# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/1063/text
# Catalogue record: 1063 — [Aufz. zur Kettenlinie]
# Incipit: G centrum gravitatis incumbit horizontaliter concursui duarum
# Date: 1691-01-15 (91-01-05)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=1063&katnr=58613
# Work: https://leibnizlegible.com/work/00068056
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 11
# Folios: Bl. 8 (from the shelfmark LH 35, 6, 11 Bl. 8): 2 pages, canvases 15–16, page ids 00068056:0015 to 00068056:0016
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068056&page=15
# Lines: 132 recognised on 2 of 2 pages, mean confidence 0.81
# 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 8r — 00068056:0015
# Source image: https://digitale-sammlungen.gwlb.de/content/00068056/jpgs/default/00000015.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 90 lines, status machine
5 Jannar. 169,
Nihil hinc
a
io pnoluanio melhodus egearu
G. centrum gravitatis incumbis horizontaliter concursui duarum 
dugrum sustinentium rectarum AG, EG, quonam in ipsummet concursum incidit
magnitzu
irdis
et pudctis A et L
gravem et datis punctis A ex L
Datis rectis AB, LM, sustirentibus rectam rigidam BM invenire puncta Bam
deblete esse ehes sit 3 medium punctum DM, debet esse h3 omnium possibilium maxima
sunt S est AB+ A A5) et SIF constantes datae
:i
sit chorda pondere carens du neque extendibilis, duabus exromitatibu
F et F ajtixa, esque ii partes aequales divisae, in punctis divisionum appendan,
tur pondera aequalia inter se 1, vel 112, vel 12, 3, quaeritur situs in quem
situs ponderum, hordaeque
Et quidem manifestum est situm ponderis  anius haberi, si ex punctis Fixis F
et F tunquam centres, radio qui dimidiae phordae aequetur, describantur arens circularis
quorum infima intersectio erit locus quaesitus
Si duo sunt pondera l et H, et puncta fixa F F sint in eodem
honitonte describenda rursus centris F et F)  radio qui sit tertra pars
Chorda descubantur arcus coculares. Iisque ita accommodetur recta magnitudine
data in(oqualis  eidem tertiae parti) ut simul utrum, arcum circularem uttingat
et punctum ejus medium tam sit deprassum, quam possitale est, is situs erit quositus
decum ubi quidem eo s casu quo F et () puncta fixa sunt in eodem horizonte
facilis onstructio est, tantum enim oportet in F(() sumere BBBsaqualem ipsi Fi ita A
medium ipsius BB, coincidat medio ipsius F,F et ex BB normaliter eductae secabunt
2s2
GFC+ Cr = FP et EB + EH. _) = FH d. bet
=12
eu lit
C1+EK esse mexima= M. Praeterea CE = IK - E CV et FC+ CE+ EB = FB
ubi habemus s iocognitas FC, CE, EB) C), E1 et totidem aquationes tollantur
+2 (6
Ci, FC, EB et fiet sFi- CP + SF1 - Ep C1 + VF P - DEA -B(F) L FB. cujm
differentialis est - Ci dC1 Df - E C1 FEH dei EY H) EI (2 0
NFp-C1
VEr- EI -BF)
)SFI - EN- c
et ex aeq.3 est dei + dEi =0 quo valore substituto in aeq. 7. evanescit tum
dEH quam dei et fit +C1, +2Ep. C1 EA B(F)
SF1= CI SEP- E C SFP- EH RF)
0
ubi ope aeq unde jam ope aequationum 6 et 9 debent inveriiri EH et C1
Quaeramamus punctum concursus rectarum Fi et (F) H, seu rectam
F(I  Et antum F ( ad FC A FL ad FE. Kursus BM ad BE, ut AL ad ( seu X)
(1
Ferem
i _ FA + Bs = FB aut ML. Est autem FI: FC: CI:: FL: FM: ML, et
(2)
BEFEM
similite (E)H: EB: EH = B(F) :: (F)L: BM: ML = B()
FC + Ci = FB BE + EH- (F) B = F j2
FC +C E+ EB = FB. dei= = dEH
CE F = Fs - EH- Ci
C1 + bi eH C1  et - BF 
FC
CE
CM + M E = CE, quaeratur CM: A EM (10)
etot
EB
ex tet MCLENI ML = (F Et: Ci  jam ex 2 e _t = Ex 1est ML = F Ct CM. CI: FC
ex 2 est ML - B(F) = BE+ EM: EH = BF: EB = FC+ CM CI = B(F) oFC,: FC
confesido aequaliones 3, 4, s sit s et Ex ∞q. S est EH - CI  SF12- C5
et ex 4 est EH = SFP = BE + (F) B. Ergo ex 3, (3, 14, fit SF- BE + (F) B - VF 2 FC2-F - B
seu (F) B = SF p - CE2 +F  - FC - SF 1- BE et ex ay. 8 fit XFp - xCt + WyVF. CF - SF. B(B
CE
eBE
et ex jam ope aequationum 6, 15, 16 inveriendae FC, CE, BE, quae tres 
in aequationibus, 6 et 15 eodem modo, se habent sed in aeq. 16 modo nonnihil diverso
ut ergo calcutus reducatur ad homoeoptotos, sic enim una quantitate inventa, eadem operas
erunt invento omnes, sit FI, a
 35) +1. et 4, sit +2 et 5 sit +1
FB
(F) B C
FC p
l(1
CE, q EB,Y. et
sig ej. 6 fiet p + 9 +r = b epegus 1i sit a
ex eq. s fiet saa -pp + Saa -= 49 + Vac - rr c et ex aeg. fict: qtaa- pp + 4 a a - 49  stac - v7 (9)
+aa -94 = - ct taa- pp + saa-rr = 3h- pa Y f 4- pp + 5 6- p. Y Vaa- rY  seu  collendo frntiones firt
Eh
4)
60 + D =   a6O 35  bis 6. 7OD = 9 et quater 6. 201- 167
 - bis 66 - bis 7 5  bis 629 1 19
MCX. CI +. EH
CM = B. CE.
=+rpC + 4 pY aa - pp + 4pr aa = rY

## Folio 8v — 00068056:0016
# Source image: https://digitale-sammlungen.gwlb.de/content/00068056/jpgs/default/00000016.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 42 lines, status machine
quid si reducamus rem ad ratiomales (aa) xp = (a A 2x ( . siet ea p - 2G : ff. 41 = aci 3
et faa p = a  As = a - 45B: f++1 = a - aff .5f ran = a: 5f + aa
(aa = pp = (aa) - 2p f + pp ff: aa seu E p= 2f,: it ffica = 2faa: a4 + s
vaa PF=
et saa - pp = a - pf: a = a - 2ffa: a a +5f = a - f a, aa + ff
seu taa -p = a. aa - f: da + ff
ita p explicando per f, et 9 per 9, et Y per (h. fiet:
idfaa bisgaa, biehaa = b ter  + biEfsa Abisqua +bishitia =  3 a =c
aa +sf aa + g9 aa + hh
ivi
bix fad aa. ss,
t
aaff aa+g9 aatsih
3 4+ aa-gg aa- hit
fi 34 - c - = = b: 2 = d 3a -C, 2 = C
ade a
25a
29a
aa - hh
t
2ha
d. aa rsf. aa rgg. aantih = faa. aa tg carhh + gaa aarsf. aa + hih + h a4. aa Y ff. a 4 F g9
da + daafsrggehti + daassog + fftih t ggts rdff ggh = fa + fa gg thi + faagytiti a
da +ga ff +hh + gaa ff hh
+ hae + ha ff +gg + haa ff99
ea +Ca55 + ggatib F C aa fgg ffiti rgu iti +  gghih = 5 a  5f 99 + 3a f 9 hi
da +das + da 55 + dSgh - af + a fg + a 59.5
ed + ed f + ea fg + ef 9h = a f + 2059 + 3 a 5gh
quibus accedat postremo equalu 3F
aa
seu B 3t 249t 5h at Naa H + 4
fit a zaagh - 3 f9
gaa fh = 4g fh
5a a f.9. = G tih f9
80
aa
38 +
l
aa = hh. = 0
fph
ita ffhh.
Hha r243 99tin