# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/DE-611-HS-958803:0486
# Permalink to this reading: https://leibnizlegible.com/page/DE-611-HS-958803:0486?run=74
# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 242v, page id DE-611-HS-958803:0486
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 239r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=486
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000486.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 recognised, mean confidence 0.82
# 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.

(0
suc
(2ob. II.
sdem positii si (Frg. T.) P2 jam sit ut funitio data iprius arcio BF.
quaeritur determinatio curvae BFN.
1.
solutio
siroe verligris inuictendo res facile expedietur: Erit eanita semper trian
ge
gulum ZLY = Liangulo 3NY seu 2Cin LM = 5Din Apo; jan vero LM
(LR -MR) ett differentia funitionum duomt aruut BFO et BFT; ut
et Api (A∞ - pc) differentia funitionum duorum aruum BFco et BFDB.
Atque sa functionum differentia eodem modo reperiuatur ut supra dulum
multiplicando sciliiet differentiatam siapliciter fupitionem neglerta
differentiali per differentian duomm aruuum BFO, BF5 nempe per IX
adeoque loco 2Cin LN = 3Bi N scribendum eit F Iip DBF Oin X
Kin DBFcoinOF. Qcconiam nunc per naturatm ellipreos OX et cot
sunt inter se aequalet et proinde TX ad 6E ut tangens ang. IFO ad
Lang. kGCo. est vero ilerum F) ad GK ut FOx sin. FOl ad cox sin-
Pcok; ergo si loco FI, Gk et FX, BZ sumantur eorum proportionalia
erit FO Sin. FO1 in tang. 1 F Oin DBFO=  coinsin. Gcokin lang. Kesco
in  BFco; sed quoniam ut conilat ex natura sinuum, tang. et secant.
sin. FOlin Lang. LFO= reitangulo inter linum totum et sin. TFO; ita
etiaa sin. Gcokintang. KGco = sin toliin sin. KGco: erit ergo FOin
sin. IFOn DBFO = Gcoin sin. kGcon DBFco; seu si loco BFO sumatur
aequisolleas BF, et loco BFco aquipollens BFG, habebitur F Opsin.
1FOin DBF =  coinsin. Kes com D BFP: adeoque sin. 1FOin DBF ad sintesco
in DBF ut Pco (90) ad FO ut sin. OF ad sin. OF, et permutando
sin. 1FOn D BF ad sin. OF ut sin. Kescoin DBFco ad sin. OF in ratio
ne conitante. Problema itaqe jam analyticum faitum eo recdit Ut quae
ratur curva BF hanc habens proprietatem ut sinus curvedinit in
quovis punito F sit ad sin. 1FOn D BF in ratione conitanti: Hoc
ut solvatur posilis ut prict (Fig. III.) BP = y, PF - X, BF - +, Sp= du
Cl = d Flvel Fm = dt; funitio data arcus BF, = v, erit nl
faciamus itaque secundum proprietatem curva modo inventamr atday
in D0
do=at: a unde hac aequatio.
t
sumtiique integralibus
aatadus
atddu
adtatus ax
dx
ac  dyr = ab
 dy2 = V seu quia a et at sunt conctantes poteu
a
simpliciter poni v - (adus
curvae quacita.
addyat
dx2
dx
at cly
:quae itaque aquatio determinat naturam
dchdrn