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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 151v, page id DE-611-HS-958803:0304
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=304
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# Lines: 32 recognised, mean confidence 0.92
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atamen
cujus jaum (exeunte februario) claristimo Groblematit authori
Bernoullo srivatium copiam feci.
Problema
Datis in plano verticali duobus punetis A et B assignare mobili
M, viam AMB, per quam gravitate sua descendens et movers
incipiens a puncto A, brevislimo tempore perveniat ad
alterum punctum B.
solutio
oucta per punctum superius datum A linea hovisontas
AC, describatus Cycloit ordinaria qua incipiat a punctoA,
et cujus diameter AD circuli generatodit AEDF qui volvitus
super AC talis rit, ut punetum describens A tranteat per
asterum punctum inferius datum 8. Dico porrionem
1B Cycloidis sic descripta proposito lativfacere.
si supponantur quod celeditatet acquilita sint in
ratione altitutitur altitudinum ementarum; dico curss
quasitam AB fore portionem circuli centoum habenti
en poritontali AC, et tranteuntis per data puncta A
a
evaderx.
et 8. Unde liquet consecturaia Galilai veram eveclare;
ab ipsius multum devessa.
mac hypothesi, reclacnero cntm etoiplo edebatu
Pandera si vocentur abcissa AC, X; applicata CB, y; et
generalites supponatur quod celeritas acquisita et descense
per altitudinem c8 exprimatur per y2a
:dico naturam
curva qualitatae exprimi per aequationem differentialen
aX =-
mymidus
Vr= mmym