202 OpUSCULA» 
VINCENTIUS RICCATUS VIRGILIO CAVIN^ 
S. P. D. 
rjTfi ex fuperioribus litteris ingens tibi videri debeat utili- 
j tas earum formularum , qusc altero in lemmate continen- 
tur ; tamen multo utiliores cognofces , poftquam oftendero , 
obtineri per eas integrationem plurium formularum « quse 
quantitates hyperbolicas , & circnlares involvunt . Formulse 
in fuperioribus litteris demonftratae funt iiujufmodi 
dS h .(p • ~ , dC n ^CP — 
~ r f 
dSc.c^ ^ ilRiil^ dCc^^^^z^Zllllil^ quibus addere po^ 
tes duas notifiimas r = C . q)*~ J^X^* , r*^ C eT c .q) . 
His fuppofitis demonftro cLuatuor theoremata , qu» fe* 
quuntur 
tnSCh.cp dO?^m-i r^SCh.cp d^p-hrCh.cp Sh.a^ 
mSsJTi'" d<p = - (rn^ y^SSh .cp'""'' dcp-^ r S h .(^""'c h .cp 
mS Cc .(p d(p =: m - i S C c .gT d(p r C c , cp"*"^ S c .(p 
m - f» — 3 — »1 •-• 1 
mSSc.(p d(p ^ m- i r^S S c .(p d(p — r S c . (p Cc.Cp- 
Omnium demonftrationes eadem methodo perficiuntur., 
Quoad primum , Manifeftum eft 
D .Ch.(p""~' Sh.(pz=i CTT^""''' Sh.(p.dCh.(p -H 
Ch.(p dSh.(p. Subftitue in hac pro dCh.(py dSh.Qp 
eorum valores , & invcnies 
D . Ch .(p""' S h.cp — 'm^ Ch . (p""'^ Sh.(p^ .dcp-^ Ch.dp"" 
.dcp. Pro Sh.cp fubftitue Ch.cp — , ut habeas 
rDCh.cp S h .(p m- 1 Ck.cp'" dcp - (^m- 1 r^ C h .(p"""^ d(p; 
-{-'Ch^^^dcp 
igitur 
— — m . _ »; «. 2 W — I 
mCh.(p dcp — m-i .r^Ch.ap d(p rD . C h .(p Sh.(p, 
five integrando 
mSC h.(p dcp:=z m- i . /S C h .(p"""^ d(p-{- r C h .cp'""' S h .(p . 
Q. E. D. 
Alte. 
