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# Piece: https://leibnizlegible.com/api/records/35502/text
# Catalogue record: 35502 — Specimen Memorabile Algorithmus Signorum, et quomodo aequationes institui possint inter ipsa signa. Et usus horum ad doctrinam de Locis
# Incipit: by-y² ⊓ v²-cv locus est ad circulum
# Date: 1674
# Akademie-Ausgabe: AA VII,7 N. 017
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=35502&katnr=39019
# 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. 242 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/LAA-BdVII7.pdf#page=242
# Work: https://leibnizlegible.com/work/00067993
# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folios: Bl. 160 (from the shelfmark LH 35, 2, 1 Bl. 160): 2 pages, canvases 321–322, page ids 00067993:0321 to 00067993:0322
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=321
# Lines: 106 recognised on 2 of 2 pages, mean confidence 0.77
# 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 160r — 00067993:0321
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000321.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 44, 2026-08-27T14:25:39Z — 44 lines, status machine
b+) v.
Ergo F
vi
8 +)y
s
fs
8 +) 9
7
a
+5 +b
1
u
Ergo +g 5 + E + l ed g 5 +C
fiet ergo + v 4 y7
( et +9 (7 + 1,
+C+b
+1, +G + 10, vel v +y + E + b 770
Erp aequatio dada. (+) by + y 3 + ) (4) expoin hanc vay AC + bisseomnutur
potest post expliationem locus est circulus; sin minus  Hyperbola.
tu brenius, quia non alius valor quam signorum quaeritur si v et y eodem
signo affecta sunt, et et si signi + et (3 +) non sunt eadem statum praedice
potest commutationem fieri non posse.
v 
Ergo by + CvHE - b  lgo y = 5 - b + ex Quod fieri
non potest, locus enim feret Triangulum. Ista ergo accuratius examinanda, ne
errore calculi labamur. Iror ine hic, quod na umparie postreman, aequa
tionem priuae, oblutus rectas a me rejectas. iti ergo dicendum
si _ signa + et  ( F) sunt eadem, et
si signa + et (3 4) sunt eadem, et + E + b (I = aliqudlocus est circulus, sin
nihil ap
monus hyperbola. Ponendo scilicet v et Y esse aliquid, non verd aihil aliad nihilo minoa
Unde si b aliquid positivum est, necesse est + esse 
loey
si item est locus (4) bys +y (3+) v () cv  1d et v+ytC+b
problema est circulus, tantum ergo necesse est +C - b esse ali Aepronde
+ vale t a 1 + n y aliquid si V + es est aliquid et nitsi nihilis mnus, si
y, ut et y. est mhilo mins. Ergo in locorum tractatione radices verae a fulsis distru-
Nendae sunt Ergo Regula: si V et V  verae sunt quantitates, et eodem
(fals
signo affectae, et c +C - b, vera grantitas est halocus (+) by = v (3.) V (49. 170
est circul. Sin mo nyprbdla. Reus + riD
0
aequatio pro eluo, abitralia,
aequatio inventa

## Folio 160v — 00067993:0322
# Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000322.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 44, 2026-08-27T14:25:39Z — 62 lines, status machine
_ by - y T v - CD locus est ad circulum. ponantur B~ yp ~ petque
sive CBB sue E 1, L, ponendo b pro C H valorer ejus ut et pro1, fiet  Y B- c
+C 1by - 5 17 v - cv + 5 vel SC + by - 5  4 B = C net + v- E
b  4
+ by - y , v
po e ponamus ob fetque - db + by - y ) v poratur in lo hanspmont bes  YV ecto
adatit
ti pogams se celas 411
ao crecestoque  silgor
 +G=vt (5vet +b +Yd
alcue. 512G vig 2.. A locqu ineociumt esse posse oiam ad Agriur
V + f Unde patet pro Esignorum Varmnon
dex (4) by + 3  HsCB unde Xic. rb (+) 9 + by + y Y Ft FBvF (+)XB , 6,
dee
Universalius:
extrahendo radicem, fiet:
nuel (1 +) b (5 +)y
+b
+(+)...
C.n
= CF) y
.
(+)....
=...
 1
velue +C
(+) 9 p
-
un (4) 1
F Resecto jam a) B quocunque signo affectum sit, et quocunque etiam signo affectum sit
(F)...
quadrato, habebimus: +y
FY  unde patet aliquam ex ambignitatibus nempe
E 4. (+) evanuisse, salva loci natura et aequationis gradu. potest a ferits. + y Y1.
EF s= jam  addatur utrolique +E, extractaque rdice habetumus c (7 +) v, ab uno latere,
F et resecta (6 +) E cater et reliquis quadratis v +E +b f Unde rem nanfesum
FE ∞ est ad simplicissimam expressionem esse reductam, duasque ambiguitates velut imitiles
Delisas satisque ex illis quae restant judicari posse, quando locus est Hyperbola
 2 aut El circulus. Nam si (3 +) e +, et 4 1 =, et c pIb, fiet V ( B - Y, et locus
Sec. sst circulus. si (3 +) e = et c5) bd et + 5 + locus ilidem est circulus fit
d. d DG enim = v2 1 d g + y
Nimirum ut locus sit circulus et necesse est esse aequatione
3.d. (8 +) v sat) y. (. f.) g 10 comprendam cum hac Ergo (5 f BY Y + 5 + b, vellof) 11 + E+b
enden hic (1 +) V +Y +C + 6 0
idcu
eandem
junctisque his aequationibus inter se, patet esse + YI (3 F)
Et ut quia (8 +)9 -E 148, erit (B +3 - + F, + t vel (8 +)  +b +c
fet ergo 4 u fs  Unde  d ponatur C p  + bib 1) d fiet b-
(8 +) 9 (1 +  + c. cgi g - (8 +) + v ) c
(8 + 19
et (8 +) g 1 + Eo F) b, hab Et pro  (8 ) substiluendo F
e habebinus: Ergo g FI (8 +) c + b, et (8 +)9 F7 (84)1, (8+) C46
Ergo fiett (8 F  (8 + )y (8 +) - 1
Vvja
- b + (2) 4. ( = 3b
1+ L + C+812250
aut 4L + +C71 + l
et siet (8 +) g  (+ 
Ergo 8 X + y (81) 4-  = 0 vel v +y + q+ 4 =0 Uo ut ipsam (8 4 polus
eliminemus, ita agendu:
verte