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# Piece: https://leibnizlegible.com/api/records/35625/text
# Catalogue record: 35625 — [De aequationibus quinti gradus, de mesolabo per anguli sectionem]: De aequationibus quinti gradus, ubi et quaedam de Mesolabo per anguli sectionem
# Incipit: [Notiz:] faut envoyer la lettre pour Mons. Fridericus Helms, à Coppenh
# Date: 1675-05
# Sender: Leibniz — Addressee: ?
# Akademie-Ausgabe: AA VII,2 N. 030
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=35625&katnr=41756
# AA VII,2: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 56–57 (from the shelfmark LH 35, 14, 1 Bl. 56-57): 4 pages, canvases 111–114, page ids 00068201:0111 to 00068201:0114
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=111
# Lines: 346 recognised on 4 of 4 pages, mean confidence 0.72
# 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 56r — 00068201:0111
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 57v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000111.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 106 lines, status machine
aquationibus quinti gradus ubiet quaedam de Misolabo per
anguli sectionem
faut envoyer la lettre pour Mons. Friderieus Helins
Coppenhaguen avec ordre  à un amy
a
de la rendre à main propre s’il s ytrouve, ou
la luy envoyer, e ceu ou il sera.
homme curieux, du quel on pourra
par chez
en france.
7 a
ar
eo
C’est un
de nouvelles
ux ans qu’il a este
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et On 10f2 + 5teb 5 + 1b3
a2d
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. a
itaque ; D a quadratus fiat
e hb - 3f2C7 - 3e 4
sit quudratus, quod facile
in numeris, si non rationatibus
25 H =. Ergo O 75D. sive O S5D
5
f3 + 163 (853) + 
3
2
eec
2
 (+ 163)35
at f 8- 116
itu
2
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sive O⊓, S-5∞ 125
quod fier si modo.
saltem planis
95-3f ex terminis secndis: extertis At ex quartis. (F3(L b ) + 11, ( +  
=Ce mu D m n. Ergo O
Est autem Oe
Y-15
3fA 43F
MAABOVEHAR et eadn shlAI fes e
vn aneno
+re f7 X
C
92 e ap
ubi focile patet literam esse in unam vel b, vel f.
esse inutioem cum simul junctae cundem sem per
faciant gradum incognitarum, et ubique reperiantur
163 ∞ =h b2
7537
X
+rflie10

## Folio 56v — 00068201:0112
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 57r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000112.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 95 lines, status machine
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cb 9b + 6b +1 H 493b + 2b
sive 6b + ab +1 70. H- 9
unde
4,36  446
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16
a
ab 7 - m 3
et (=m) + m D hM ral  mtrs 10
16) 16
sive m -akm + 8al 0
retpo  a l-nihi ponamus an
stabit:  m +tim ran
sioc m3 + 4li n + 8an. enor
32 m a si substitutis iterum valoribus: Errvr
48 64b  +3,6b in +3, 4 b m + m  -2 6b4b 6b 2m +8 4b3
146
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Hic autem si nullus in calculo error
aliquid lucrati sumus, nempe us
aliquod
problema quod pendet a nesolabo
possimus construere per Trisectricem,
modo nullus sit error in calculo
1267

## Folio 57r — 00068201:0113
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 56v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000113.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 74 lines, status machine
 1e y 1SC no multiplicetur haec aequatio per y4
 -uN y +usy
x - 1 a. +1 N 17
4X  H6Ay
+a2 16a2
G
a
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--
quy
+ 5
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+ 3X.
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4a
+ 1253.
12a
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62a
- se
16a3
Ssi X+ b + sac + 10 aed
sac + 1(5) ad
VN 2b Z- 3
a
a
12X)
fit
n
s
=b -
y = by + ac
y +N. + aq
 + by racV
+Y. apb.. +pacY 3
aq.. 1cqb. +agac
Y +by + ac
y7 + by + ac y
+Y.. + rb. +rac
ve
V= 3mn y - m
 +cu p
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m)
V  X  pun. - n P
conferendo pp, b + p.
m ac + rb 1a9
Z) X + ah 10. ZHX + P
3 + 3pY + 3p Y + p3
+a
PN b +r. 2 b + brer. p b2+ 3b + 3br +
3ac  b e b (+ 2br) + r. et fict: r - b br + b  ( +b) - 2b + nac
et fiet: r F + b + s-3624 12 ac
+bac f ac S - 36 4 ac - 8b - 2bb + 36 -36 tac + 3bb 46 . .  - 36 thtbac
ot 27a h 5N 2
+ b +3b s... - 3b +36 ac b + -3b 5....
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72
12.
+ 36... -...
10
e
ut
+b2
F1in
. f
a 6 resi st
= lYy + bc
+bc Y
2bc.
+bc
c

## Folio 57v — 00068201:0114
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 56r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000114.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 71 lines, status machine
 ap + d sap, B). FI ap sap + 3cd ap + 2cd
X+ - libX + a1b 0.
  ACx c
XrX+ ad no. ponendo ZB X +e
X
ar
a3
X 2H X+ 2X0 + e
cZH 4 CX + ce
ad
ad
vete
vel
+rCX + e
a
d
ce
ad
+1b X
ad
204b. + 2e lb3 x
X X - 5 H
n
XCnihXe
m= n.
X
fa X
Rectius ita:
1
e
.-
+ f
F..
.
tintilis explicatio est,
et ficui potest:
2C +C⊓ 9
e e ree + ad Ha ap
sed et X + 3f. X +3f X
tebi.
1ab15
+
l7
el..
.-
e
1d
et tib
2
1d..
+5mn am
X + 3fX + 3FX
hrb.f
e
.
eb.f
netie. 2C1BX
=etib
ce.
=ad..
C2 1b
ad.
ad
.
f3 aequando cum X. + 3f X +aqX + ar B
fiet b, 29 +7f a  unde in fier: arri aqf + 1b
t
et b A- a9b + 3fa b. eit arp agf + = 1a 9b +3l5a b
ti si b cum be-3f +3fa
ergo ar aqfh2- 1a suf risa
77i sa