^<58 Opuscula . 
bus BF, CE = dx , erit F Cj^dy, 'ED = ^ y\ & BC 
= d x^-h dy\ CD — ^ dx'--^- dy'- ; iinus vero anguli F B C 
= , eiufque cofinus = _J:^ , & finus 
yj d x' -i-dy^ / dx"- -h d f 
anguli ECD — — eiufgue cofinusi^ 
^dx'-\~dy' s/dx'--^dy^' 
unJe colligitur finus ditferentiac angulorum eorumdem 
r ' V — d X d ^4 „ • 1 
^ — -- — « rer ea ig tur, qux paulo ante 
y/dx'-\-tifsJdx'--\-dy'' 
demonftrata funt , erit ^.lllS^^ -^-_df_ -^V d x^ + dy ^ 
d X { d y — d y ) 
= 2^, nempe quantitas conftans . Quoniam jy" ~y-{-dy^ 
ideoque dy —dy -\-ddy, fi fiant in icquatione inventa fub- 
ftitutiones , terminique , qui prx aliis innnitefimi funt , de- 
leantur, prodibit ^-l—Jlj^J^ ^l. —h, A J integrationem po- 
— d X d d y 
natur dy -= pdx^ unde ddy — d^dx^ ^ y/ d x^ -h ^jy* 
— d Xy/ i : perfedifque fublliiutionibus , vertetur aequa* 
. . , ^ / _ — d^ . j y i-\-p P 
tio in hanc — -. . — — , qux incegrata dat — 
= — ~r~~~' '^^' 7* conftans quantitas in ipfa integra- 
tione adiita. Reltituatur ^pro/>, exfiftetque — 
a X 
— llhl , ac tandem dy = — — , qux illa ipfa 
h s/ i^c^- xf—h^h 
efi: catenarix curvse aequatio , quam raathematicorum prin- 
ceps Leonhardus Eulerus in immortaii libro de curvis ma- 
ximi minimive proprietate gaudcntibus pag. i)S invenit. 
