# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068196:0646
# Permalink to this reading: https://leibnizlegible.com/page/00068196:0646?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 325v, page id 00068196:0646
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 326r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=646
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000646.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 26 lines, status machine
# Lines: 26 recognised, mean confidence 0.87
# 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.

Cuis aliquadiscaentiarum evanescit, id
Aliter Cdy +11 20 20y+21 = 6. Ex 2 sib
20dy + y+20 + d11, tulle ag = 8 Ex 3 tolle ay
fit (+20edy+) eydeo + cdu  et fit
2d edy
20. 11
ut ante
y = 10 +11 X + 12 X + 13X + 14X ete Zidendum an y et dus possint habere divisorem, communem
dy =  1. 1 +2.2X +3 13X f2 nX eu
sit y = ZV erit dy = Z dv + vsZ si jam y et du habeant
ntique etam du etum vel utique si dis
maxiuum communem divisorem v,
divisibilis per V, erit Zdv divisibilis per v. Ergo el dx  divisibias pe
item
non potest, vel. Z et V habent communem divisorem.
et do et v habent communem divisorem, vel Z est divisibilis per v. Aid dx et
D non habent coem divisorem, ponamus etrim y et du eoem divisorem habentes
esse assamtos, ut sint mini infimi; seu ut divisor communis, non habeat Hursus
Gu
umpua differentia coem divisorem. Ergo 2 dividi potest per 
faliamus y = covo fiet du = VD deo + 2cov dv it hac rioce videt posse
vetdu habere communem divisorem h. y = C0 V fty = v deo +v co do
ergo communis divisor ipsius y et dus est v si y = cd V qtalay - v 9dco, V. co g. d +q  do
et communis, livisor esto  q. Gene aliar si y divisibile per v: erit dy d sibele per v 2 2t
ergo y et diy condivisihiles per vn-
vv