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# Piece: https://leibnizlegible.com/api/records/37030/text
# Catalogue record: 37030 — A circulo partem imperatam abscindere ducta recta:
# Incipit: Sit circulus centro A, radio AB descriptus. Circumferentia sit
# Date: 1676-07
# Akademie-Ausgabe: AA VII,6 N. 045
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=37030&katnr=Cc2+1508%2FA
# AA VII,6: 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-6
# In the Akademie-Ausgabe: AA VII,6, p. 495 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/LAA-BdVII6.pdf#page=495
# Work: https://leibnizlegible.com/work/00068199
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folios: Bl. 152 (from the shelfmark LH 35, 13, 2c Bl. 152 (=B)): 2 pages, canvases 303–304, page ids 00068199:0303 to 00068199:0304
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=303
# Lines: 120 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 152r — 00068199:0303
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000303.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 81 lines, status machine
ducta recta:
A circulo partem imperatam abscindere: ut tertiam  aliame:
sit circulus centro A, radio AB descriptiis. Circumferentia sit c radius
erit circulus rC. recta abscndens A CD. diametro AB perpendicularis
quae debet esse portio circuli Y fiet: portio CDBCp r
sit BTp y. erit BEH
AEpjor- 282
ur.
CE,
26
y2 in CE dabit DCAD. et fier
ABBY. Ergo CE 2y12
TB1Y
jam ex dato non tangens est: tangente auu est, - X, Y5 Y7 r+ y)
rty
2Vr3 Ey3
rtyr
sive reducendo ad communem denominutorem; 2yr + E Yr - 2 y r3,
r ytt
H CAD fulerum
ac BC. a aBFC.
AY sectori CADBC. ergo segmentum CDBCF ar = CABF ar-   Eyr 
quod ebet aequari Cd pE
cujus aequationis ope inveniri deberipsi g.
2y2
Notandium tantum debere esse
y radio minorem. loco aequatiduis: a e Y- 7 + x - 77. Ccc.. substitu. potest
haec: ex dato arcu BC, avenire AE sinum complementi sit:
sinis complementi, seu (Cyr
et rursus 1
+ r+gr 1I
ac
  12,3, + 1,21514,5,8
2
rayr
ry )aY( 2r - a + at a auferendus est tandem
T,2 1, 2, 34 1, 2, 9455
valor velissius a, velissius  adhabendumm ultimam aequationem
optrige sic
lrianus. ABC est radius in sinum 4. pono ogc, sinus ex ave ad-
12, 3
+1
1,23,45
emes Y( +   AY  Y seu (rA + R E A erc (+ Y +N)
rua sepautir CAD CFBC e)
112, 3
2, 2,4, 5
coY
db
11t
ex quaoquatione e resolvata invenietur quod si sit areus tam parvus, 
ut circibeo ejus pars
A5 tuto negligi possit poterir circuus dividi in ratione data, solu radicis
cubive extractione;  sci et fier. A + Y 6 paulo major vero. Est in fallor
theorema, si circuli plures in uno puncto ailter in altero, in b uno se puncto tragant, segmenta
esse ut circulos. Hinc ut GFBG ad CDBC, ut circulus ad circusum ponatur circulus exterior esse
decupque interioris, etiam segmentum decuptum erit. Ergo erit et  sui circule tertia pars, com nihis
segmenti area est:  Y + y 7 + Y nc 2. quaeritur aliquod
pr
segmentum quod ad daetum rationem habent tatum, radbedius id eru:
  V + C. = C4 VC
203
R
2∞3
V7VVec pr y47
opus erit tantum sumere V ad y, ut est t Y b ad b. ponro ope logarihinorum
perpulchia londi posset abula segmento rum Circuli, ad aream ejus da Nimirum segmentum
appellato circulo 100000, segment quod sit 10000 10000( ex. seu seu segmenti
chorda quod sit 1. 2. 3. erc. posito circulo, vel si mavis p
 metior est via prior qua invenimus posito radio A, radio 1. fore  duplum
segmentum. A
= A
ere
1,2,3 1, 2,3, 4,5
Erq semmenta, modo arcysit radii portio minor, tertia
potens dici sermenta fore inter se ut arcus, cuitque error
modo notabilis, sedhod de terminari potest; quantus sit
illud interum poted quomodo possit facite abscndi a Circulo portio cerlesima aliaque ad genus,
smplia radicis cubliae extractione
positi
aru CBD

## Folio 152v — 00068199:0304
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000304.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine
e
.
t.
C. 2 ar de D..
t. dot 3+
a p  - 13+ +- f7
22 ab vc2 isa
1  3 1
5
7
e
n
a b C
a+b
a3    F  atc ate
ao
cedu
aec
2a + t
a2 62 C2
5. a +X a2 t29∞122
b +X b2 126x4 X2
c +x c2 prcx 722
as
b + 2
c+2
Ce
15
simn
+ a
BD
vod
1 AD
1
F)
ase
a ce
b+Cp.
e