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# Title: LBr. 396 · Hermann
# Folio 12v, page id DE-611-HS-973581:0024
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 13r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-973581&page=24
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-973581/jpgs/default/00000024.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 308, 2026-09-10T21:39:34Z — 36 lines, status machine
# Lines: 36 recognised, mean confidence 0.83
# 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.

Jua invitatione pristinam speculationem resumam, quam sane atilisrima
esse nemo Analystarum negare poterit. Nam invento modo quo in data
aliqua serie radices ab invice dircriminari possint, multum huud elutie-
luminis affulgebit simile quid praestandi in seriebus transcendentes quantitatus
exprimentibus; verum haec disquititio magnis diffiultatibus urgeri videtur
et quanquam aliquatenus assognari possit, quandonam seriet radices ma-
ginarias aut impossibiles involvet, spponendo imaginarium dare serieu
 advergentem sed potius in infonitam excurrentem, hoc est cu jus ter-
mini sdant tandem quavis data majores. Si verto gr. detur haec series
49
29
X = -2 + LL +
19
+ 59
P5
non
14g
9
420
B1C
im
132G
B13
+ ec.
Ubi si q = pp, seriet fdet advergens, ad eoque involvet radices possibiles, sed so
P= = Vq apparebit eam fi eri advergenten atque adeo radicet ce reales
2
Sed has radices in soriebus mayir implicitis finitis exprimere valoribus
maxima difficultas est: non nunquam facile succedit, ut in hoc exelo
ubi observo hanc scriem multiplicatam per p pro ducere quantitatem
qua litera aut valore q quadratum seriei excedet, adeoquehi à serie
dematur =p et retiduum X - = p
quadretur, siet BX -  p = 4 p- q adeoque X - 2 p
quod indicat, suneviorem seriem radices designare aequationis quadratica
XX - pX 1 9=0
Verum Pudices simititer ex Seriebus