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XXIII. tfhe general Mathematical Laws which regulate 
and. extend Proportion univerfally, or , a Method of 
comparing Magnitudes of any Kind together , in all the 
pojfible Degrees of Increafe and Decreafe. By James 
Glenie, A. M. and Lieutenant in the Royal Regiment of 
Artillery, 
Read March 6, / g ^HE do&rine of proportion laid down 
1777* fa 
by euclid, and the application of it 
given by him in his Elements, form the bails of almoft 
all the geometrical reafoning made ufe of by mathema- 
ticians both ancient and modern. But the reafonings of 
geometers with regard to proportional magnitudes have 
feldom been carried beyond the triplicate ratio , which is 
the proportion that iimilar folids have to one another 
when referred to their homologous linear dimeniions. 
This boundary, however, comprehends but a very 
limited portion of univerfal comparifon, and almoft va- 
niilies into nothing when referred to that endlefs variety 
of relations, which muft neceflarily take place between 
geometrical magnitudes, in the infinite polfible degrees 
of increafe and decreafe. The firft of thefe takes in but 
a very 
