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# Page: https://leibnizlegible.com/page/DE-611-HS-958803:0055
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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 28r, page id DE-611-HS-958803:0055
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 29v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=55
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000055.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.93
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

nr
pi
posse
ope solarum differentialium.
Nam
descensus ipsi vel ascensus verticales
 ponderis et contranondii sunt ordinatae
elementa ordinatarum. Ut ergo maneal
aequitibrum in motu, debent ascensus hi vel
descensus elementares esse ponderbus recipro
ce proportionales. Ergo
id es ipsae ordinatae, quae est ipsissima constru
Ad quod raigium attinet
Ao Tua.
noravi ea occasione, verissimum mihi vider
quod onla  terminus summator
 termini irrationalis debeat continere
eandem erratio nalttatem. Cujus rei demon
stratio quam tugni, pendet ab hac
psucntosa
consideratione glneracissima quod termini
et differentia vel seu te summa et
terminus debent habere eicudem numdrum
seu valorum
radicuni. qua
quonam quivis valor termi
mi suum habebit valorem differentia
respondentem. Hinc etiam dedapi consi–
derationes quibus brevercr multum contrahitur
quadraturarum anquisitio sed prosequi non
iptalia dudrit donsunave
vecabit. Si tii aliquando vcabit eo adber
fere animum, libenter mittam quales cunque
meas in eam rem considerationes. Notavi
sane ibidem osculationes pe revocari ad differen
ias differentiarum visas tamen est usus quoque
calculi reciproci differentialis hic non conbemuendi
Non miror si din pressisti considerationem
triam aequationum differentialium mechanne
construendarum. possum duere me quoque ibi
integrali