Summation of Series. 415 
rational, the unknown quantities exterminated may alfo be 
integral or rational. 24. In thé Medit. are given rules for 
finding the different and correfpondent roots of an equation, 
whofe refolution is given. 25. Mr. DE LA GRANGE has recom- 
mended my new transformation of equations, publifhed in the 
Mifcell. which perhaps is not lefs general nor elegant than any 
yet publifhed ; and in the Meditat. 1770 is given a method very 
ufeful in finding the co-efficients. 
If either here, or in the preface to the Medit. Algebraice, 
T have afcribed to myfelf any algebraical, or in the properties 
of curve lines any geometrical, or in the Medit. Analyt. any 
analytical invention, which has been before publifhed by any 
other perfon, I can only plead ignorance of it, and fhall on 
the very firft conviction acknowledge it. 
I muft further add, that I have been able to carry my alge- 
braical improvements into geometry; for from them, with 
fome geometrical principles added, I have (unlefs I am de- 
ceived) deduced as many new properties of conic fections and 
curve lines as have been publifhed by any one fince the great 
geometrician APOLLONIUS. 

