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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 147v, page id DE-611-HS-958803:0296
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 149r); this page is its left half.
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dum arculum cerin ratione composita ex simplici divertia spatiolorm
percurrendorum Mn, Ce et subduplicata recproca altitudinum MD, CG
id eit tempus per Mm. tempus per Ce:: Ma
CK:: MD. CNC:: LMD. VCX) rma
CC
Mo req i (ob Mm. Ce:: Mk
NC+
VMDVCG:: NCG. VCF; quohiam autem
CG odenra eit M hor quon CF, erit elian tempus per Mon mihus quat
tempus per ce et potioin jure mminus quatu tempus per Ce hypotenn
tan frianguli neclanguli Cec. Ergo ten pus per onnes Mm id eit
per eycloidemm AMB et Minus quatu teu pus per omtes Cc id est per
lineat ACB. 9. es d.
Ortendendum adhuc mertat (ut problemati pletistine satiiat
quomodo a punito, dato tanguat vertice describende sit brachy.
dochrona seu cycloit transitura per aliud punitum datut; quon
sic facillitie expeditur: conjungantur duopunita data A, B(F ig. II
per lineam rectesa AB, et super hocizontalo seL.describatur cy dois qua
cunque libuerit inilium sumens in A secantu rectatm AB in R; quo facto
fiat ut sR ad Asila diameter cireul: Genitout cycloidis AR5 ad
quartam quae erit dianeler cueul genuoris eycloidis quanita ABC
hancitura e 
Aate Siina soa postum quia itercim natie prodam,
anino revolven ineaperlatam illam identitatem icoitiona Hugenia
na nostraeq Bracmullechrona, Quod notabile praterea exirlimo
illud eit quod hacedentitas in sola hypotheri Galilui reperitur,
adeo ut vel ex ea consicere luceat illati Katura esse consentuneate
quod quemadiodum seuper operati solet modo simplicissimo, ita et
scc per unam eanerqe lineam praset duo diverra officia, cum in
geavis alia hypothesi duabus ad id opus escllineis alia netpe pro
oscillationibus agcedenturnis et alia pro aeterrimo detenur. Ut si
et. gr. celeritates gravium cadentium escent non cnsduplicata sed
subtriplicata ratione altitudinum, brachydorhrora foret alge–
braica iochrona autem transendent; berun Lsceleritates esteut
ut iprae allitudinet, utraque fieret algebraica, illa quidem circu–
laris, hac vero pelta.
Non ingratum fore Geometiis judico, L: appendicis loco solutio
nem ipris dedero problematis consideratione pariter digniscimmi,
quod et occasione praecedeptis inter scribendum in mentem incidit:
CpC∞. IV.
Occaritem in platoverlicali calva PB (quate Synchronam appellare