(seq. 1)

Cambridge 26 {December} 1787.

{Reverend} Sir,

Last {August} I gave the Academy a solution
of the problem requiring the Duplication of the
Cube, which you will find stated in the Dictio-
nary of Arts & Sciences. The difficulty consisted on
finding two mean proportionals between two
given extremes. Having surmounted that dif-
ficulty in my former paper, I have prepared
another for the next meeting, to shew how any
required series of proportionals may be ascer-
tained geometrically when the extremes are li-
mited. I am not wrong I believe in mentioning
this subject to you, as you have now been long
eno' in the study to begin to relish it.

Yours affectionately
James Winthrop

{Reverend} {William} Bentley-