The Parisian problem
Date
December 1667/January 1668
Creator
John Collins (1625 - 1683, British) , Mathematician, Mathematician
Object type
Archive reference number
Manuscript page number
p2
Material
Dimensions
height (page): 303mm
width (page): 195mm
width (page): 195mm
Subject
Description
These diagrams pertain to John Collins's solution to the ‘French’ or ‘Parisian’ problem set 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 his letter to Oldenburg dated 8 February 1668.
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 his letter to Oldenburg dated 8 February 1668.
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 Collins (1625 - 1683, British) , Mathematician, Mathematician
John Wallis (1616 - 1703, British) , Mathematician
John Wallis (1616 - 1703, British) , Mathematician
Associated place