# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/DE-611-HS-958800:0107
# Permalink to this reading: https://leibnizlegible.com/page/DE-611-HS-958800:0107?run=156
# Title: LBr. 56 · Bernoulli, Jac.
# Folio 54r, page id DE-611-HS-958800:0107
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 51v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958800&page=107
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958800/jpgs/default/00000107.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 156, 2026-09-10T04:16:19Z — 36 lines, status machine
# Lines: 36 recognised, mean confidence 0.95
# 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.

endi promoveatur. Itaque molitue aliquando sum novam
Characteristicam silus, differentem a nostra analy si hactenus
cognita, quae proxrie est characteristica magnitudinis
quae tamen situs characteristice ae ipsa quodam sui genenis
dalculo constaret. Sed facilius est talia invenire quam elabo–
rare. Illud ingenio, hoc tempore, eo labore constati
siplacet
Artequam hinc abeam, sißi ac (I. Nermanno commendabo
inquisitionem quandam circa series infinitas, quae non dum, quod
cium, habetur, et tamen, atean sufficientem cognitio-
video enim Te peculiaristudio inseriobus infinitis versam nec minore successu
nem est necessaria ois cujurlibet aequationis radicem fa–
cile exsiberi posse per seriem infinitam, modumue id praestande
generali canone a me datum aliquando in Actis, quando
valorem, radicis
Dn. Facio respondi, statimus ibi prodire, si omnes coefficien-
tes
erminorum aequationes, in quibus est y, sunt aequales
manente sola indeterminata,
nihilo verum cum extractio talis pertineat etiam ad eas
aequationes, quae sunt impossibiles,
deberet id ex ipso valore
rationaliter
rdicis per seriem infinitam expresso posse internorci empe
tunc necesse est, ut series, si per pantes sumatur, continueus
producatur quaesito non advergat, se non ita accedat,
ut ostendi possit differentiam tandem fier minorem qu
vis datu. Cum vero id non semper facite ex serie  appa-
id colligatur
reat, oxur est indicia posse constitui, ex quibus apponeat
o nempe
eruta
utnumseries sit advergens vel non: In dicia, inquam, sun la
ex ipsa serie, non ex aequatione, unde est deduita series, pre-
sertim cum intendum ignoretur hoc aequatio, ae saepe series
do id licet, plane difficultate caret, cum tantum formu significet quantitatem transcendentem, quae ex nulla hu-