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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 21, page id 175906937X:0045
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=45
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000045.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 73 lines, status machine
# Lines: 73 recognised, mean confidence 0.77
# 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.

Dec dI
AM, qua
Jomina.
Ori tue.
etm. UB
11a5CC
delieule
Tanquam
nieaten,
Foccitalte
uE d, auI
scrivele
aCom.
ubmeri.
came
I reGII.
16, qui
Muou
adctatur
acur de
Fo.m a
1
e lesibo
11616
bp1
110
BLA T EE E SE OS EINFN ERS ALTS.
producto scribendum esse numeraiorem aa. Non secussI
2.
mulciplicetur per a - b, productum erit bb. Unde patet ad muI-
ciplicandum per 2ab; quoniam mulciplicato, per 2b, prO-
ductum ecta; superesteantum ut hoc productum adturc mulcixsi
cetur per a, ut habeatur quaelicum productum aa. Similicer ad
mulciplicandum = per 2 a b: cum mulciplicato = Per 2, Hac r; hinc
mulciplicandum tancum rectaox per ab, de tir productum quaesi-
cum 1 ab seu ab. Fclic de aliis.
De Deductione fractionum ad simpliciores.
AaC
Am ad reducendum Fractionem, ad simpliciorem; elisa com-
munilitera c, qua tam in numeratore quam in denominatore
3
reperitur, hiec . Sic e ad abbreriandum =: elisisliceris a, b,
numeratoris acque denominatoris, hoc est diriso tam abs quam
abcperab; het =.
Eodem modo ad abbreriandum
aac aad
cd -ad: quoniam dirilo
AACPEECA, OrITUT=, id quod mulciplicatum per cd -d d, pro-
ducit aac = a ad; hinc
ccum, eric
aac = aad
ca- ad ad minores terminos redu-
Pariratione ad reducendum 2ac = aad - bbc f bb d
cd- dd
: quia (uE
supra) diriso a acpered, oritur, id quod mulciplicatum per
Cd --dd, producie a ac = aad; eE rUEIUS = b bc divilo per cd,
Oritur - =, quod percd = d d mulciplicaturm producit - bbc
abbreriatum, Facic = 2 = bb
Lbbd: hinc 2ac = aa d - bbc. +- bbd
cd - dd
ab ccoomm. = 4abCC m3 P
SiCe
oop PZ = Ampo qt abbreriatum, Facie
Non secus
2a C- a a d = a6 d + a a d
cd- ad
a cemm
PPZY.
reducitur ad  vel
A6
PaG. 2140
lin. 15.