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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 7
# Folio 10r, page id 00068052:0019
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068052&page=19
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 82 lines, status machine
# Lines: 82 recognised, mean confidence 0.79
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n
C
C
centr gnravitatis semper habemrus proprietates abundam
larndovas
si scilicet fingamus lineas quae silas esse calenarias
suspensas seddifformis gravitatis. sic enim
L
quovis data linea
produpi potest. Sit scil.  elementum curvae guive in ratione aliqua p: at et fiet
dementam momentam ejus ex axc. f SpyYax+a et TA distantia centrigiaioitalis
euit
et
carvo
S (1)
y ax +dy: AAprdx +du=
2
s= AT s C Rursus y - t: X :: dy: dx
(2)
Fit:  seu FB X dy ger ydx -  t dx = Xdy. seu tdx = Cy tx - X dus
(4)
seu t = y = x dy: ex en dt = (dy) = X d. dy: dx ( dy
etgo
Aursus A ex Y est  by Sdx + dst = t p dX + au + Sp Ndx + dg at et -
sit. PVax +a: (PSax+du  dt: + py ax + dyt: t (podx ra l
2
en perine
Spyida ta
se2
sed in aqu. G sobsuento calorem te sit: ipsius f sit py ta et propat due ponendo n
fit  y dn = + dn + n dt sen (y an = +n quod constat ex aequ. 1. Et
pro t substimendo ociorem fit: (y dn Z  (y ard = Xdu an: dx  = nX d dy: dx
per 3
e si
divisione facta per rsit X sit an: n = -dy ddy: dx: sg: dx. Ergo 
fit dy: dx = a: p assumia constante a, ad implenda legem homogenectum
Eegue  seu an: a = dx: dy sit dys constans fiet du: a day: dy
2
parsus
nius ope tollatur _, ex aeg. 5, et fit ydu  f an + adx: du at. et sallendo  det
at fiet (Y du) = y dn) = X dy: ax an D a a dx: dy X d dyi de sec ila tantum 
s
l
lq
redditur, aequ. I1. Ergo quia n: a axidus faciamus dus constantem, et fiet.
1167
du: a dax: dy. et sit  = jam dn= pax + dit et ddn= dp rau tdus +paxdlx: tad
Et etat
se 15
Si in aeg. 15 substituaes tollas dx per aequ. 11. fiet: du p dus n +a: a
video non esse opus supponere dy esse constantem. Hinc si p detur ex y sen
habetur lineut
si constet quomodo pondus catena varietur pro recessu ab axe,
Ergo si detur p
est
et rursus quia tollento du, fiet: d dn = p exernn + aa: n
ex x seu recessura vertice. Atidem habetur solutio. Nam data n per x aut y+
e
utique solutio quadratoria habetur, pet 11. Rursus ex 14 et 18. sit 
fit dax a: dx= pdus Snitaa :n ubi si tollamus n per 11. fiet arqualis quaedam non bene tractabilis
19
Eix gy. 16 se collamu ex et dap. per aeg. 1t. et 4 fiet Ean dx dn:p + Bady: a dndus: a : dh:p
c.
5
per
seu dan: dn F ap: p  ppn du: dna si  poneretur staneet  log. du= tn dy: ar
A esset, p= 1. fieuet ddri du) ex dex. Ergo per 14 fieret. Cin = dx dy: a. seu du= Xdy:a + dy 
sad in aeg. 1b relento p. si pro plolx substituas vatorem ex 14, fiet: cia = Apdn: p + ppdx: du Andy: a sed ita
si
res non aque procedit  sed et sine dius summa obtineri pt, cum B datur ex X sit cmm
nam
Pax
du: Suntaa. Ergo spdx = AAnn + aa +d. sed si _C praeter aegu. 11. et 15 unde
(22
uit ceg. 1b. daretur e simul per X et y. imo fate at simul er dx ty  uo posset ex his haberi lice bit s
rem abtentare per aliam bram sit. cb. data peradbxa seu callundantia
oterento plur puncta us albi
promotio
Catenarie
ad satenam
difarmem
pondere