De Arithmetische en Geometrische fondamenten … In veele verscheydene constighe question, soo geometrice door linien, als arithmetice door irrationale ghetallen, cock door den regel coss, ende de tafelen sinuum ghesolveert.

Leiden: Joost van Colster and Jacob Marcus, 1615.

First edition, in which Ceulen calculated the value of π to 33 decimal places, the most accurate value obtained up to that time. He used the method of Archimedes’ On the measurement of the circle, enclosing a circle between polygons with larger and larger numbers of sides.


First edition of this rare work, containing the best approximation to the value of π achieved at that time.

“Van Ceulen was an indefatigable computer and concentrated on the computation of π sometimes called Ludolph’s number … He became acquainted with Archimedes’ The measurement of the circle … Van Ceulen began to work in the spirit of Archimedes, computing the sides of more regular polygons inscribed within and circumscribed about a circle than Archimedes had and inventing a special short division for such computation … In his Arithmetische en Geometrische fondamenten (1615), published by his widow, he reached thirty-three decimal places, always enclosing π between an upper and a lower limit” (DSB).

Originally from Germany, Ceulen (1540-1610) spent most of his life in Holland and was one of the most important Dutch mathematicians of his time. His work on the calculation of π shows him to have been “as expert in trigonometry as his contemporary Viète. In 1595 the two men competed in the solution of a forty-fifth degree equation proposed by Van Roomen in his Ideae mathematicae (1593) and recognized its relation to the expression of sin 45A in terms of sin A” (ibid.). Van Ceulen’s influence continued through his pupil Willebrord Snel. “In his Cyclometricus (1621), [Snel] published Van Ceulen’s final triumph: π to thirty-five decimal places. This was inscribed on his tombstone in the Pieterskerk in Leiden” (ibid.).” Snel published a Latin translation of the present work in 1615, but it is haphazard and full of mistakes.

Bierens de Haan 839; DSB III: 181; Parkinson p. 56.

Folio (295 x 197 mm), pp. [iv], 271 [1:blank]. Contemporary flexible vellum. The present copy of the Arithmetische is a variant issue, with a woodcut geometrical device on the title replacing the engraved portrait found in most other copies. A very good and untouched copy in it's original state.

Item #3273

Price: $4,850.00

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