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# Piece: https://leibnizlegible.com/api/records/67881/text
# Catalogue record: 67881 — Aequatio solida II
# Incipit: Est Aequatio data Solida, quomodocunque affecta, nisi quod secundo Ter
# Date: 1674-07
# Akademie-Ausgabe: AA VII,7 N. 025
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=67881&katnr=Cc2+854%2FE
# AA VII,7: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-vii-7
# In the Akademie-Ausgabe: AA VII,7, p. 311 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/LAA-BdVII7.pdf#page=311
# Work: https://leibnizlegible.com/work/00069349
# Title: Leibniz-Handschriften zur Philosophie LH 4, 5, 10
# Folios: Bl. 71 (from the shelfmark LH 4, 5, 10 Bl. 71.74): 2 pages, canvases 141–142, page ids 00069349:0141 to 00069349:0142
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00069349&page=141
# Lines: 174 recognised on 2 of 2 pages, mean confidence 0.69
# 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.
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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 71r — 00069349:0141
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 74v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00069349/jpgs/default/00000141.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 96 lines, status machine
Esto. Aequatiodata Solida, quomodocunque affecta, nisi quod secundo termino
carere debet
Aegrano arbitraria
 bmY  = bnV + b p, sive y +bm
-ny +bp
onatur V e gV + h - b- bm, eoque valore in locum ejus substituto, fiet
qV + h - b (bm + bm)
-ny +bp
6
7 b
multiplicando per crucem
sive (V s+BV B
Or +h b -bm
en
-bmg
auferatur ab uno a quationis hag latere,  ab altero ejus d valor
v
(+ 2B9. X
Enus 
=
1
=
nt
S
(- β4
X + bm β
+ b3p
a
gu
= bm
-nb V
p 92
+bm
+b5
gr
- (7
CV H d
qu
l
ya
Guam Aequationem ad Circulum
esse manifestum est.
Aequationem arbitrariam assumtam multiplice multiplicemus per  dabit:
N
a
a lateribus respondentibus aequationis superioris multiplicatione per trucem prodactae
fiet:
N
+B V
3 op- nb V +b3p
gn
v
quam aequationem sectionis Conita indefinitae inventam, conferamus cum
aequatione sectionis lonicae datae, 2r ==C y W et ponendo cop yt e fiet
+R
+
Hhac = B + bm +X. item  H L+
v
gu
Ergo bm +X4 et
Ergo βe bm., et g B F
+2Y
1Z
N
WVH VFK
Si posuissemus ab initio V bm h V gB,
in navissima aequatione Conica indesmita, V simplex
pret terminus erannisset, ergo K foret po
, et e  + nb - 2Y
sed inde sequitur
contradictio, vel sallum nimia delerminatio ex porissimo val ipsius e, qui adhuc
superest.
inventam,
priore
Igitur utilius videtur resumere aequationem scheda spacata
ubi l. et c. relicta sunt. Ponatur C 10. Jamq
s
aequationes instituantur g  - β + l ilem g  +bml - bin - β3
v
collatisque his duobus valoribus, fiet
Ex
32 +bml Vn +212+c 
Fit +l +l
a
2
Porro KF + ebr b pC
l
3
s
es
-2re 42
mum
itemqe  5 b n ( 4bm c) = 4 B bn t 4C2 +C (4 
N
n Fg g  e
19

## Folio 71v — 00069349:0142
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 74r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00069349/jpgs/default/00000142.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 78 lines, status machine
Be +7
ess
K  ~bp - 2re
et K=
sive k2
9t
gre = +BV
-bn
Ze
q
= 2Y
1 3a - 2rc + XV et N = L - 2bm + s
=b3p
fietque conferendo
= 63p
b2
R A = 2re =r
+ 2bm - β
-b3p
==bmo
C
Ut plurs indeterminatas nan liscamur, ita faciumus:
Noy adlus dom ABC
=ny 10bp
A5D
+teno
-b2p-bem
.Un pro y ponendo g V + ny +C. fiet:
oyu
ant  sgvtu+ASLy +ASbm 10b
Et multiplicando per cracema
=Sny +dbp+ bg: ByibC
D2tq DhAAmYV+ BAScq +ASIBgVV+ Idbmeqt
sas
+Sgen VV + XSpOV + X5cDV + ASIB. VFNobnon
la
+_. Nesoc + 1Sub a V + 1tc + 16lDc Y rN obm dC AE
dun+b
e es s 
b ni +
7 - Sn18b7 + sbp 1662
e
bC
Ab hac aequatione auferatur  aequatio ipsius V valorem assumtum
eximens ducda in β63 seu  Asi u
ga
E β b3gV, +b2 myf bhC
Vedinandoque fiet ut autem yD exunescat, multipei ejus ponantur
 esse o: seu X ng+ N 18g+ n
570
Ergo erit 2M  - l. seu (ne = l. Quo in locum prioris su bstitato,
ostinataque aequatione, fiet:
16Bn V.
-βb
615gu
a1
(+A (+XSgDC B (-0 idcg
+ASbme
+Ad nBC2
+281012
+β2 b3 M
+SnaB62
-845 gr
+ 2Y
D
+18 +8 2 L
+NdbmBC
+β263C
e bp 16
159
+2re
L-adbmq
6
ge
639
 an1.
2
comparandecum