First edition of the first extensive, separately published textbook on integral calculus, by Louis Carré (1663-1711), French mathematician and private teacher at Paris, published 44 years before Leonard Euler's classic textbook. It includes a wide variety of practical applications, including the measurement of surface areas, the determination of the volumes and centres of gravity of solid bodies, and problems of dynamics.
With a contemporary owner's name on the title-page, a later 18th-century manuscript note on the endleaf and a couple manuscript notes in the text. A failed attempt to wash out the owner's name on the title-page has left a small faint stain. With the title-page slightly foxed and an occasional minor spot, but still in very good condition and with very large margins. The binding shows some cracks in the hinges, superficial damage to the leather and some corners skilfully repaired, but is still good and structurally sound. The most thorough presentation of integral calculus to its date. Goldsmith BMC STC French 345; I. Grattan-Guinness, ed., Landmark writings in Western mathematics 1640-1940 (2005), p. 56; Poggendorff I, 383-384.