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# Catalogue record: 15946 — Johann Bernoulli für Leibniz und die Acta eruditorum. Curvatura radii in diaphanis non uniformibus. Beilage zu N. 14
# Incipit: Tot quidem hactenus apparuerunt methodi quas maximorum et minimorum vo
# Date: 1696-07-31
# Sender: Bernoulli, Joh. — Addressee: (Acta Eruditorum)
# Akademie-Ausgabe: AA III,7 N. 015
# Other printings: -Gerhardt: Mathematische Schriften, Bd. 1-7, 1849-1863, 3 S. 302-309. -E: Acta erud., Mai 1697, S. 206-211 (teilw.).; danach: 1. Opuscula omnia Actis eruditorum Lipsiensibus inserta 3, Venedig 1742, S. 302-306; 2. Joh. Bernoulli, Opera 1, 1742, S. 187-193; 3. Bernoulli, Streitschriften, 1991, S. 263-270.
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=15946&katnr=30283
# AA III,7: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-iii-7
# In the Akademie-Ausgabe: AA III,7, p. 142 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/III7A.pdf#page=142
# Work: https://leibnizlegible.com/work/DE-611-HS-958803
# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folios: Bl. 146 (from the shelfmark LBr 57, 1 Bl. 146.150.147.149.148): 2 pages, canvases 293–294, page ids DE-611-HS-958803:0293 to DE-611-HS-958803:0294
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=293
# Lines: 84 recognised on 2 of 2 pages, mean confidence 0.88
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 146r — DE-611-HS-958803:0293
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 150v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000293.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
Joh. Bernoulli Curvatura radii in Dcaphanis non uniformibur
solutio Gemina analytice inventa et syutheliie. demonitrata)
e
Problematis a se in actis.. .. proposit. de invenienda
Linea Bruchyitochrona, id ert, in iqua grave a dato
L∞.
punito ad datum punctum brevis
C
decurris Copmntio ercurona
decurrit, et de curva syncheona, seu radiorum focis unda
c
et constructio curvae synchronae, seu undae radiorum lucis
Tot quidem Cartenus apparuerunt methodi quas maximorum et
Mnimorum vorant, uet sihil fere tat subtile rcdare videatur ham
concertent materiam, quod earum auimine penetraré se posse non
putent illo qeci se vel Aeutores ipios vel Huitommm asseclas gloriantur.
Interim jurent quantum volent in verba Magiitri, videbant si tenta
re velint nochum problema minimme oercein intra anguuos metho
dorun suaram lisiter, qui eourqe tantun sere extendunt  et datis
pluribas infinitiive quantitatibur invetienda sil una maxima vel
Minisma: berum ubic iprae quantitates, quod imtorio contingit, ex
quabus elgenda mexita vel tuinima non mag sunt determinata
C
quam id iprum quod quacitur, hoc opus hictabrr eu tredeant Car
tercus, Termati, Robervallius aliique oeiolia ita acriter propractantia
suae cujulque methodi languata profocis et aris militabant, et fateant
eagenue hce sibi aqua harere. Kon metum eit hec etiak volo alio
ex
rum inventa explodere praecliterunt ulique multa, et firem quem siti
proporuerant egregie conseuit: sunt; quemadmodun enim de hujurmo
di Maxisnorum et mitimorum concideratione hil quicquam in eorum
scriptis reperitur, ita pariter pro aliit quat comunibus resolvendis
sucas methodor hon venditarant.
Con ego pollueor universalem methodum, quam quie truitra qua reret
led peculiares meder non solun quidem in soc sed in pluutas aliis sue
cedentes, quibus problema Roc feliciter enodavi, solutionemq, meam
dum alii atrar quarerent Celeb. Leibhilio ilatim submiltere decreoi
ut illam quondam cum publico comunicaret cum sua si quam re
percret, de quo quidem non dubitabam, sagacistitm viri ingenium
plus Patis compertut habens; et reapre dum hac scribo ex priva
tis ejus literir quibus me screbio cohohettat intelligo supra spet ipsi
si
placuisse, et (quod illum, ut dicit, pulchritu dine sua ut potrum Evatu
problema meutm)

## Folio 146v — DE-611-HS-958803:0294
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 150r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000294.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
ad sentraheret) protinus solutionis factum esce compotem. Qeud alii
praectiterint exitur moncrabit: diguum utique oportet sit hoc problema
cui solvendo aliqued temporit conseerent Geonetrae, cum tanto viro
negotiis licit dirtractissimo ita visum fuerit, ut horatu suam non
incliliter collocasse exirtimaverit; Et ed iprum illis fatir luri
etto, quod s solverint ad secretistimat veritatet, quat sine hoc vix
est ut assequantur, aditum habituri scat.
Euid quod magis mmiramur quam quod Hugenins primmus invenit,
in Cycloide vulgars grave facele descennus etochronor, a quocunqe
excloidis puneto incipiat moveri; sed hecrio an non obaupetrat
plane cum dixero hanc eptissimam Cycloidem irochionam Huge
maram esse horhem Brachyclochronan quaesitum, ad cujus
e
cognitionem decabur viis perveni indireua altera, altera dirula
ariclendo prioromirum consensum detex: inter curvitatem Radio
lumitis in medio continuie variante et Curoum noitram brachyito
chronam, aliaque observavi inglubus hetrio quod arcani subert.
quad proderit in dioptricis: quamobrema verum evit peod in propon
sitione problehatie asserveret, non in huda speculatione consice
re sed in alis scientis in dioptinis puta cirato habere tam
masimum. Sed ut quae diximus re ipsa contiienti e priorem
solvendi modum
Fermateur en Epirtola ad De la Chatubre (vid. Epirt. Carteti Edit.
Lat. Tom H1Y p. 147. et Tertati Oper. mathem. p. 156 segg.) prituus Etabi
livit radiua lumisis ex medio rarion in denrim tranteunten ila
refriagi ad perpendicularem ut habita ratione temporis, radius
(qui a punito luminanle ad punctum illuminatum sucestivet
procedere supponituur) viata faciat brevissitata, ex quo princi–
incidentia
pio ocendit, sinum anguli repartionis esce ad situm anguli re-
fractionis en natione data directa mediorum raritatun vel re
ciproca denritatum, id ert in ipra ratione velocitatum, quibus
radius media penetrat. Quod portea Acutis. Leibnitius in Ait.
Erud. 1682 pas. 185 segy. et Kob. Hugenius in suo trait. De Lumine
pag. 40 sececinetius demonitierunt, iprumque principium physicuta
termetin
vel metaphycicum potius quod sua demonstratione Geohetrica con
tentus et oscitanter satis de jure suo decedens Clerselerio urgente
deserccisse videtur, validistimis argumeatis attruperuat.
Scnunc