Opuscula, 
Sint iam redlx graves non tres folum , fed quotlibet 
«t a \ d'\ d'', a\ a"' &c. , anguiique , quos cum verticaii- 
bus faciunt, vocentur <:]: , ct;', (p'', 9"', 9 9", CP^' &c. 5i lufpenfae 
in acquiiibrio confiiiant, dubium non elc , qLin omncs in 
uno eodem verticali plano veifentur; vedari eniai debent , 
quemadmodum ollendimus , ternx; quod fieri nequit, quin 
verfentur omnes . Dubium pr^terea non eil , quin omnes 
fimui itare debeant aequationes , quarum unamquamque ex 
ternarum redarum conjparatione oiiri modo demonara- 
vimus , nimirum 
fin(^ — q:').finqD" '{d-^d') — Cm{(p~c^'' yCmcp '{a-\-d ) 
finCo?' — q?")-fin C'\{d'-\-d'') =r:fin(-p" — ^'").(]n q?' .(^/-f-^" ) 
{m{(o'~c^''')'(m(v''''{d''-\-d'') = (m{'i)'' —(^'^^-Cm -f.^d^-^-d'') 
fin(y'— V^).fin9' ■{d''-\-a'') = fin(rp Cp" ).fin ^,^^(^^"-4^^) 
fm(^'^— f ).fin (^'\{a'-^a''') - fin(q)" — (p^^fin^ ^(«"^4-/?" ) 
&c. &c. 
Qu2e quidem aequationes fi omnes fimul muitiplicentur , pa- 
tet, deletis fadoribus communibus , prodire acquacionem 
fin ('p — (p').(ia ^''.fin (p"- (^^''-f-^^^^rrfin^cp'' — cp^^yfin (p.fin (\'{a-\-d) , 
. £m(D^'Cm^^'.{a^-^a''') fm o?.fin a-'.(^+^') ^ 
ideit - — I— - L — pr— , — . Ex quo per- 
fin(r/ — r ) lin(p"-q}) 
fpicuum fit, fi redx dux accipiantur , altera alteri pro.<i- 
msL^a^^ a''''^\ quarum anguli cum verticalibus fint 9^^, cp**'^' , 
r . fmcpf^fin.^to^+^.^^f^-f-^^-^') a . 
lore quantitatem I -5- - ^ conitantem, qux- 
cumque fint redix illx duae, qux accep^-x faerunt; eil enini 
, fin (l?.fin cr*«(/!Z-l-^') ,. 
quantitas feaec eiclem ilii ^ — - , iperpetuo xquaiis, 
(in {v—V ) ^ 
Sint denique redx graves numero infinitse , magnitudi- 
ne infinite parvae , ui curva exfiihit catenaria . Ex didis ii- 
quet , curvam hanc in uno eodemque verticaii piano iace- 
re totam : quare gH eius curvatura fimplex . Sit ergo ABM 
{Fig.^.) eius pirs quxlibet : atque inteiiigintur ordmarae 
tres Iiorizontales p B , P C , tt D , paribus , iifque infinite par- 
vis intervailis inter fe dilfitae , occurrentes axi verticali KP 
in p , P , 7r . Vocetur p B y , P G —y : duclifque vcrticaii- 
L 1 2 bus 
