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# Piece: https://leibnizlegible.com/api/records/60524/text
# Catalogue record: 60524 — Potentiae serierum. Item Methodus compendiosa substituendi et incognitas tollendi, nunc demum deprehensa
# Incipit: y aeqv a] + bx + cxx + dx³ + ex^4 + fx^5 + gx^6 +hx^7 etc.
# Date: 1681-10
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60524&katnr=57120
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 278–279 (from the shelfmark LH 35, 13, 1 Bl. 278-279): 4 pages, canvases 551–554, page ids 00068196:0551 to 00068196:0554
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=551
# Lines: 104 recognised on 3 of 4 pages, mean confidence 0.81
# 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 278r — 00068196:0551
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 279v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000551.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 68 lines, status machine
octobi. 1601
copen ps
potentiae serterum item Methodus substitnendi.
incognitas tollendi, none demum veprehensa
y aequ a) + b X + CxX + dX + ex + f x + g X= h BC.
dus aego + b +2CX + 3dXX + 4 ex + 5fX + 6g X etc
ydus aequ. B bbX + Cb xx +db X a eb x + fbX + gG Xs etc
+2ac.) + 2bc +2cc +2dC t2e +ifC
 + 3ad 130d +3Cd +3dd +3ed
+aaC) +abe +4ce +4d e
2yty se yy aequ 2bax H 2bbXX + rebX + 2db ~ 1 2 eb X +2 sb X + 3GbX erc
+2. 29 + 2 2bc +22 al +22de +2rec f2. 2fc etc
2.3 ad) renbd +23cd +2god +23 d et
e
 ere ere et
aqulagx
aepubxt
yy aequ.
 ct 
ut emai
bb. XX + 2bCX + 2bd X + 2bC X + 2bfX +2bgX
lad7
+ cc X +2cd +2ce) +2cf
2de
+ dd
aCX X+
Ergo et is du compendiosius haberi potest:
(+boX + 3bC X +4bd X + 5be x +b fX5 +7b9X
+2Cc +51d +6ce 47 et
1. +3dd +7 de
y’aqu. a + 3abX. + 3ac X + 3adX + 3a CX +3a s X + 3agX et
+3ab + 6abc +6abd +6abe 46abf. et
+hac tbacd 46ace et
+3add erc et
y aequ. lX +
pota
im ide u crpragta
omittatur a
seu ponatur
a aequ. 0. quia
in differentiali
seu dus non
extat
et
Elegans hic
consensus
dubrum
C
licta
enuntiando
odoeum
y+ aego a + 4 abX + +a CX
6ab
+ b3X + et
+ +aed X + 4a CX + 4a fX + 449 X. ere
Aabc gabd nale a
+6ac tacd H
+a
+4ab +1abc +12abd snabe
+na bc 154 abed +24 ab cex
+12 abd
eu
ene
tantum pro a. b. 1. praecedentis
endo Ec. d. B.
+X + eu.
+aac tnaca. Hhac nos
+nacoknad

## Folio 278v — 00068196:0552
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 279r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000552.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 12 lines, status machine
 aequ a + B. erit y aqu a +Za b + Z
il
132
e
e
2 112, 3
903
a P. 9c.
ergo si e fta y sit series infinita, et a sit 1. et sit
Z q. Z quantitas trans cendens, vel irrationalis, vel in definita vel
yt quantitas transcendens, habaebitur series infinita in qua nulla
erit quantitas trauscendens

## Folio 279r — 00068196:0553
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 278v); this page is its right half.
# No recognised text on this page (recognized).

## Folio 279v — 00068196:0554
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 278r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000554.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 24 lines, status machine
infinita
sit aequatio Ca aequalt +mt+ nt + p  +9F etc. Et sit alda aequatio
finita quidem, sed indefinita: 1, At + 12 1 + 13 l e t+ 5 t aequ. 20a+2 1t + 22
Y + 10t + 20 t + 30 + + 40 f +50 t aqu ora + opta + 21 ta + 31 t a + 41 t a +51 t a et
Hom on t op t4 01t 
+0r a + uta 122ta +3 a 142t a +52t a  t + o3a + uta + 23 Fa rtatas
qan
+04 tod
vam tian a
Eth e
sa
+04H 104
o+a =IEta +a tAC a + 44t a + 54 t a etc. L es a +sta +25Pa +3slatat estâ
-04a - 14ta 24l a- (5a - 44 a - 4l a eu
Tollenda jam est a ex aequ. 2. ope aequ. 1. multiplicando eam
per fant altiore aequationis 2. et cum ipsa a coefficientes ut ita partes altiores
partium
continue; reducantur ad inferiores: ita exempli causa C sustulimus et omnes
ejus terminos neduximus ad terminos comphehensos in D.  Nam ex. 90
20a   404ha +04lLa +04mt a + 04nta +04 pt a+02 qt a est oq. 8.
Hoc modo Eodem modo omnes termini in quibus a reducentur ad terminos
in quibus solum a. Et hi denique ad eosi in quibus solum a. quod denique omnino tolletu
Hac methodo tollendi evicatur Substitutio potentiarum, et hoc habet
commodi, quod in puris et affectis est facilis.