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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 315v, page id DE-611-HS-958803:0632
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resolvere et ductu Circini et reoula construere poterit)
2n q
cc -bb.
nCLM
+ na Z 2n - 2 b2n - 2
c
- b2n
a +V2n
cc- bb. Deinde
sumatur etiam AR aegralis cidem Radici sect aucta semi,
paramctro id est ut AR sit ∞ LA + D Z, junvatur LR
ejus (Facta LSx semiparametro, avatur parallela S R. Q0o
M
facto, fiat ut B ad c ita x seu Lead As x AD, cui inclirectum
adjiciatur PQ x semiparametro; ducta Je fiat parallela Vo
Ex puncto V grod distat a F semiparametro. Brisceanda jam
sunt Ak A A0 in punctis St et 1 ex quibus denique ductae
ari parallela s2, JN resecabunt arcum parabolicum opta,
tum MN, quem dieo habere ad arcum propositum BCrati,
onem datam u act A. Q. C. EF.
Hinc paret quomodo (ut fieri interdum posse comperi) da
dix est omavinaria; problema tunc fore impossibile: et re
vera demonstrari potest. quod si eo casu ulla alia Mlothodo
ad arcum BC posset assionari alius MN in ratione i ad
et ipsa rectificatio Arcus parabolica sequeretur, quae cum
pro desperata passim a Geometris haberetur, ejusqu’impossin
bilitas tantum non apodictice ostensa jam sit, aquam pro
fecto epumice postutabit qui tunc quoque problemati satissar
cere conaretur. Vnde collivendum est. hanc nostram para,
bolicas comparandi rationem et perfectissimani esse et oc,
neralissimam; perfectam nimirum, quia possibile solvat, im
possibile rero deteoit: generalem autem quonium sue cedit sive
ratio data nad  sit numeri ad numerum, sive non; sive usit
numerus inteoen sive fractus. Ostendlit et iam Arcui BCalium
agralem sect dissimilem sumi non posse, in casu enim rationis
agralitatis id est quando nx Streus quidem MN aequalis
eracit arcui BC sed cidem Aiam conoruit seu similis est,
unde nihil obtines. ast hoc ne mirere, quod ex dura quadam
necessitate ita fieri debuit et aliter non poruit; dares utinam
duos arcus parabolicos dissimiles et aequales, remunerarem eones
oium inventum rectificatione parabola vel si mavis quadratura
Olyperbola.
Caeferum isdem principus usus etiam hoc inveni Datis
duobus, tribus, pluribusre arcubus parabolicis disoreoatim,
assionare alium arcum continuum omnibus Mlis simul aqua
Tem, Quod heic latius explicarem, nisi et aliis quaerendi eam,
pum relinguendum censerem, qui funclamentum prioris probe
intellexerit, etiam in hoc haud difirulter penetrabit, licet
multo proliriori calculo sit opus.