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# Piece: https://leibnizlegible.com/api/records/59323/text
# Catalogue record: 59323 — [Aufz. zu Potenzreihenentwicklung]
# Incipit: series infinita exhibet relationem generalem inter duas quantitates
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=59323&katnr=57519
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 318–319 (from the shelfmark LH 35, 13, 1 Bl. 318-319): 4 pages, canvases 631–634, page ids 00068196:0631 to 00068196:0634
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=631
# Lines: 156 recognised on 4 of 4 pages, mean confidence 0.79
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 318r — 00068196:0631
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 319v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000631.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 65 lines, status machine
eseries infimta er phibent relationem generalem
inter duas quantitates, v. g. sit y =  X potest poni
 y = 1 X + 12 X + 13X + 14X + t. posito X esse minus quam 1. et
vel y = 1 + 12 = 13 + 1a  + esc posito X esse maj. quam 1
possit et relatio generalis ex primi per continuationem exponentium in infi–
nitum vg. y- xe
n log
xiite
neeses ita lag. y = 1 log a (10X)
etc
XC  (Y)d= X loglogus = log. logix = nX  log 1X
tor
etc
nx
et log (logsloglogus - loglog 10 X) = log. 1X) - log 1X = lg 23 X log (13X). 144. et 
lognX
sed hoc  lommo sed t non ita commod. est haec relatio
ob comprehensiones perpetuas
Quaevis quantitas X potest exprim per   10 4, 2 + 12 2 +1. 5 + 14 4 4 et
ubi pono 10, 11, 12, 13, etc. non posse esse quantitatem nisi 0 vel 1
quonioro
sit jam sit X abscissa et Y ordinata quaeritur dx exprimi possit. Dico non posse,
sed assumi contantem. sit jam g = 20 + a2, + n2 + 23X + et. potest dici y
Sax
30+31 2+322 + 33. 8 + erc A potest poni 30 - , 420 et 31 = + 21 - dys etc
erit semper ovel 1. utcunque appropiaquent sibi ipsae y
drtax = 21. id hic insigne, quod non assuigitur ad potentias
X
jy- 10 + 2. 20 212 + 2. 20. 2 7 + 333
N5
20.2 20. 2 20. B 20
H1.
2. 22 2. 23
22. 
+ 21. 4. 22122 +2.27 2 + 21. 24. 2
15
21.
222)
23.
2026 202
H. 24 22. 25
2324
sed incommodum
hic quod coefficientes
sunt inconstantes.
Sed po  constantibus perdentur melius procedere expressio per
quaenitur summa progress. Har
dyadicas.
esto sum (+ +  +  + 9) aliquousque nempe finita:
y = 10+ 112 + 122 + 3. 2 + etc. posito seriem esse periodicam. Possumus scire credo
 in unteressum, qo quuo sid quam quoo que numer non excedat periodus
+.1 =
100
e
So da
a 100
 108H 100 +2
100
10013
Lu=1 - 2
14 = = 2
 2, = 1 - 2 +4 Y + 16-32
100
100+4
4 - 5 + 16

## Folio 318v — 00068196:0632
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 319r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000632.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 2 lines, status machine
FRIED WILHELM LEIBNIZ
RSACSCM CHIOLSOLIO

## Folio 319r — 00068196:0633
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 318v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000633.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
3.C ps

## Folio 319v — 00068196:0634
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 318r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000634.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 88 lines, status machine
100 105 - 100.
lod
s
1000 Eooc
100 10000 1000000
100. et = - = 1 + 001 + 000eI + 4000051 + 00000ral + 00000 000VOI 400000V00V0VOI
100-1 (00 -2 1c-3
100 2 = =- = 1 + 002 + 000b 4 7 0000008 + 0vo0 av16 + o o0 vr 134 40000000000064
100-1
0c
100
1- 100
100-3
100
= 2 =
12
etc et
100+1
10
1F003 + c9 +00000D7 +000000VXY 4 00000000243 + 0000000000729
k et et et
etc
etc
- = 1 - 003 +0000 9 -00000027 +0000uav B1 - 00 v0v050243 +00000000V0 7X)
10072 = 17 700
100-
etc
= 1 = 002 + 0000 4 -500v 400000 16-00000032 40000VV64
1100
1
10013 1 + 700
etc etc
et etc etc etc etc etc
Ergo ((100 + 100 + ete usque ad 100.) + (100 108 + et usqe ad 10
100-1 100-2
100 -99) N1voF,  100 +2
etc
=100 s(= + L + het ud =
1c +99)
2 3
erit Se+ Snam funt 199 + sum pueidratorm + Sum biquadr. B + sun. bicub fg + etc
10000
1000000 106000 100000DWV
eliduntur autem naturales, cubi, jurdesoludi, seu dignitates impares
termino
continuare licet quousus libet, error est minor summa sequente
Nolatu dignum est series signorum non alternantium, quae fiunt
199
ex alternantibus per elisionem, participare de hac earum commoditate
ut erpor minor sit termino sequente
isem est si nro 100 sumatur numerus cquicuaque, ut pro ut scilicet
su assumuntur tramionii seu recipioci summandi
procedendum est eousque donec sumna dignitatum exiguam rationem
habeat ad suum divisrem
Haec methodus non potest esse utilis, nisi quis tubulam habeat
pro summis potentiarum aliquousque produxtis Ni faltor Tabula talis
aliqua est videndum un talis Tabula sit e opere (ergusonis
 + 15 + etc = 2 = (1) + 1
1)  l 9)  + 2, + etc =
+ = + + + = t es = = = 1) +(3)
16 64
vodx 
 X
Ergo 1 - = - +) XY
seu , - = =
= 1
-
-
ux + d
X
+S
 ab X = 2 usque ad X ultinum naturatem
CX + dy utdo - X = X+ dY
quem cunque
=X+ dx + X+de - XV
NFd rdo - xFdx = X F (Etdx)  - 1 _tde) - x = 2 X  vodba
et du
 av
+
Ergo (X + dx) - X = (X + dX) (
12 X. M, + 2. C-1. C-2 XC 3+ etc
sit X = +a _ = et e = 2 fint d (X = 2t 2 d2
Zd
Eeti
2.
 Z. 2V + 41
qu (2247d2)
ei