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# Piece: https://leibnizlegible.com/api/records/55773/text
# Catalogue record: 55773 — Quadratura per tangentes
# Incipit: BG ⊓ DF AF ⊓ EF
# Date: 1676-05
# Akademie-Ausgabe: AA VII,1 N. 104
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=55773&katnr=Cc2+1248
# AA VII,1: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 358 (from the shelfmark LH 35, 13, 1 Bl. 358): 2 pages, canvases 711–712, page ids 00068196:0711 to 00068196:0712
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=711
# Lines: 109 recognised on 2 of 2 pages, mean confidence 0.75
# 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 358r — 00068196:0711
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000711.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 88 lines, status machine
igura segmentorum
prencipim ncum quo ostendo sumncam ocruorentium tangenti aequim dipeo sgmento
nullo negotio constendit dimensionem cyclocidis et omnium tjus partium 8 Mrensionem
etiam segmenti, coclocidalis mei absolutem. Num semper Cd EF sau fisau
y
BDEa
Alo EGA Eet en
segmenta
retao cyiloerdis ad circulu, sed et omnim partium ad circuli
in circulo. du catur
AB, curi tangente
baarrant. produc
EDBACE quarabilis g et etc aequatur quadrato
a r
itur dimidio ertus seu
et EHBsC aequabili
dimidio EC AF H BDE. Hinc facile demconstratur
LH 35, XH, 1, f. 357.
dum occurrant trantro
Ac preducta ps
AL poneum
ut 2E A
raX X
V unde
at- pXt  Ly sive
hvc l cax- x
p
Tam ut EC ad EF, su ut Fq
dea
ax seut  ad ax
1-X 
Trax
seu ut a -X ad T2aX = X, seu  sinus complementi ad simum rectum
ita FLZX. FH p, b. ad HG
sin comp. 
sive ponendo a = x py. fiet. Va- y
sive a- av
(a- y
Ergo. HG p siv. dest. b b trax- x
sin. ypl.  a = X
D HG. Jam AGp ax +trax- 
V Sa- y
frane a - X
quorum summa peniet exquad.
Cic, quia summa omnium AGp MADM
Hinc ergo et HG pender ex g. circ. Ejus momentum ex busi ND est bra-y. pendet
ex Ellipsi. momentum ex EN, sunt eiu B et fit b a - b  cujus datur dimensio
alsoluta. Ergo et onentum ex EF, seu ba trax X, vel 9. ba   C-yb arip
=X
cnda ex quad cic. haberi pt quod et jam lum patet.
ABB X. eius
GBEpE A172
erit X, 2a2
a2+72
qua datiue qur tangertes
et 7X + a X = 2aZf0.
sive, axce.
2a -XFI2
DEF Ran -X = YaX B Brax  - ax
Vrax-
A y - Z
Ergo DFH DE +  BE eiit H BC y Z + Z 3CZ
Ergo DFB Trax - x - ; ax F 3ax - X, 3aY - Xt TraX. X
sive 3a
scaxx
Trax -X
2aX - X)
quae lde x2aX - X. Haeesimul sumta quad rabilia.
2a - X ad ex Hyperb
La = X
probleme que Mons. Osannem pue propo Trome
difficale: sit numerus dutus, v.g. 10. dividatur
in pantes duas: 9. 1. et 8. 2. et 7. 3. er 6. 4. erc
ho quaeritar summa rectang ulorum sub ipsis. 9. 16. 21 4 etc.
hoc ait condinere ad solidum sphaerae Ego sic cocipro
sit b. colum erunt partes: y. Bb -1. quae ductae
cu se invicem: by -y. Hoc At summi ergo quaeritur
omnium . by= v. sed his nihil faciliqus. A Et
vedeo a manisestum exhibere adam sphaerae,
quia quadrata a 42aX - +V sunt 2aX 
ad est X 2a- X. ubi solum ponitura-
seu diaimeter. Nihil facilius. sed ille in lrve
genere problematum non ita exercitatus est.
ax + x. Ergo
BG5 D
AE, EF
besi)
LH. 35, XII, 1, f. 358.

## Folio 358v — 00068196:0712
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000712.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 21 lines, status machine
ocura
de
c
s
1g0
10
+10 1144 e
1ad anoret 1
dda -.
ni e
1
e
e
e
e
idemale
c
a
a
e
d