Opuscuia . 209 
iiumerus logarithmi quacfitus . Per M agatur RMS paraliela 
HG, & vocetur HI = Facile invenies KK = Ks = 
Praeterca R M =: - -- - — - ; ergo M S = 
crgo 5 0.= -r^— ; ^ed KS= - -^^ ; igitur KQ_^ 
yji .V rr \l ^ 
z z 
1/2 , rz^-^rr rr^-^-rz r,y/r-{-z 
- = - „ . „ = . qui 
|/rr — 2Z yjl.yjrr — zz . s/ r r — zz v/ 2 • v/ 
t nt 
eft numerus logarithmi analogi ; ergo — 
Si vero non t^ngens HI , fed cotangens LO data fuerit, 
haec vocetur = u. Fafta fubftitntione invenies ' -^^^ _^ 
/ — — *^ 
/ -1 "tl^ . Hi omnes logarithmi funt analogi , in quibus 
fcilicet fubtangens / , protonumerus = -4- , 
Deinde inveniendus eft nuraerus , cu/us logarlthmus hy- 
perbolicus iit xqualis logarithmo analogo dati numeri . Duc 
H P normalem alfymptoto , deinde abfcinde K N = K H — r j, 
& duc NT norraaiem aflymptoto . Datus numerus fit KQ^j 
cujus logarithmus analogus eft , Qujsfitus niimer^s 
fit KZ, cujus iqgarithmus hyperboiicus erit i - Z . ^rgQ 
ex conditione problematis H P QM = T NZ V , & dpmpto 
communi T N Q.M erit H P N T - M Q^Z V ; ergo ex ' hy- 
perbolse proprietate K P : K N : : K Q: KZ i atqui K P : K N : : 
-il-:/-:: 1:^/2: ergo KQ:KZ:: 1:^2, & KQ^2 = KZ. 
Itaque numeriis logarithmi analogi multiplicatus per ^/2 dat 
numerum sequalis logarithmi hyperbolici . 
His prsemifiis quoniam demonftravi S -^^-^^ — ^ ' 
S h . ^ r 
exiftente cotangeiite LO = C/z.fe, erit S =: I „ 
L-_!Jli' , qui lcgarithmus eft analogus ; ergo S =s 
\ / C h ip — r S h . <^ 
T.V.F.IL Dd Ir. 
