TALBOT8929

Edinb.

Jan^y 8^th

My Dear Charles

I return M^r Nesbitt’s ¹ letter. I hope you received mine of yesterday, containing a reply to M^r N’s questions.

The problem about the Centre of gravity of a Trapezium is a proof of great geometrical sagacity, but I think if you construct the figure with a Ruler you may perhaps perceive the demonstration of it.

I told you I think that I had found a very neat solution of a theorem which Professor Kelland ² had obtained by means of Sir W. Hamilton’s ³ doctrine of Quaternions ⁴ – viz. in any triangle the centre of circumscribed circle centre of gravity, and concourse of perpendiculars from angles on sides lie in a straight line, and so that the centre of gravity always trisects the distance between the 2 others.

To which I added the following, for which Professor Kelland gave me Κυδος ⁵

The centre of the six-point circle lies in the same straight line and always bisects it.

N.B. The six-point circle is that which passes thro’ the middle points of the sides, and which always passes thro’ the feet of the 3 perpendiculars from angles on sides.

Professor Tait ⁶ says that Quaternions ought not to be employed for solving such simple matters, but kept in reserve for the higher geometry.

Your mother ⁷ has sent you today an old Courant containing an account of the models for the Prince Consort’s ⁸ Memorial – They are now on exhibition here but we have not yet seen them. We think of going there tomorrow.

Your aff^te

Father

Envelope:

C. H. Talbot Esq
M^r Prichard’s ⁹
Architect
Llandaff