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XXXIX. A Letter to the Right Honourable 
Hugh Earl of Marchmont* F. R. S. con- 
cerning the SeEtions of a Solid, hitherto 
not confdered by Geometers ; from William 
Brakenridge, D. D. ReElor of St. Michael 
Baffilhaw London, and F. R. S. 
on it, makes me prefume to lay before you the fol- 
lowing fpeculations. Your benevolence to all philo- 
fophical Inquiries encourages me, and the perfonal 
regard I have for your Lordfhip induces me to do 
myfelf this honour ; and tho’ what I offer at prefent 
may be of no great confequence, I am perfuaded, 
that every little acceffion to our knowlege will give 
you fome pleafure, as you very well know, that all 
our improvements in fcience are flow, and from 
fmall beginnings. You have here a new method of 
confidering fome geometrical curves, from the fec- 
tions of a folid, hitherto not taken notice of, and by 
which, in particular, you will fee, that the two in- 
finite curve lines from the fedtion of the cone, are 
alfo the fedtions of this j which may be of fome ufe, 
as it feems to extend our views of their nature and 
properties. The defeription of it is very eafy and 
obvious, and it has fomething remarkable in its 
form, that tho , in the moft Ample cafe, it is gene- 
rated and bounded by right lines, the furface is in-, 
curvated. The folid is thus deferibed. 
My Lord, 
T OUR knowlege in Geometry, and 
L the other Sciences that depend up- 
3 
Let 
