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# Title: LBr. 57, 2 · Bernoulli, Joh.
# Folio 160v, page id DE-611-HS-3653099:0320
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 161r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-3653099&page=320
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-3653099/jpgs/default/00000320.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.88
# 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.
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# After the first blank line: the recognised lines in reading order, one per line.

G9XNF
GN
2G9, unde elemento G9 utrobiqu per divisinem destruito,
s
emergit aequatio in terminis finitis seuordinanis KHxGN + NFXGK
= 2GNXGL, quae quia KA = GF - Gk, et NF = GF-GN mutatur
in hanc GFXGN = 4GNnGk- GF XGK, adeoque Gk=
GNxGX
4GN - GF
quod ipsum eit theorema quod Tibi perscripseram, ob simplicitatem
exprestionis non parum atile futurum in catoptucis ad catarantticas
fine maguo labore invenierdas; cum aliis formula ordinaria ex
primens radium reflexum ope raii circuli osculaatis multo magis sit
composita, quisse in cejus terminis reperias solida et planasi ava
altiores dicensiones, quando nortia continet dualapat planum et
lireas. Ati pratenea mihi suat modi non mirus elegantes ad pra
dcitam pastiam formulat perveniendi, quorum unus petitur es hac
eat nota proprietate, quod suma angulorum binis radus iicidea
tibus proxiniis, biaitque item reflexis contentorum aequatr suo resperti
ve angulo ad centrum circuli osculatoris bis sumto, nempe N+ k= 2D
svc eit quod tres anguli N, D. K sunt aritametice contnue pro
portionales: Ex quo vel in hansitu concludere potes, radium
reflexum GK pro diversitate Lorum angulorum tribus modis variare
poste; angulus enim N aut minor est rang. D, quo casu Gk erit fi
nita et asprimans id est versus concavam spenili partem sumenda:
aut N aequalis ert 2D, et tunc GK abit in infinitua; aut n major
et 28, id quod reddit GK finitam sed negativam, hoc est sumendam
versus converam seculi partem; ex hisce tribus casibus primus tan
tum est quem adnittit solutio a, quam reliqui duo mutilem et
e
viritam redduat, ob rationea quam ex praecedentibus meis litteris notti–
Ut vero hanc cautionem quo parto dirtinite determinaveron, nunc
aviro quoniam petis edoceam; consideres velim meam formulam
GK.
GKxG
4GN-97 patebit ulique oportere 4GN majorem este quam
GF si velimus ut GK fiat affrimans et finita, alioquin certe aut
regans aut iafinita evaderet; unde jam consat spenitum sphaericum
ut pro transformatione curva alicuss in se redeuntis uti liter adhibero
petit spatae renitudions esse detere, ut es qurocansus cnroai data