# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1032977698:0235
# Permalink to this reading: https://leibnizlegible.com/page/1032977698:0235?run=74
# 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 213, page id 1032977698:0235
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1032977698&page=235
# Source image: https://digitale-sammlungen.gwlb.de/content/1032977698/jpgs/default/00000235.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine
# Lines: 31 recognised, mean confidence 0.81
# 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.

CAP. III. Analysis Infinitorum.
L
nia Z; _ ANTIIEa b dCteeMiHAFA, UF OIHIA
by ad omnia b2; A jam expetantur (olida co.
noidica, reducantur by e b Z ad circulos,
Bc
aC Aat by =: 2r, _C bZ = 2r, Crit, SeDOTFa
ratione 2r, applicata 7 Q Ccu k = NBy, et
QN SCu B = sbZ; _ COlIduM ex AGO cir-
ca AO seuomnia 2r ad solidum ex AOF
Bh
circacandem 10 seuomnia 2r, ut spatium
AFO seu omnia p ad spatium A MO sCu Om
nia Z: unde pOTitO A O: X _ yy = 2 YX X X,
erie k4 = 2 2Er = = BB∞ ∞ : e, dato lOCOIPFIHS
Z, IMnOTCTCCL CUIVR N C proprietas, cum
Sit Bh= bZ.
Si quis autem malit solida tubulata seu annu-
laria: detuE CIFCA aXCM AO FigUr2 AGL,
Cujus applicata 0) N = 2 0) = 2; item alia
AF M, cujus applicata QS = D 9 = y, Crit
Figura prima ad secundam uc omnia 2 ad omnia
y. Ccu assumta b determinata, _ r prO nu-
mero, uc omnia rbz ad omnia rby; quorum
utrum que si reducatur ad armillas seu quadrato-
rum differentias pro acquirendis Colidis annula-
ribus juXFa 5. 20. Hatg. rbZ = k k - BB, 8
b y
f = ut 2, Crie Bh = kk = r bZ, d
ut V= ff = rby. Cum aurem, cu hh, tumm a u
SInC