i66 ANNOTATIONES IN 10CPM 



Problema. 



Innenire feriem quantitatum : a , b , c , d , e % 

 f , etc. cuius haec fit proprietas , vt fit : 

 c(c-b)—#{b-a) • d{d-c)={c{-b) ; <^-0=J4^) etc. 

 feu vt quantitates inde deriuatae 



b{b-a); c(c-bj, d{d-c)\ e{e-d),f{f-e\t\z. 

 «tecrefcant feeundum rationem quadruplam. 



Solutio. 



Cum fit tang. | <$> z~ cot. | (J) - 2 cot. (J) , fi mul- 

 tiplicemus vtrinque per cot.^Cj), ob tang \ (p cot. | (f> 

 — 1 erit coj.^$(cot.^(|)-2cot.(p) — 1. Statuatur er- 

 go tf-rcot. (p,b~ \r cot. -J $;<;= \r eot. |(J)^-^cot4$,etc. 

 eritque 



2 F 6 (V J -r)^i hinc b{b-a)^ 

 T»T— rj~* hinc <:(£—£) — —* 

 7^-rj — l hmc d(d—c)z-^s 



etc, 

 Quare liaec feries 



a-rcot <J)^=Ircot.|(});^=:ircot. 4 (J)^z:^cot.|(l);etc. 

 hanc habet proprietatem , vt quantuates mde formatae 



b(b-ay,c{c-b),d(d-c');e{e-dy, etc. 

 in ratione quadrupla decrefcant. 



Coroll. z. 



