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# Piece: https://leibnizlegible.com/api/records/6355/text
# Catalogue record: 6355 — Leibniz an Rudolf Christian von Bodenhausen
# Incipit: Ich will den Calculum ab ovo reassumieren, ob er vielleicht mit M.h.H.
# Date: 1696-01-13 (96-01-03)
# Sender: Leibniz — Addressee: Bodenhausen, R.C.
# Akademie-Ausgabe: AA III,6 N. 194
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=6355&katnr=42029
# AA III,6: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-iii-6
# In the Akademie-Ausgabe: AA III,6, p. 183 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/III6B.pdf#page=183
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 112 (from the shelfmark LH 35, 8, 30 Bl. 112): 2 pages, canvases 223–224, page ids 00068124:0223 to 00068124:0224
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=223
# Lines: 93 recognised on 2 of 2 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.
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# 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 112r — 00068124:0223
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000223.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 88 lines, status machine
id ciill den Calculum ab ovo reassumiaem, ob vae wirruht mil russe Baroum sulff und
rath zu ende hubringe, es seg gerich, daß man dadurch den Zapetr ertriche, oda wofaher daß in dadurcs
nicht gumhaltus. H purd prolangit 
1DD
en
un y aO aq ses + ab .
(126)
les
austataa SX segi iis aqsest, damit se tractieet ment mit q, air  mit b. laeinmoß man nars
bel ibus antrae g das a solest vnestitu han. Nun danib man dirsaequationem in numeris
ss saltem quoad X indeterminatam, ne illa vinculum ingrediatur prestitu, ib gebe
a
den quantitatibus A, Q und 3 gomiste valores per ipsam X expressos. sit ita que
 (2d0) N = c + eX + f XX et (3to) d = g + h +K et (4to) B = m L n X. heruy
a
na
man nun die aequ. 4. auterget duris 194. 2, 3,4, so wirs daraust:
agses = agcc + 29ceX + 29c FXX .
+gee 0. +29efX +
a
abg9+ 2bgh a + 2bgk 00
1(5t0)
a
a
a
+ bth ao + 2bhK AV + bHK.
a
aa
Baqu. seu icoincidenscam
vel comparanda cum h
q
m +4mnX + 6mmny XX + +ml X + nE
a
aa
a
a
sit compendii causa (6to)
D = gef tbhK D = gec t bhg
5 = 4SS tbKK
4 -a9 ee ta hh
Q- Cc t ab99
Z= agc f + abgK
2= 7 +24
Hinc ex 5 et 6 fiet (7 mo)
n = q n = 5 2Wn = D 2mN = C
et denique ommnn= Q
H  Ret fet C agcC K alygC e WL aqat
Hinc ex 7 fiet (8v0) nn = 1(8:6) et mntnn =  D + O, : 2 Y (4:6). itaque
datur m et n plane, posito haberi  C, D et 8 Cum ergo articulo 7 exhibean,
tur praestandae aquationes comparatitiae seu coincidentiales numero quinque; et ope earum
jam duae literae sint inventae, m, et n; supersunt reperiendae adhuc tres, adeoque tribus
tantum opus est aequationibus quam simplicissime ex istis quinque derivandis, quales esse
imo. A
iomo)
reperio 300 = 268 et 3DD = 248 et 07 = 46 Nam cum C sit 2mn
Bno
utique 300 erit 12mmn, et cum S sit r, et Y sit ommun erit 258 etiam 12mmn; et proende
fit 300 = 28Y, ut dictum; et ita de caeteris  Ergo O, D, 6, E, & explicando per artic. 6.
fiet (9n0) 3(2) (ges FbhK) = ~ IFsAbKK, 29c 5 1gee + 2bgK + bhih
et (10m0) 3() (quC + bh9) = 2, quet bgg, 2geftgee t2bgk + b hh
et (11mo) qef +bhk, qec +bhg = 4, 95f + bKK, qcet bgg
seu
300 = 26 (2 + 2t)
30D = 29 (4 +2t)
OD = 450
Hic jam reditur ad calculum in novissima mea jam descriptum, nempe ponendo T(12mo) esse
K = fg: C (quod verum esse inveni) satissiet aequationi g, ut in ea pro K substituendo hunc valorem
ipsius X coincidat cum aequ. 10. itaque duae solum restant aequs nempe 10 et 11, in quibus tollatur K,
eio
substituto valore ex 12 et fiet ∞3 _ S= afF, ocetbgg et (14to) Z-F, qec + b) et
(16+
(156) O = aF, qec +bhg. Hinc ex aeq. 10 fiet 3(2) ec + bhg) =9 cet bgg, qee + bhh + 265 (9cc + b99), et
c
ee
ex aeq. 11 fiet (17mo) qectblg af, 2sqec tbha) = 4B (3 (9cC +b99). jam ope ag9. 16 et 17
10va
poterimus bis habere vatorem ipsius f. Nam ex Eaeq. 16 est t. C
3( Gec +bhy) - 9 2(9cc + bgg, que +blh)  (ycc +bg9
e
et ex eq. 17 est (19 n0) 45 4f: C = (2) (qec + bh9): ( I (4cc + b2D). Unde ex 18 et 19 fiet
Cmo
(20m l (gec + bh9) = qcc +bgg, gee + bhh. seu gueecc + bbhngus +2gec bhg = ggucee + bbgottr
seu fiet (240) rechg= cchh +ggee seu cchh, +ggee-rechus B echht qugge
seu 2yoch = ge
0
seu c: 9 = h:  = f: K sed hoc male; ita enim s et + interse
rationem haben habent constantem contra desiderata
ab2d =

## Folio 112v — 00068124:0224
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000224.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 5 lines, status machine
e
te n
2 q
2ua
CHSISC