[ 43 + 3 
XXX. Geometrical Solutions of three cele- 
brated Agronomical Problems, by the late 
Dr. Henry Pemberton, F. R. S. Com- 
municated by Matthew Raper, FJqi 
F. R. S. 
Read June 4, 
1772. 
Lemma. 
T 'O form a triangle with two given 
-/ides, that the rett angle under the 
fine of the angle contained by the two 
sriven [ides, and the tangent of the angle oppofite 
,o the lejjer of the given fides, fiaU be the greatejl 
that can be. 
Let [Tab. XII. Fig. i.] ^ two given fides be 
equal to AB and AC: round the 
the interval AC, defcribe the circle CUfc, ana 
produce B A to E ; take B F a mean proportional 
between BE and BC, and ereft the perpendicular 
F G, and complete the triangle A O is. 
Here the fine of BAG is to the radius as FG to 
AG and .he tangent of ABG to the radius a F G 
to FB: therefore, the reftangle under the fine ot 
BAG and the tangent of A B G is to the 
