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# Piece: https://leibnizlegible.com/api/records/28174/text
# Catalogue record: 28174 — Mathemat. Aufzeichnungen
# Incipit: Duplex aeqvalitas:bx + am = pp et cx + an = qq aeqvandi qvadrato fiat
# Date: 1716-03-14
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=28174&katnr=56051
# Work: https://leibnizlegible.com/work/DE-611-HS-861255
# Title: LBr. 705 · Overbeck
# Folios: Bl. 53 (from the shelfmark LBr 705 Bl. 53): 2 pages, canvases 105–106, page ids DE-611-HS-861255:0105 to DE-611-HS-861255:0106
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=105
# Lines: 60 recognised on 2 of 2 pages, mean confidence 0.79
# 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.
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# 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 53r — DE-611-HS-861255:0105
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000105.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 51 lines, status machine
Vous allons seurement rompre avec
es lures, nous aurons en Hongne
d
sen transqlvanre de seuls
imperiaur cent et dix milles
nommes effecti
Ex maist d’une letre de Vcune
de 14 de Mar
Duplex aequalitas: b. X +am  et CX +an=  Nquand
Ili. bfZbg
ac 7+
quadrato fiat b X = 
fiet a bg:, app - abf = alim = 7
et acg:, hgq = ac f= atn =
Z
L
= bz P)
evanescit q
fiet e bhuus = abcffabhn = chppC abc f)- actm
intem habetur solutio
evanescit h, nec quicquam lucramur. Si b: c quadratus
 (y L ad item si absin -acum, :b
d
Nil prodm.
quid si faliamius X
fint bfque +bag + amZtamh
fiet
urt actm -abk, sit pC .C sit
+h
quadratus, jam habebitur
qq quadeato, vel ep. quar
saPp. seu Cit equale dleu
 +h abg + amh - sipp acg +ant hgu
us
q
p0 - m -bF qq - an X
abusque (t antipe et hopqu-(an + F) albanti
amnoq t estibo
laq aequ.
acq 
lianbusatitu
amhqqe (+ appo) =(am Abs a (Cgtnh)
Cana D) +bfhqu
pameqs fnamut fabs egtabs nti)
siat  b ag - fl) 99 = a abn  = C (ag- fh) pp = aq ra C1
abnis
Hoc solvi potest si  sit quagcatus Het enim bgq- P = pameb4a0a
. demth
nabud tuemst
potas jum svel k 20sm equ pp- abn- acm, et
eomelcunt 9, F, t Ergo suffieit prius 9. fh

## Folio 53v — DE-611-HS-861255:0106
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000106.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 9 lines, status machine
duplexaequalitas GX. +am = p CX + an = qq
EbX + fam = fpp  gcx + gan = 999
sit f = C et g = b, fint tcam = cpp - 694
Hinc si b vel es quadratus habetuo solutio. Item
a
i pp. si a Cem= Bn): C est quaratus vel albn- Cn):b
si bxtam, et ex + an si nt primi interse et
proinctum est quadrarum, ets etiam singuli sunt
quad