# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/53925/text
# Catalogue record: 53925 — [Math. Aufz.]
# Incipit: 3 = 3e/e = 3e • 1/e
# Date: 1713
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=53925&katnr=45752
# Work: https://leibnizlegible.com/work/DE-611-HS-957479
# Title: LBr. 454 · Augustin Thomas à S.Josepho
# Folios: Bl. 35 (from the shelfmark LBr 454 Bl. 35): 2 pages, canvases 69–70, page ids DE-611-HS-957479:0069 to DE-611-HS-957479:0070
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-957479&page=69
# Lines: 93 recognised on 2 of 2 pages, mean confidence 0.68
# 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 35r — DE-611-HS-957479:0069
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-957479/jpgs/default/00000069.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 88 lines, status machine
e
e
2C. it jam 3e+= rr
A= 3C et a
de + Z = tv
a
+L E b = 3. fi et X + = = vverit 3C+1
C
Si X :b = C: I, et ex X + b fit be + L = vo
y = 2b sit quodrato biquadratus, erit poterit intelligi sumum
x
+ L = yy sit b = FI X =
Y
et
na
=
ita X+ agy dat F + 1. or vo
Tit
fa:g
q
2, fint Z +.
 anir Er
4, seugAnY + fy3 = In 99. cum f et _ sint primu
rr inter se, ans est erposeton ponus, sit rasigia
n na.  cagnqu qua foglo=ngu
sit delrt esse tr disibili er n, sit fL ven et H  treo, to
e
Si sit X = fiet tunc ex X +b =yy, fiet = + by =D Y
duorim quadratarm XX + bb
aia
seu n +  L
n
e a sid 1 Ande omnia ponamus faus esse
primitivu, necesse est ut l fsn, vel Y in integer si f=n: fier
otrraros sit
9fY + 13 = fgq et relesse est 9 posse dividi per Y, et fit seu g= rv. a fiet.
4F + rY BfYVD: aa, ergo necesse est 9 dividi,: s per Y , 1t Y posse dividi per f
nisin
pt fict 1n Ea sen artt, aerr pro va A. a et qu ald a fFWiaa
P
ftt
fL
a
C+
LuV
 seu du+
Et F. 1.H   e
V. E ditim  Sed hinc sequitur itiam f 12
aa Et fua
d
seu ffor +
quia uae alioquigdicedi posset per tcum posutuns primos inter se. et
aa
fir  paV aaq  air dc = YVD 19 dii sib. per Y, fiet
sin aW +t
q= ruia. en Ar ta aW+ar = vi
moduon produentes iphius
a nemper Y et to detent aequam 410 Et b21: , rWo et X =1. Y
sit Nin integer eut
y- a:a a gnur afr=ngustet onnnt fnWo=onaequ
ae
a
a tan
 LDd = aahKK
fD th  aββ nt gB= tk
s
1v = 90
e
Ergo h = a et fit a + fD = auKK
r=nu, q= nbβ y = dB: M XC id
a = B. Et 1D3=KX. sit Z + = =gy L
paa, AuK.
e
L(9La N ergo V est dirisibile per , et fiet B = bβ. a, et t
1g +599D= aBβB. Ergo q dividi potest per D, sit g = Dti ut fir
a
s
a
mannu + fnua= aq et int q - n D: a Ergo a pot sua)
se fet q sunt primo iacise, ergo lo divitibile per D, et fiet Wd AB: a
a
d
fit 1 Ff93 = 
+
 B: d X = 1: 9)
:B
1dc
dd

## Folio 35v — DE-611-HS-957479:0070
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-957479/jpgs/default/00000070.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 82, 2026-09-09T18:17:48Z — 5 lines, status machine
noiscue ramores
aIUIr.
Br. 454
70
t