“296 od NEW SERIES for the\ 
28. Tus feries, however, admits of being expreffed _ under 
another form, better adapted to eaicnlation, and to effect this 
an 
transformation, Jet us begin aie the term aut 4, i A In 
—cof2A 
this quantity let 2 1+ cof2A be fubflituted for tan’ A; it has 
i rove *S : Se A ar aA 
becomes, after proper reduction, S22 taaole AltA aioe 
gain, in this expreflion let Je be fubftituted for 
cof’ 2 A, we then get 
g+4tanvA — 130of 4 A+ 12: cof2 A’ 
tant AD * 3+ cof4 A—4 cola A ” 
THE yemaining terms of the feries, which are fimilar to one 
another, and of the form 4 tan’ — = eee 3 an A, let's of a 
AA ol 
Like» transformation ;. for “ ye ‘ fubftituting”’ —e for 
Ate yep, &) 5 347 
i ; 1 
r+ cof = A io 
tan*— A, and again ——*- for cof"! Ai in n the Sor we 
2n 
eet é 
ber ig tot Ao coll a 
oa TatsuntZa= 
s Eeqotta Siidigo dot Zacpoq eat Lia > 
(998313 
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