title page, at the same date.

references: DSB [VII, p.558/559 : "(Lagny) was a tutor in the Noailles family and the author of a study on coinage. His collaboration with L’Hospital and his first publication concerning the approximate calculation of irrationals (1690–1691) show that he was a good mathematician. (...)Lagny’s work belonged to a type of computational mathematics at once outmoded and unappreciated. He lived during the creation of integral calculus without being affected by it. While the idea of the function was gaining dominance, he continued to approach mathematical problems—both ancient problems such as the solution of equations and new one such as the solution of equations and new ones such as integration—with the aid of numerical tables. Employing with great skill the property possessed by algebraic forms of corresponding to tables in which the differences of a determined order are constant, he recognized the existence of transcendental numbers in the calculation of series.

Lagny made pertinent observations on convergence, in connection with the series that he utilized to calculate the first 120 decimal places in the value of π He attempted to establish trigonometric tables through the use of transcription into binary arithmetic, which he termed “natural logarithm” and the properties of which he discovered independently of Leipniz.

In this regard his meeting with the inventor of the differential and integral calculus is interesting, but it was only the momentary crossing of very interesting, but it was only the momentary crossing of very different paths. Lagny generally confined himself to numerical computation and practical solutions, notably the goniometry necessary for navigators. Nevertheless, his works retain a certain didactic value."].

Price : 400 €