## 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 45

*A*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

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Price:
$4,850.00
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