The Parisian problem
Date
8 February 1668
Creator
John Wallis (1616 - 1703, British) , Mathematician
Object type
Archive reference number
Manuscript page number
p1
Material
Dimensions
height (page): 310mm
width (page): 195mm
width (page): 195mm
Subject
Description
Diagrams from John Wallis’s letter to Henry Oldenburg dated 8 February 1668. These pertain to Wallis’s solution to the ‘French’ or ‘Parisian’ problem sent as a challenge by François Dulaurens, the author of Specimina mathematica (1667). The problem was reported at the meeting of the Royal Society on 12 December 1667 and sent on to John Collins, William Brouncker and John Wallis.
The problem, as understood by Wallis, was as follows: 'given in number the circle CBD with radius CB, and the inscribed line BD protracted as far as may be desired beyond the circle, yet so that BY drawn parallel to CF may cut the circle in Y. To find the true value of the line BY, not an approximation (which may easily be obtained from a table of sines)'.
In his letter to Wallis dated 24 December 1667, Henry Oldenburg mentioned that 'a certain person here' (identified by R. A. Hall and M. B. Hall as John Collins) had surmised that BY was a rational quantity, but had not offered a proof, since William Brouncker thought that GF might prove irrational. Wallis offered his proof that BY was rational in this letter to Oldenburg dated 8 February 1668. Wallis notes in this letter that his solution 'doeth not disagree' from William Brouncker's solution (Cl.P/24/11), but that the process is different.
The problem, as understood by Wallis, was as follows: 'given in number the circle CBD with radius CB, and the inscribed line BD protracted as far as may be desired beyond the circle, yet so that BY drawn parallel to CF may cut the circle in Y. To find the true value of the line BY, not an approximation (which may easily be obtained from a table of sines)'.
In his letter to Wallis dated 24 December 1667, Henry Oldenburg mentioned that 'a certain person here' (identified by R. A. Hall and M. B. Hall as John Collins) had surmised that BY was a rational quantity, but had not offered a proof, since William Brouncker thought that GF might prove irrational. Wallis offered his proof that BY was rational in this letter to Oldenburg dated 8 February 1668. Wallis notes in this letter that his solution 'doeth not disagree' from William Brouncker's solution (Cl.P/24/11), but that the process is different.
Object history
12 December 1667, ‘[Mr. Oldenburg] brought in an algebraical problem sent to him from Paris, as proposed by Monsr. de Laurens, which was ordered to be communicated for solution to Mr. Collins’ (Birch 2:226).
Related fellows
John Wallis (1616 - 1703, British) , Mathematician
Associated place