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# Piece: https://leibnizlegible.com/api/records/762/text
# Catalogue record: 762 — Exponentes radicum Pronicarum, et alia id genus:
# Incipit: x² + x aequ. b erit x aequ. bω
# Date: 1679-05 (79-05)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=762&katnr=58340
# Work: https://leibnizlegible.com/work/00068033
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 15
# Folios: Bl. 17 (from the shelfmark LH 35, 5, 15 Bl. 17): 2 pages, canvases 33–34, page ids 00068033:0033 to 00068033:0034
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068033&page=33
# Lines: 130 recognised on 2 of 2 pages, mean confidence 0.76
# 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 17r — 00068033:0033
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000033.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 62 lines, status machine
umi 1679
linca pronica lomnitemin x ponentes
simili descubenda per a
assuncendo _+B valde
parr existerse (.
2 2
 et
es
O
C
radicum
lonicarum etalia
id genus
 potest unilis sumisatis paroe et per omnes numeros tanseatur
4 24
120
1co
X+X aequ. b. erit Xaequ. b.
appellatur X radius pronica ex b. Ce
ef  potent curva  excogitari similis
logari dinicae. Nimirum puto in se invidem
duc debere X b adius ordinuta X.
abscissa co.
ret si ducantur
invicem X, X + b. X+ 2b. X+ 3b et
bel ec
Solarunt et media inter haec
pronice proportionalia inveniri vag.
sit X X1B 2+b
et debet
X+B esse ponice proportionale inter C
sint temuni. X. X+bX X + 3bX  eta
inter X et bX quaeritur media proportionalis
provice pronice sic enim nunc loqui placet
ea sit Y.
X X. X+B.
producentes aliter
assumumus prodmentes.
X
(4
X + β X +B. etc. eta
productum pronicum erit.
~co
2
ere
assumendi erunt
x+b et quidem
determinate hoc modo :
X
2, v
y+X
ecout
  Bβ2B, X,
etc
L es Bst
ubi co exprimat enumerum proiventium
eic l
2
2
continuctum
Hinc jam et facile intelligitur quomodo
e

## Folio 17v — 00068033:0034
# Source image: https://digitale-sammlungen.gwlb.de/content/00068033/jpgs/default/00000034.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 68 lines, status machine
feli sint invicem tres sthoniei
d consrentivi. Sequentis enim prsumimis
n cot1
 CF erminus erit X4Cd XE
 co+2.
Ls
atque ita porro.
exempili gratia. primus:
tertius: 
z
Xx
(3
eB,
2(3
ce
et tertii
1) 
X
1.2 (, X
q
2.
ter bi primi termmus.  comparari debet
cum Xa cergo erit Z aequ. L. sed
Cd
c diaseitur, terminus comparori debet cum X + bX quod
difficile videtur cujus illic sint termini tres hic
2
Hunc rei remedium forte haberi
si prociudentes ponantur esse
X + β
egin
X + β.
conferanda
tera
YX +2C.
t
VX +3BX
cum
fient
p rotucho
+25X
X + bX
es
VX + 26X + X
sed comparatio non procedit; estque res in numeris
nisi forte pe
e
finitis imposibilis interpdolatio
transiendentes. Niimorum ita lex
XD +35 BX
extracta quaedam radix dare debet X +bX quod nonnisi
ranscendenter feli potest. Ut ores generalius praestetu
debet ponn X aegants et X=bX aequales dnibus tetm
pronicis uno intervallo remitis in sene pronica Generali
A
12
C+
c6 +
e
e
t
erit
 ecundus:
s
e
1
da duo.
egrolent tate