Opuscula* 199 
Ex his aliud lemma deduco , quod hifce formulis conti- 
netur dSh,p=: — . dCh.p^ — 
dSc .(p^ ; » dC c.p^- . 
In hyperbola conftat Ch .<p — -h S h . p ; ergo fumptis 
differentiis C h . O - dC h . (p — S h . p . d S h . p , five dCh.p^ 
S h ■ 9 . d S h .9 ,oT ^ Ch .p. dCh , 9 „. , . ^ 
, dSh.O^ Qui valores 111 fuperio- 
Ch.9 ^ Sh.9 ^ , 
re fubftituti prsebent formulas duas C h . <p , dS h . p — '-^ ' 
Lh .9 
dSh ,(p = rdp, .dCh.p Sh,p,dCh.<p^rdp; 
atqui CAT^* — ShTp^ — r^; ergo fa(fla fubftitutione , expur- 
gatifque formulis dSh.(p = - ^^J'''^ , dC h . p ^^*^^ . 
Simili raiiocinio utens in circulo , adhibita sequatione 
ipli propria Cc.<p^— r^-— Sc.p perveniam ad formulas 
d S c - ' ^ , dC c .(^^ — d<pSc . 9 Qy^-^ formulce ex 
ipfa infpedione figurae deducunlur . Nam trianguium infini- 
tefimum Fef eft fimile FDC; igitur 
CF:CD::Ff: fe, CF;DF::Ff: Fe ^ 
r :Cc.<p: :d(p:dSc.(^, r : S c .(^-.idcs^: dC q .(^ ) ^ 
bus fuperiores formulse itatim prodeunt . 
His demonftratis ad rem accedo propius . Quifque videt 
identicas efle , ac proinde xquales hujufmodi formulas 
Sh .«)-\-Ch .0) Sh.ntp-hCh.n^ . . .. - 
; — = -pr, —Fj ■» denommatores enim iidem lunC 
cum numeratoribus . jMultiplicetur utraque per n d Cp ^ & fiet 
d 9 . Sh .f -f- d ^ . Ch . f nd9.Sh.np-{-vd(pCh.n9 
" Ch.f'-^Sh.<p ~ Ch.n^-hSb.np ' ^^^^^ 
probatis dcoS h .<t> r dC h .(p ^ nd(^ .Sh .ncp — rdCh.nO^ 
d(p .C h .(p — r d S h . (p , n icp C h .fi(p =z rd S h . ncp; 
crgo faflis fubftitutionibus proveniet 
rdCh .a-i-rdSh. a rdCh.nip-\-rdSh.n9 ^ 
"• —cr^-iTT = -crTTTTIT;,-- Utraque expref- 
lio eft logirithmica . Pofita lyftem^itis fubtangente — ftat 
integratio , hac fervata conditione , ur quuma?, & JA.cpr^a, 
fu Ch.^ =.r . Habebitur nlC h .(p~r Sh .9 
