# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068255:0107
# Permalink to this reading: https://leibnizlegible.com/page/00068255:0107?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 54r, page id 00068255:0107
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 55v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=107
# Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000107.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 69 lines, status machine
# Lines: 69 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.

posito a, b, c, etc esse ovel 1
In addendis notis dyadicis, quaerendoque a+b, vel a +b+c etc
ita ut colnae cumma exhibeat valores Luptarum dyadicarum didribute perc
posito a et b, et c, ipsas numenos a, b, c, ete significare evel
130 per columnas cinveni methodum generalem, et in qua quaevis literae semper eodem
se habet modo, cujus tundamentum est hoc Hhrorema a + ab (+a
t
tib
-nab
LSed deprehendi, theoremata qua ita prodeunt, esse nonnihil implicata, ut nondum
ut nondum occurrerit plogressus eorum infinitum, quia satis temporis
inquisitioni continuandae impendere non licuit  juterea anteu occurrit alia
methodus minus compo ubi theoremata sunt multa minus composita
quoniam nunquam literae ducuntur in seinvicem; ubi mihi statini
se obtulit regula procedende in infinitum stm
pergendo exhibebo aliquot theorematu, ut discrimen magis appareat a
lequente secur posteriore, quam subjiciam.
a+b = ab) a + b - 2ab: Addatur E quaeritur atb + c. Addatur c ad
cotumnam primam seu sedem primam, nempe a dextris, seu addidebent in unum
1 a + b -2ab et (C fiol ac +be val ) et per praecedens theorema,
tractando a +b- 2ub ut _, et C. ut b,) fiet ac +bc - habc a+ b - 2 ab +c
=2acC 2bc F 4 abc. = ac + bC  - 2 abc . a +b+ C   (ab 1 ac +bC) + 4 abc
add Adendo Additis Addendo C ad a+b, addidimus jam ad (a + b 2ab
sed restat ad huc ab) graliquam valoris, et fiet tandem
a +b +C = ab 1 ab + ac + ber (4 a +b +C - 2 (ab + ac +bc) + 4 abc
u t t
Addamus d siet Ex antir  ad primani columnam  fiet 41b  id(abracibo
+4 abcd + abia a +b+ C+d. 7ab, ac +bC) + 4abcAi) + 4d (ab tacibC))
ta Addamus duas secundas columnas fint isn ac
da 6d abealbed a rac Labed b abd
proterta: (Xd Cabrac +bC) BabedC abcd 2d (abrac +bCB 1Zabed +12 ab 1) + Wabed Babed at
at prohovaset unda uunda filtab +ac +bC Ta bet d (a + bt
pro param tia cosimna, a
-2d6 ab + ac +1dF, bc) + gab 2abcd. + Itaque tandem e
a +b+cd= abcd (. arhabed 
a abc
+ ab
aot Eodemue modo perso
2ab
+ 4abc
=8 abed
ad a+b +c+d +Ctita
1. porto.
sed quia sed quia calculus paulo est prolixior, et licet in prima sec
depterrima columna appareat regula non aeque tamen facile in
sequentibus eruitur, obtulisque sese alia Methodus multo simplicior, in
qua numeri progresionis duptae, vel alii quicunque occurrant, imo
temf ductus quidem ex literis in se invicem. Id saltem  ab est
qu literae a, b, cd, etc non tractentur non eodem modo verum
ne id quidem male. Quia revera compendio servi magis notae
neultrant in intima ejus quem exprimunt numori; si distingua
mas eas quo novissime aequantur o, ab hisquae prius. Nem
Siat duae notae a et b. quarum quaelibet, significare so
o vel 1x et quidem si  alterntia solum debeat esse o; altera
manente , tunc ea quae  fit, un soa 0 fit, vocetur
a. litaque a erit ea quae sola o fieri potest, b vero ea, quae
His positis considero quadratum
non est o, nisi ambae sint 0.
 numeni b-a esse aequale ipsi b - a, et adeo fore b- a = bta- 2ab
a sed quia
seu b+a=   2 ab +b- a seu b + a = ba
semper ponr potest in ba esse b =1, ideo ponitpotest bra 1 a) - a. idque
aliter et brevius demonstrari poterat hoc modoa 2a -atb= a +b. Ergo
arba na ai, An atb a
Franhanc
putique prae
ferendam
enseo,
la