# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068124:0043
# Permalink to this reading: https://leibnizlegible.com/page/00068124:0043?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 22r, page id 00068124:0043
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 21v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=43
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000043.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 32 lines, status machine
# Lines: 32 recognised, mean confidence 0.88
# 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.

sit divisor ipsius p, et secundum residuum eundem, qui sit divisor summ
termini aequationis data veluti w; hi residui erunt ille b, huc c
et dividi poterit aequatio data per b + cx. Quod si quocunque assum
d
to h semper habetur aliquis ipsius in divisor, qui dat residuos eosde
s
b primum, c secundum, d tertium, ita ut b sit divisor ipsius p, et
d divisor ipsius w: Poterit aequatio data dividi per b + CX + dxx; Et
Nempe itat
porro ssi assumto quocunque h semper habetur divisor respondentis m
qui snti verbique ratia B
eosdem: oprimum, c secunduma, d tertium e quartur
plares aut paulciores ita ut primus fb sitdivi (b) sit divisor ipsius B, et altimin
ita ut b sit dritor iohus o, et e divisor ipsius n poterit aequatio drvii per
per
sit divisor ipsius  W; poterit aequario dividi
b+ CX F dxx + ex. Et ita porro. Ubi notandum, si talis consensur
residuorum pluribus modis obtineatur, pluribus modis succedere divi
sionem Formula datae, et semper rem, si semel succedit, bis succedere
debere. Nam si aequatio divisibilis est per aliam, etiam divisibilis est
per prioris divisionis quotientem.
Ratio horum omnium facilis est. Sit aequatio vel formula p. F gX
t. FXX + 5 X3 + FX4 L VXS = WX6 = O: quaeritur an sit divisibilio
per aliam b + CX + d XX + ex3 = D. Utramque si explices per y + M
vel per y + (4) vel per y + (Chd), erit ultimus terminus aequationis e
e
O factae, p + qh + rhh + 5h3 + F h+ + vh  = w h- m; divisibilis per
s
ultimum terminum aequationis aD  facta, b + ch + d hh + etc=
Itaque patet fore
F gh F rhh + 5h3
AF+ vhs 1 wh= m divisibilem per brcha dhhred