Diagram for doubling the cube
Date
1 October 1661
Creator
Unknown, Artist
Object type
Archive reference number
Manuscript page number
p11
Material
Dimensions
height (page): 326mm
width (page): 209mm
width (page): 209mm
Subject
Description
At the meeting of the Royal Society on 4 September 1661, Sir Paul Neile brought in a paper, endorsed by the King, of Thomas Hobbes's proposal of how to double the cube (stated as finding two proportionals between two straight lines given). The ancient problem of doubling the cube (i.e. using only a compass and straightedge to construct a cube which has double the volume of a given cube), is now known to be impossible. William Brouncker was asked to examine Hobbes's solution, which he found erroneous as is explained here, where he comments on the diagram used by Hobbes.
There are other versions of this image at RBO/1/100v, RBC/1/104 and MS/776/094.
There are other versions of this image at RBO/1/100v, RBC/1/104 and MS/776/094.
Transcription
The Authors first mistake is in thinking that F.G. doth passe through H. And the ground of that mistake is another that immediately followes vis. That B.N. is to BK, and NF is to FK and consequently HN to HK as NF to FK. & there HF divide the Angle NHK into two equall parts and cotinued divided also the Angles L.H.O. in the same ma[nner] & therefore must cut AB. at G. so that GB. must be equ[al] to BF. But NF is to FK. (not as BN to BK. for th[e] to HK. but) as BN is to BF, or BF to BK. for th[e] immediate difference of proportionalls are as the immediate proportionals themselves.
Transcribed by the Making Visible project
Transcribed by the Making Visible project
Object history
At the meeting of the Royal Society on 4 September 1661, ‘A proposition of Mr. Hobbes for finding two mean proportionals between two strait lines given, was delivered to the Society by Sir Paul Neile from the king, indorsed with this majesty’s own hand, and was ordered to be registered; as was afterwards the answer to the problem, by lord viscount Brouncker’ (Birch 1:42). The date on which this was entered in the Register Book is given as 1 October, probably to await Brouncker's refutation.
Related fellows
Paul Neile (British) , Astronomer
William Brouncker, 2nd Viscount Brouncker of Lyons (1620 - 1684, British) , Mathematician
William Brouncker, 2nd Viscount Brouncker of Lyons (1620 - 1684, British) , Mathematician
Associated place