# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068197:0044
# Permalink to this reading: https://leibnizlegible.com/page/00068197:0044?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 22v, page id 00068197:0044
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 23r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=44
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000044.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
# Lines: 98 recognised, mean confidence 0.76
# 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.

itaque compendi causa aftriab af -r sab
vocemus
 aβ
Et ex aq. 1. fiet a) = Aagh + ht dac. 
est 95.
aW
af +r vac
a)
af -r tac
aE
Ixog. 2. fit. L au = agh - ht sab = ag. tiab, cha srab
 ahistac
b5+ ∞95
Ex aeq. 4 fit  aa BC ( qu( ah - 5 aC) - +aa 3 3 (u (ah + 5 ab) = agrt sab, aht s ab, qu ( at - 5 Vac)
Exaequ. 1. fret : aa)
Ex aeq.2 fit
fa
a
= a +d c
h
aa n = a + b  
4ge
paf sac (-aar racrabs= Aaghilam
4 ibc lac + obc sab
Eodemmodo ex aequ. t et 2 quaeremns +
aaW L 4 agh,:  agtu
=aa + 4agh,: Acgh
e
 sac = tad
Uit
+acc rab  Y Aacgh
atb  rb sac
Lacuo -agha): lab. s =
- (2 + 3) tab  E + b
vil _aas ab At  Taturac - 4agh sab
C
=+ 4 abgh
vac
rab
vel fab (aas- 4agli) + Var saatae ragti)
agic lab + b tac
aaf gagh
e
aghrbc
st- aat
Hbc
(af- 49h lab. laD + artbe
= 4 gh, b dac + C sab = - agh, obe, lab + tac + 4gh Hbc
Hec peracto redeanis ad Hunc Hos valores ipsorum  + , et T. d possemus substitutre
 determinatio. Sit ob  l- +(H = 4am) = Ir + (CNN - 4aK), fiet
Il +. _H) - (3ln = H =  (1 -am (+ XV. (D) aK + (2) S(l- aam, AN - 4a X)
agagtac
aa95Yab
ah+Srab
ah -5 sac
Ot + aags vab
EE Caag +at 1ab)
ahu s vac, qu (est tab) art stab, qusel siu.)
a BB (aagah - at ah lac + aa s C) bat  saagah + atahiab + ac
V 55
ta95 Vab
seu fiit qus _t = g5) (tab + sac) = (3 (2aagh - 2 at abC + (aht + ag5) (+ab - Vac)
aags, sac
aa BB= aaf- iafrYab -abr
aaEZ- aaff + rafr tac - aCH
o (P. . Apul P lab e plac)
=( (aagh+ a Cst - 4 (ant + ag5) +C) ( poio ht 4 gr L0
-ye (aagh+ abst + Cant Fags) iab p. q r abt fa) Btacts saba as t dact
si faceremus L. + e = 0, seu ht +9p =0 magnafieret calculi contractio
 jam ex aequ. 1. erat aa B+rrac = 4aagh + Aa C GE Et ifin. Arg. 2. aaque tabur rasrtab = gaaght q abst fit gaagu= qul afgrtac) -qacC
sin fes prasse atrr t ragritaet ast abrr F rasr vab;in qacabs  se ele  rai cherteord gs e B)
 ohet = (b-c) an +g sr (b sac = C Ab): ga a (b - c)
ficrenim en (lib  + hinet: aque = ghre - stet. aequit AA = 4 am Et aep 2. pp = 4 a9
eragrine
c
al +ssab, ah -5Vac, ah + sb, a h- 5 Vac
eetq (aagati Lat atitab = aats Hbe, + aagah - at ahibac - aa st + bc)
Zaagsic
 aass-afrrac-arribe
natr sab
a(37 ((augratitab, atrus ac) fang- atrae, al t stab)
inde aamm + Aaa KK () 8 aa mk = asam at) ((t IlHa -llrur ibaa m. H. gatull. ganna
est autem l = aa B: alitstab, et ex = aa Z:, an - s taC, et m = acq+at sab et K = aagu - at Hac
H
aequ. 
a
in aeq. G, et habebitur buvalor ipsius gh per r et 5. Inde etium hoec tollentur ex 7. 6.
sed quoniam has contractiones adhibui, tentare volo an non liceat sumplicite
Edhibere N = D sine divulsioneque ita enim minus minor adhibita erit
ah +stab, ah - 5Yac
quslangu t at aniat aastibe f. aagat, + at ab la (L aat. t ibc
 et divisis omnibus per 4, fit qu (M- K) = l_ (mt L) = KI  = M AN
etfirt ((aa g + at Yab, ah - 5 raC) = (a ag - at tac; Mah +5 tab))
qu 
etfiat snd sublalisfractio ib
a
seu
nempe fiet