# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/62783/text
# Catalogue record: 62783 — De via centri gravitatis
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=62783&katnr=60303
# Work: https://leibnizlegible.com/work/00068534
# Title: Leibniz-Handschriften zur Mechanik: Dynamika LH 37, 5
# Folios: Bl. 48–49 (from the shelfmark LH 37, 5 Bl. 48-49): 4 pages, canvases 95–98, page ids 00068534:0095 to 00068534:0098
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068534&page=95
# Lines: 196 recognised on 2 of 4 pages, mean confidence 0.70
# 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 48r — 00068534:0095
# Scan: The same scan is also registered as fol. 49v; its text is given once, here.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068534/jpgs/default/00000095.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 132 lines, status machine
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sis suo per
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+3
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d f. C.
de
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duo addantur ad so invicem fiet.
++ ne x +mon-  X etc nio tuxx et  uri
305x
+ P+ m pr X  mm.  st X et. in  20+ u+  Xerc.) 30. + 3IX +52Xe
Ea um X et in B m  X uju moga t rorratX, A 2 
sit formula 30.31X ea teminoaum t erit 30 +3IX e  a - 2ax CA FX terme
in terminorm ++2 = 2n + 2M
urum F+2. Ergu est X 2m jam sit 1otuxer. tercinorum P
jam C+X in B 1 uXer +
et 20 +4 x erc. terminorum q ergo fiet inp umq- +
altissimus terminus ipsius compositi vle 2n p vel 2mq vel si dueo
termino aequales adeoque se destinunt, fiet aliquis inferior
debet esse ergo e summa duarum formularum
Quam maximi cujusque termini sunt rup unius et 2mg
alterius e habere maximum terminum superioibus scilicet
diquodduam formula
sed difficultas est in qarav seu numero arbitrariarun,
nam ut coparentur C+X in bFXm cum 30+3IX a raxta
a
c et b; et has el debemus habere.  ergo res succedit Sed ad
comparationem nominaloris cum numeratore instituendam
modit habemus arbitrarias p+g pro terminis compa–
eaudis 2np vel 2mqe, hoc est Tnp amqampas tnrma
x-inp specimen calerli
E p. d 2 4. E. - + 3E
debet esse non p p + 9-1 ses
inpextamipq   sed si npi et mis sunt aequales M. A  A 3
emq
x-pamque amuiq aupans ot seu n = mgq. pp  soui protir
de via centii gravitatis
si circa centrum A feratur
si AB ad angulos rectos incedat per rectam AA
timulque Cd per rectam AB (utique manitestum est
aream comprehensam inter cd primam et postrema
a et inter dd et CC, aequari  rectangulo
ex Cd in lineam EE Est autim EE via
centri gravitatis quatenus est generans
hoc est via centri gravitatis de via centri F
rectae generantis, quodenus inde detrahitur via quam
habet quatemusnia generat sed per sua vestigia
incedit hoc est quatenus cd propeditur in restA
quatenus enim centrum F per hoc ascendit se
re recedit ab AA, tantum rursus descendere
ponatur versus A, et incidet semperim E
ponatur esse filum. G.AM, quod deinde
transeat in EG2A 2 et itn porro et
sit via centri gravitatis fili FF ea via non sufficit
p+ 9 1 vm 4u. p non haec debent H debet duci in filum ad habendamaream spatis 1A. GG2G3
fiet 2mgg non p p+ 4-1
in integris. Quid ergo si sic in casu aequalitatus p = 2m94- q- 
(quia enim haec aequad in interies ideo ab ea iicipiandum et 
Cnpp= e maque. Ergo 4un4q am - 4m  + a 8. 24 + n-n q
Eogu n necessano dividi debet per 4a. sit eeim ebd esse integer. e
Y = M: 4 4m - 4m 4 491 qui
no restimgaum id aequalitatem utique e
eliam nrigus non eZm
odsudisem atu sa
Eju
non su
non B. 2m9g 4+1 E. rgo
St itm quaqui seo hoc non est 
sed debet via sumi quo restat, directio naliter inde detrahendo
via
gliscil. sit enim via fici it via centri 1F2F consideretur
quo sit via centri quatenus filum ex (1M)2A (1G) tranus fertur 2 M 2A 2G
on
centur ipsius (2M 2A.G) centrum est ect CF) in recta 1FCF
parallela ipsi AA et aquali ipsi mem). sed deinde transluto fileo in 2M A
centrum est in EF, ideo motus (1F2F est inutilis seu detrahendus. restat motus
IF (AF
dobis serviens. similite
2F(2F) et ita porro, e hoc addi debe
irvicem, in quo est difficultas
omnis dimensienus
i
1B, 2B 3B
s dsi
G.
F
quia non coherestus mere a ta piroiam can  at e e qpitet

## Folio 48v — 00068534:0096
# Scan: The same scan is also registered as fol. 49r; its text is given once, here.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068534/jpgs/default/00000096.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 64 lines, status machine
Ex coptanda les celeulits lats
qua labentes ipso 23,
e
dia umus
dub ex trenmritatibus
eccurrat extremitatibus dicinis
e
1nemi
erpe tipsi 3, et
Eauli tt e stiteri
ad
d
X2
te
a e
Nh. Hic exemplum a culandi
 infinite parvas ds
nit
25..  23
u
in
omanentes,
lineam connecten qi sat Algebraica
 
i
 ea B q isper dari ex A4 et 45
debet 23 transferri in H12 et 12.13. in
1131. (13) et 23 22. 23 in (3). (14)
sit A4 X et ∞ Fx
sit A1, vel A20 X et 1020, vel 2030, et 
sit Ex, ponamus 45 dari, ex X et dx, similiterque 23 id
est inte rrapta sautur ex continuis. jam ipsa interrapea sunt
jungenda inter se quoritur relatio constans inter A100, et 10(11
A2021 208 (11), 300- 12) et c. sit 4100  Vel A. 200. sit _Z
et 100. (11) sit   quoritur otulio inter Z et V. hansferneur
ergo (2. 3. ulcunque in (11) (12) eiq adjungatur 12. 13 anguli
(17 (17. (13 quocunque. Ex assum ts 100(11) et 100. 200, et 200. 300 dalisu
magnitudinibus ipsarm (y(iZ, et. 12 ) 13) hoc est ex A ek 45
A 10 et 10. 20, item eodem modo ex A20, et 20. 30
positione puncta (11. (12, (13) Ergo dubitur A300pr = 24 10
seu Z+ dx et A300 seu lZ) = Z + dx + 1d7)
200(12) seu (Y) riemus 300 (13) seupr
vel alite
Jingantur (19, (2) (13) positione data et sit 31 ∞1) (12)
angulus nellus da adeoque ratio  100. 61 ad 16 (11) assum; potest,
similiter ratio 200 (12) ad 6EC 200. 462, et ratio
300(13) ad 300. 63. Ergo Jan  100. 61 ess ad
14 (1) ut datur ex 100. (1) per (1) (12) et 100. 200 et
(11) (2) datur per A10 et 10. 20. datur ergo relatio
inter 61 ( et 100 (u) et 410 nedentibus r0o . 20, et 100. 2
et simulis plane relatio inter 62. 200
e tulli
Icug rclatio quaecunque inter AW et A10o dabitur et relatio.
inter Aro, et et ratio 100. 200 ad 10. 20 per A10.
restat ergo relatio intr 61. 100, et 100. 11 et  et A 100
tantum ergo relatio talis assumenda ut 61 evanes cat
vel aequatu aque rdv.  =  x 0. res
ergo eo redit ut quantitas  (data per X) resolvatur in
dux quadrata quorum latera sint summabilia, e
xx= 2aX +aa sit BtoL IXt 3X
litus sumbili est  on 202 + Pex etce rattum 204 2ux 22 X etc haec
a + bm
2
1

## Folio 49r — 00068534:0097
# The same scan as fol. 48v (00068534:0096), where its text is given.

## Folio 49v — 00068534:0098
# The same scan as fol. 48r (00068534:0095), where its text is given.