Opuscula. 2S7 
Exemplum quintum & ultimum .Pofito 3^ = 2^ 
quaeratur integrale y(piicpSh.<p,Ch.cp , Theorcma cafui huic 
— — —4 — _ — 3 
excepto conveniens eft^.( — Sh.9 ~{- 2 S h , cp Ch 
~2Sh.a).Ch .(p -i-C h . (p —r"^ ' Multiphcetur per - 
ut proveniat . (^- 2 5 S h .q) +4 J5 S h ,<p C h 
^ .3 ■ — 4 
— 4BSh.^.Ch.9 + iB C h .cp =z 2 By\ 
Hoc prxmiffb quxfita fummatoria fupponatur elTe 
_4 3 < z ■ t 
y(:p,{JSh.(p~{-Abh.(p .Ch.cp-\-A' Sh,(]p .Ch . <p 
-{-A"'Sh.(p.Ch, (^ +^""Ch.(p 
— Sjii({>»{Abh,cp~hASh.(p,C h.cD b h ,(p ,Ch.<p 
+ ^"Sh.(p.ChT^ H-^^"^Ch . (p'* )^Br^(p\ 
Hsec differencietur , omiffis terminfs fefe ex contrarjetate fi- 
gnorum elidentibus , tum pro 2 B (p d cp ejus valor inventus 
fubilituatur 
/ _4 -3 —-2 " 
; 2 A::»h,(p +2Aiih.(p Ch,cp-V2 ^h cp . Ch .cp 
y(pel(p ( +4^bh.9.Ch.(^+3^'Sh.(p.Ch.qD 
' '/ 4 — 3 — a -i 
^ J S b .p -hiA :ih.(p .C h.(p--{-^ A" Sh,(p ,Ch,cp 
( 4 — 3 
{ - 2 Bb h .(V ~\- ^ B bh. ip, . Ch , cp 
+ 2 -4'"S h .*.cJh 
-\- 2 A' S h ^ (p , l; II 
+ 4^"" S h . .C h , ® 
— 4S Sh.o^.Ch.cp H-^BCh.^'* ) 
Comparatio cum propofita dat quinque scquauones fequentes 
1.=» 2 ^-h^^— 2 B — 0, 2.^ ^A-hiA-i- 1 A-{-^B — o, 3.^ 3 A 
•\-2A-^zA''-o,^.^iA'-^iA \ -h^A'"-^B=:r,^.^ A''-h2A"' 
+ 2 B=:o . A quarta auferatur quinca niulriph"cata per 2, & orirur 
6.^ zA''—-SB—f'. Prima ducla in 2 auferatur a fecunda, & 
oritur 7.^ 2 8 S = 0 . Ex fexta , & feptima colliguntur va- 
lores B — — ^ r , A' r.Satis eft ponere hos valores in pri- 
ma , tertia , & quinta, quia pofiti in fecunda, Ss: quarta 
dant acquationes eafdem . Prodibunt itaque aequationes trcs 
8.* 
