town of Hindustan, province of Delhi, forty miles south-west from the city of Delhi. It is possessed by a native chief, one of the numerous British tributaries. Long. 76° 42'. E. Lat. 28° 13'. N.
Reyneau, Charles Rene, commonly known by the name of Father Reynneau, a celebrated mathematician of France, was born in the year 1656, at Brissac, in the province of Anjou. When twenty years of age, he connected himself with the Oratorians, a sort of religious order, the members of which lived in community without binding themselves to the observance of any vows, and turned their chief attention to the instruction of youth. He afterwards taught philosophy at Pezenos, and next at Toulon, which requiring some degree of geometrical knowledge, he became extremely fond of that science, and cultivated and improved it to a great extent. He was, in consequence of his knowledge, invited to fill the mathematical chair at Angers in 1683, and he was also elected a member of the academy in 1694.
He undertook to reduce into a body, for the benefit of his pupils, the chief theories which were scattered throughout the works of Newton, Descartes, Leibnitz, Bernoulli, the Leipzig Acts, the Memoirs of the Academy of Paris, and several other works, to which he gave the name of Analyse Demonstrée, or Analysis Demonstrated, and which was published in 1708, in two vols. quarto.
He gave to this work the name of Analysis Demonstrated, because he therein demonstrates various methods which had not been demonstrated by their authors, or, at least, not with sufficient accuracy and perspicuity. This work of Reynneau was very much applauded, and it became a general maxim in France, that to follow him was the best, if not the only way, to make any extraordinary progress in the study of mathematics.
Such was his ambition to be useful, that in 1714 he published his Science du Calcul des Grandeur, intended for the benefit of such as were wholly unacquainted with the science of geometry. Of this work a very able judge was pleased to observe, that "though several books had already appeared upon the same subject, such a treatise as that before him was still wanting, as in it everything was handled in a manner sufficiently extensive, and at the same time with all possible exactness and perspicuity." Although many branches of the mathematics had been well discussed prior to his time, no good elements were to be met with, even of practical geometry.
When the Royal Academy of Sciences at Paris gave admission to other learned and eminent men, Father Rey-
nean was received into the number. The works already mentioned are all he ever published, or perhaps ever composed, with the exception of a little piece upon logic; and materials for a second volume of his Science du Calcul were left behind him in manuscript. Towards the close of life he was too much afflicted with sickness to give much application to study; and he died in 1728, at seventy-two years of age. His many virtues and extensive erudition made this event much regretted by all who had the pleasure of being acquainted with him. It was regarded as an honour and a happiness by the first men in France to number him amongst their friends, such as the chancellor of the kingdom, and Malebranche, of the latter of whom Reynneau was a faithful and zealous disciple.