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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 160v, page id 00067993:0322
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=322
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 44, 2026-08-27T14:25:39Z — 62 lines, status machine
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_ 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