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# Title: [Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductae] Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductæ (shelfmark Leibn. Marg. 149)
# Folio 77, page id 1032977698:0099
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1032977698&page=99
# Source image: https://digitale-sammlungen.gwlb.de/content/1032977698/jpgs/default/00000099.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
# Lines: 41 recognised, mean confidence 0.83
# 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.

sa
do
10
M
1
s
C AP. I.
Analysis Infinitorum.
nem; quam inter sese habene FD _ OB; SCWInFeKCCPEA
ec applicara ejusdem crianguli. Cutm autem mulcis qui
dem modis haec quaestio porsicrariari, pecique, uc. daco
in criangulo TDe punctoD, inrenIaTUF CUrVa ADE, ip:
Jam rectam TF in daco puncto concingens: underum cur-
VX ParAMeTeF, icem AC sCux, post peneralem CUEVEntu
ram cognitam inrectisanda Forenc. Duin _ plurimis modis
diverta, circa rectas curralque semutuo rangentes, quaeri
pollene, proeorum diversirare, quae taniquam dara suxpo-
nunEur. HxCVerolicet ex Facili, praecedentibus percer-
tis, consequantur, in rrronum stariam unum aur alcerum
exemplum addemus.
72. SIEFIT. X, reCta Z D in inHIIMIM VeETUS
Lprorenta, cjusq: positio respectu linee 75d-
ta, in eaque astionatum punctum D, Oporiet
curram AD F hanc rectam in Drangenrem de-
SIgNaEC. DuCta ex D reCta D 9 ipsi Z O HOEM2
li, aut ad quemlibet datum angulum, (IE eX
trianruliz
Dproprietate (Fact a F :t, d 9D: y)
Perpetuo p: g:: F: y, unde equatio crianguli
pF =gy, vocatisque ut luDea, AP = DH: e,
_ FHI: a, crie haec reducta ad infiniresimas
ge pa, qux in omnibus hilce casibus ob-
tinet.
lam quaeratur parabola AD F. iplaur rectani
YD in PUNCTO D tangenS, cujis xquatio
rX = yy, Facto Ag: x; dabit haec ad inFini-
e
relimasredacta re =i 2 ay: Unde  27
90
unde cum p ec g item t ee y in triansulo
data Cine (priariguli enim proprierAS ec punCrum