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XXX. Geometrical Solutions of three cele- 

 brated Agronomical Problems ^ by the late 

 Dr. Henry Pemberton, F. R. S. Com- 

 municated by Matthew Raper, Mff* 

 F. i?. S. 



Lemma, 



Read June 4, ^'t — Q form a triangle with two given 



JL Jides, that the rectangle under the 



Jine of the angle contained by the two 



given .fides j and the tangent of the angle oppofete 



to the lejjer of the given fides, foall be the greateft 



that can be. 



Let [Tab. XII. Fig. i.] the two given fides be 

 equal to A B and A C : round the center A, with 

 the interval AC, defcribe the circle CDE, and 

 produce B A to E ; take B F a mean proportional 

 between BE and BC, and erect the perpendicular 

 F G, and complete the triangle A G B. 



Here the fine of BAG is to the radius, as FG to 

 AG 5 and the tangent of ABG to the radius, as F G 

 to FB: therefore, the rectangle under the fine of 

 BAG and the tangent of A B G is to the fquare of 



the 



