# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068208:0078
# Permalink to this reading: https://leibnizlegible.com/page/00068208:0078?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 6
# Folio 38v, page id 00068208:0078
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 39r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068208&page=78
# Source image: https://digitale-sammlungen.gwlb.de/content/00068208/jpgs/default/00000078.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 67 lines, status machine
# Lines: 67 recognised, mean confidence 0.86
# 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.

ipsius co substituendo in praecedenti analogia, fiee. et
at ex pracedenti analogia. erut co aequal. X dyia ergo
hos duos valores aequando fiet: a dx: b aequ Xdus: a, seu
fiet:  dy aequal aa dx: bX seu yb aa aequal sdx
C
sive si progressiones sint ut numeri erunt circulationes
ut logarithini, hoc est, si rad  anguli PA.N, PA
sint progressionis arithmetica, erunt radii seu rectae convergentes
a curra ad potum, P1N p2N, p3N, propressionis geometricae.
Habetur autem simensio huius curvae ratione addmodum
facili ita ut habita dimensione arcus unius habeatur
dimensio aliorum omnium. Cum enim sint A0d;. N. D, 2N.d erc.
ipsis A.N, 1N2N, 2N3D p etc. proportionales erunt ergo
N
en pe
ergo
Centro P. radio pA describatur arus secans rectas
ex
yo  PA N
A0d+1NI D est L D
A0d L 1N.D+ 2NId est PA- P N
s
et  summa omniam
AiN+ IN ae est A2N
A, N+INZN +ZN3N est A3N
cep
A Ergo erit A2N ad A3N, ut
ut est
N ad 3L3V
eN
A P N
grN ad 34
3N
vel
2
ergo ipse rectao  paut tunt curvis AN proportionates.
rect
itaque sidetur ratio unus curraes, ad arcus curvae, ut A3N, ab
a
suctm convergentem PN, vet differentiam ejus a costi con
 e
stante Radi centro p radio
so
Ergo erit A2 N ad A3N ut 292N ad 3q3N, ergo
ipsae rectae qN eunt curvis AN proportiona
arcus ut A1N
itaque si unius curvae dimensio detur, ex data sua
Fimo habem resta 2
est respondente, etiam reliquaerum arcuum
Et cum non seleat
d
dimensio dabitur
Thombo tamdin manere, quia portim
petui pphaerae in qua versata est, pro plano haberi
possit.
thombicae navis in uno
sufficietcegathoc ista ad dimensionem cursus navis
et contra ex data dimensione cursus per aestimatiionem solitam
ad inveniendam exi punctum rhembicad quod navis pervenit.
summa
arcus absolute
est enim A.N
secans anguli
datae per-
PAIN, ad
radium m
ad Aod, ut omnium