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# Piece: https://leibnizlegible.com/api/records/55774/text
# Catalogue record: 55774 — Evolutio in quadraticis, biquadraticis et omnibus potestatibus paribus supponit evolvendum esse affirmativum aut habere + praefixum
# Incipit: [L:] Haec scripsit Osannam. [L]: Rhonius... Haec scripsi anno 1672...
# Date: 1672
# Akademie-Ausgabe: AA VII,1 N. 105
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=55774&katnr=Cc2+1540
# AA VII,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 60 (from the shelfmark LH 35, 8, 30 Bl. 60 (=Cc2_277)): 2 pages, canvases 119–120, page ids 00068124:0119 to 00068124:0120
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=119
# Lines: 60 recognised on 2 of 2 pages, mean confidence 0.84
# 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 60r — 00068124:0119
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000119.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 55 lines, status machine
a + ab
Evolutio in
+ a2
+ a
+ a2
quadraticis
a
+ a2
DCa = 423
X
biquadraticis et omnibus potest atibus panbu
supponit E volvendum esse
affirmativum aut
deg
habere praefixum
422
Hac scripsit Osannam
Phonius. Quot dimensiones vel potestates habet aequatio, tot habet divisores, qui sunt
quaedam binomia vel residua consistentia ex incognita quantitato et radice
ut: aequatio: (X2 - 4 X - 19XI + 106X - 120 =0.) potest dividi per
 X - 4. X - 3, X - 2, et X + ) et ideo:
Haec ille:
=
+ 4
+ 3 l ut facile probari potest.
12
probemus ergo, si X = + 4 + 3 + 2 -5. Ergo X = 4. Hoc applicemus aequationi
256 - 256 314 424
X4 = 4X - 19 XX + 106X - 120 = O
data
(+ 4
Sed non video qua consequentia ex aequatione duxerit  haac aequationem: X = + 3
quae fuerit
Haec scripsi anno 1672. Unde ignorantia inea illis temporitus hs
aestimari potest, ignorabam enim intelligi debere radices esse
vel 3f 2. vel 3. vel 4, vel - 5. Excimplum quo apparet quam saepe
Ab 16
1t
0
a a + oa +0 a +0a +0a
2
a 11 1.
X +5
quae nobis clara sunt lectori non semper
 Ergo si sit a 1
talia appareant, etiam diligentis
b.
y + b.
a B 1.
X X+Fa (I a.
xet a e a  ad ( b et fict: y +b y+b e b.
X+ y
+ b p7 qu
al
2

## Folio 60v — 00068124:0120
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000120.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 5 lines, status machine
sIZBIBI
RSÄCHSISCHE LANDESBIBLO
eeeeeeeeeeeeeeeeeeeeeeeeeee
alutr: LH 35, 8, 30, (120]-60V∞
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