# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00067993:0083
# Permalink to this reading: https://leibnizlegible.com/page/00067993:0083?run=39
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 42r, page id 00067993:0083
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 41v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=83
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000083.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 33 lines, status machine
# Lines: 33 recognised, mean confidence 0.79
# 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.

da = dP +. Ergo dda (= + da P + dP dF) = f, dd P + d P da + d P F da
aat. 
At : 14
e itaque dda di = da dd P + d p da + da dp
da idpr
Resumamus: da = dx:r da = dt: p F B(= sAx: -X ergo d 3 Z lx:1- X 
1
) line sic;
jam C = 1 -X et ade = + dx. Ergo d B= - dx: C similiter d - dr: Y. Ergo per 1 et 6
fiet da: dP = dx: - dr, jam dx: dr = +: 1. Ergo per 2 et 8 fit da = - dP. f
Ergo cujus diffralis est ada = - ddP t = di dF. seu ex 2. fit dd a = dd P. + - d p da - dP t da
in qua seg. po b substiluendo valerem ex oy. 9. fit dd a L - dd .  da: dB - d P. da - +P d: d
seu dd dda d = + ddp da = dD da - + a3 ubi cum quaeritur a ex P.
faciemus ddP =0 et fiet, dda il = - dP da- da sed cum quaeritur id exa
faciemus dd a = 0 et fiet de dp + da = d d p
si C+51 = - dt: t
da = t:  1XF. Ergo dst: da = - 1 F F 1 + = - 1. t - t
n f33 B+ sC +. sit arcus a, siu
ratis 
3
i arcus a sium retus r, fist a = r  +=  4 5 X Cc pua - Y. + t rr A +   B+  rC eu
M arcus a, sinus versua, tantur l. filt a = A + =P. Z
Si nilus capiendus in ratione data ad alium arcum opumetem l. florda artus dati N, et arcus quaesitus ad
arcum datum ut n ad 1, et erit argus quasiti horda oS + 1 nn V2A + q- nn ~ B + 2s nn VC er
ubi si n sit namem impao series desunt esse infinita, et prodit aequatio eadem quoe prodit per vulgarem Algebr
Ac
5. 2sC
sit ratius 1. alicus a tanguns 4, quadrantis 1 arcus 9, et 2a -q = e et siet
ad mult plietadum datum angutifuali per numerum n
51 = e r GC +7  +61
5040
25.7C
17