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# Piece: https://leibnizlegible.com/api/records/28811/text
# Catalogue record: 28811 — [Math. Unters.]
# Incipit: Si radius circuli sit 1. subtensa seu chorda arcus dati sit c. et detu
# Date: 1683
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=28811&katnr=39600
# Work: https://leibnizlegible.com/work/00068195
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folios: Bl. 59–60 (from the shelfmark LH 35, 12, 2 Bl. 59-60): 4 pages, canvases 117–120, page ids 00068195:0117 to 00068195:0120
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=117
# Lines: 142 recognised on 3 of 4 pages, mean confidence 0.76
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# 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 59r — 00068195:0117
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 60v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000117.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
seu chorda
si radius circuli sit, 1. subtensa arcus dati  sit c.
erit et detur alius arcus, cujus ratio ad datum sit data, v.
exit ejus subtensa dicatur X, fiet
A aequ.
v =c + Secc -1 +
c + + c-1
itaque si C sit aequalis radio, escilicet subtensa sextantis,
et quaeratur arcus cujus ratio ad sextantem sit quae D ad 1,
seu posita periphenia p, erit sextans Z P. quaeraturque subtersa
arcus, qui sit  P e ejusq subtensa sit X, ert
erit X aequ (V) 2 + 3 - 3 +
2+ 1-3
et si arcus vocetur cujus substensa est X vocotur ), erit
Raer.
inter drcum. et suam subtensam generalem
7
sit radius 1.
et:
X aequ.
Peripheria circuli p. arcus a chorda ejus X
2+ 5-3 +
-6y
+
Si C ponatur subtensa quadvantis, quae est aequalis 12, posito rudio 1.
fiet a aequ. et quaeratur subtensa arcus, qui sit  vp seu erit
Baequ 4
v
et
Xaequ (43
seu
Y
61+ 1-1 +
12
qy
1+ f-1
n ponaturradius circuli,  arcus quadrantis 4 arcus datus y, ejus subtensa X
erit X aequ. 7: 4
e
= y5a
i + -1 4t
1+ f-1. Si sumamus semiqua
deantem circulifeentur, erisque arcum appellemus da semiperipheriam circuli,
eanque vocemus  seu g
vut X aequ 
1+ sut
12
1
+1-1
12
1
)in sac
9
s2
-3. 9) 1+ f.1
12

## Folio 59v — 00068195:0118
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 60r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000118.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 61 lines, status machine
sit jam q aequ _  m. sit lZ aequ n lm seu fit
E aequ. n sIm. si jam m sit quantitas constans, eut
erit. dZ aqu dn lm aequ dz:
sit jam Z aequ m et W aequ Y m nit du lmaequ dz: M et
-dn ln aequ. du. m s _ Ergo dZ aequ an Im M et duaego du lm n
sit jam X aequZ+ W et _( M aegu. +
V
12
 et n aequ. 329
et: de  dn aequ. dy: qo et du + di aequdx.
1+ Su
Ergo habenus dx aequ.  1-
dy
V2 3
is
12
+S
12
si faca eligamus posteriorem expressionem ipsius X quae etiam est
aptior, ubi habetur tam 1+ V-t quam 1 - S-1. Ret
taciemus q aequ m et W aequ h. et y+ Waegt.
et N aequo y: q, et m aequ. 1t sa et haequ 1= f-1
(2
12
2
et fiet dZ aequ du: lm. m et du aequ du. Ih. h
est autem dy du aequ dy: 9 et dx aequ dz + d N.
Ergor fiet 4
quoniam
de
 aequ.
dy
l.1+-P= EI2 (0)Ss
Il s2
1+ s1 in + ut F 1- S.1 facit 2 Hinc 1- s-1 aequ=
et loqs 1- s-1 seu l1 - s-1 aequ l2 = l1 + s-1
scribi potest
vel 
EX
dy
aego
l1+ s lqe Cy I et Sac
1+ 8at = = 12
y1. 1tS
se
12
y
4
1- Lat
se
+
.Ergo et
l. +s+ LI2
1+S-1
sit jam yaequ 9. fiet dx aqu lig s. 1- t  S. 2. Posito ergo quadratura leu
dys
in hoc casu speciali, et existente dx hoc cafh aeg. 9
19
habita tangente lineae sinuum
dy
fiet 49: s.2 aequ l1+ s-1 = L2. licebit ergo amatri logarithmum ipsius

## Folio 60r — 00068195:0119
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 59v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000119.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 25 lines, status machine
. l14 f-1 s imaginariae quantitatis,  hac una quadratura
supposita in aliis omnibus amoliri, quod si adhuc unam assumamus
quadraturam; v. g. eo casu quo y aequ 29 licebit ad huc alite
amoliri fint enim  aequ. 1+ s-t -2
Esto
autem
2
d
cly
qui
14 = 1- Y. 1
3 - 143 -, - s, - 5 - 1 aegu β.
fiet (- 1 + Y∞1 4+, - s- 1 -2 (- 2 4, 4 L-2 aequ (3
si jam sit dx: dus aequ. f. fiet l1+ S-1  - = (2 aego f9t
nam
S1 +  - 1 - 21 -  -1 aego 2 1-1 aequ
2
H1
Ergo qui novus valor utiliter conferetur priori 49: d-2
quia datur relatao inter f et 4 aliunde sed hoc omnia
quae hic tantum ne effluant, in chartam conjicie
erunt accuratius ex hibenda.
e
1- s-
12

## Folio 60v — 00068195:0120
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 59r); this page is its left half.
# No recognised text on this page (recognized).