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# Piece: https://leibnizlegible.com/api/records/423/text
# Catalogue record: 423 — Linea centrorum gravitatis
# Incipit: Sint A1A centra gravitatis triangulorum C1B2B, C2B3B, etc.
# Date: 1676
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=423&katnr=57999
# Work: https://leibnizlegible.com/work/00068199
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folios: Bl. 155–156 (from the shelfmark LH 35, 13, 2c Bl. 155-156): 4 pages, canvases 309–312, page ids 00068199:0309 to 00068199:0312
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=309
# Lines: 192 recognised on 4 of 4 pages, mean confidence 0.84
# 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.
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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 155r — 00068199:0309
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 156v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000309.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 41 lines, status machine
2
de
linea centrorum
gravitalis
sint AA centra
gravitalis hian
gulorum. C1B2B, 
C2 (3B etc.
Centum gravitatis ipsius
C, B 3B est 2E. jo
bisecans 1A2A, vel 1E2A.
jungatur 2E3A, et trisecetur
in 3E Euit 3E centrum gravi
datis sec ipsius C1B4B.
jungatur 3E4A et
quadrisecetur in GE
et ita eut 4E centru
gravitatis ipsiu
C1B5B. et ita
poro iisque ad a
antam
 quod sit cennu
s
gravitatis totius
sectoris LCM
incipitantem N sic ut sit LN
dimidia CN. Et siminer se in
radio quocunque c
ut sA, ita at P5A dimidia ipsius C5 A
atque inde ducatur recta SH.R ad R centra in gravitatis
is ipsia sectoris CL P. erit sA. R in lineae centiorm gravitulis
ineps centrorum gravitatis (eritam ordine etengens et similiter si in altima, CM sumatur ex
esicnt sit MV dimidia CY. jancta CZ S4 et
tangi juncta ex praevemon tratis Tangit ujamque. Ergo sesea inde ad centum zaritatis sectoris et M dumri nempe
ducator recta Mus fanget lincam centrorum. ponamus
F jomnes 1E2E2E3E524E esse aequales, pihnt patabere
 reoremus gentrale rectam 4A4E a centro extrema particula (ABSB) nempe
circibri VN et VAM quaecitur quis dobrat esse ang utque MVN ut coincidat eom ? a 4B ductam ad centrum graritalis ipsius C, B5B, nempe ad 4 toti bineae centrorum
nempe NE4E aequatei adeoque rectam VZ aequari lincae NEF
31
3E 4G

## Folio 155v — 00068199:0310
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 156r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000310.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
finc sequitur et praxis generatis mirabilis
data linea centioium gnitalis, figuruum
invenire cujus ea confineat centra gravitalis
exempli causa sectorum sit linea proposita
bm
EQ santo in ea puncto E et
ducta laagente EA, sam aequali
ipsi  arcui NE primum
manifestum est linea NEZ
esse lineam centro rum quivitu
curvoi
AV. sed
velimus esse liveam centrorum
gravitatis sectorum seu frgurae
tuncs
p sumto quocunue puncto 
et junctis CA, ac productis in R sic ut fiat AB
dimidia psius  CA, et descripta linem
LBB fore  erit
liven NEE ipsa
gunitalis
nep centrorum sigurae sectorum LC
eG
Hinc muu habetur mirabile. data
sectorm
quacunque fiquia CLB si cujusque radii
ex centro educti cB, sumatur tertia pars B
habebitur nona linea B
quohaca
quae eandem cum proposite figura sectorum habet
lineam centrocum gravitatis NEE
patat et
rins bam qus
gingamnemfigorum cbb
sic dioue in lgnuata ut si
ipsae AA ipsis nitingali
si a Qe detrhatur: AE seu  arcus E 2e sidum fore aum ZE
AaEF aequalis
itaque si ad 2A tnasferalu
F
in producta DE sumatur F aequalis AZ Cut
N
ea AcC ea linea ipsius NEE evolutiare descripen
qaga

## Folio 156r — 00068199:0311
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 155v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000311.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
lan linea
EE, ut est tinca focorum ipsius A
FC seu centrorum oscula linea centrouu
ssculationis ipsius. NC t NFF ita
est binea centrorum gravitatis ipsius NAA
problem. ergo data curvae invenire
ineam centionm gravitatis etivm
huc redi
uvo
sic potent proponi. datu linca
data livea AAL invenire A
F
curvam talem NFF ut 
perpendicularis dF educta et
currae NA occuriens in A et
bisecta FA inE, clculus centro E
1
radio EF descriplus
osculetur in 
curvam NF
patet aile
posse esse infinitur seu non
omnes transire per N esse lamer omnes parne
as
inter se sed
Cangn
pole
l
s
k. C
fore semper unum
de
i forte res melius resolvi
hoc modo quod si consideretur
posse formari
ilas
problema formato sic ut si si qu ex F perpendiculenle
educatur rectu FA detracta inde datio  MN
reliquin bisicetur eandem EE. Et ope hupus considera,
e
tons videndum quae prodeant; ita enim veugusi ob
 s ab A(F) detrahatur data semper prodibil
punitum F. ali problema ho Taugentium con-
tringitur ad determinatur unde fortasse facilitas
+
proporeales seu st sit 243A, ad  A  A ut hiang. 3BaB ad triau c4BGR
in colculo.
intertatis s a didtio in riangule
AF
 SA
nam dal tantem postatatam publem
datis intinua AA punctis 2A_A. inveniis et
54 ut resta
mi
tale et sit hinng. CZA4A ad triang. 144+ A ab
quad fnsH. sit 
ata
est
method
Hc. Sum
a
vel quod eodem redit _ sit 324H ad +ASH si C7BB, ad CABSB. posito esse 
Bk semper dimibum CH. quo ulique ide feroitque peodit eadem lineo centioumpote

## Folio 156v — 00068199:0312
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 155r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000312.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
si lineam centromd gavitatie curvo possemus inviure
per Enthyuses seu rectificaves, quarundum descirpti
biliu curvarum, haberemus de sideratum alud magnam
Non lantm in Hugenii ed
et in sehitarusiu evolatio
nibus locum habet
ut Benera
deblo
ut ge
nonam linem
NEE ila secari, ut
anguli, 1F2E2( ex 2F3E3F
semper sint aequales ugo tripa
erunt in duplicata ratione aterum scmbatiur
circulu quicunque, et per centrum C
neantur ecta ad circulim radii CG
ipsi EF parullel et ipso
super punctis G et erit
adplau erigantur
Et perpendiculanter erigueantur super punctis
et
recta qua sunt duplicata rave ipsam EF et saper
ficres cylinirica inde secta erit proportionals
ipsi figurae
s
NE
s-
communis extreu
de quibus constet 
si duae curvae identur  M
centra gravieatis coincidere,
e
et NAq quarum canlum gravilanis
G coincidat, necesse est
nempe
centra sumendo factas) se se f, tongere in 9. qi nam VZ
Equ
tangunt invicem, potest uni esse puo mea methode quadratularum
sperialium. Ino hias amplius demonstratur id summe mrum contats
au frae pona (it surn y. dooparcus circuli in earum tinerceohon
dilem sit. sint diro unud
e necessaat bi occartt alice
cextrum gracitatis e. idautem necessario est in alterfecava
vertarum Morchovum A. et Ha Sapiliamm tarc lirea