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# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 9
# Folio 4v, page id 00068162:0008
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 3r); this page is its left half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 78 lines, status machine
# Lines: 78 recognised, mean confidence 0.85
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habeo sustectam falsitatis.
estos arcus lingis rectis aequales
 Equidem supponendo infinitis
sit circulus ABC. in cum puncto E, sit
tangens infinte parva DE, et ipsi AC
EF, et BG sunus  angri la
BGH similia adeoque BE,
parallela DF ad quam perpendicularis
AHB. erunt trangula DFE et
ut BH ad BG. Jam celerit pon
deris descendentis po
tatem aequalie celeitati pri
pE DF. spatia autem inaequalia fun
vis enut spatia celeritates.
ut spatia percursa reciproce ergo et vires,
vis et ponderis incircumferentiae circuli puncto B
descensui motientis est ad vim corporis in jusdem libera descendentis in
perpendientari t,
raum B4 Eodem modo vis ponderis in  LD. ad vimpondens
in Nequ est ut Pm ad sinum radium HM.
Jam ponamus pondus descendisse per LD, mnon ert vis i eAt
sinc u acceleratione, ducenda est, quae cum sit infinite parva
s descendentis
(DF ad DE, seu ut rabus BH, ad Anagi
nullam in ea considerabimus accelerationem. Ponendo rodium .
in LD erit  PM
dato, em te mpore minore quovis dato BC
spatium BD  in tempore DE, et spatio
Erit tempus quo percuritur spat
ad tempus quo percurritur spatium AI
ait ADE ad AFG, seu in duplicuta spattor
latione. itoque si mobite
spatium . pedis unius descende
haen s simpulo secundo unico, descendet per
duorum sempulis secundis quatuor, aetque ita relardacitur mns
Jam contraflugamus AB esse vel AD vel AF esse 
leum et BC DE, FG esse spatium, erunt spatia percursa
in suplicata temporum raive, et per consequens; ita motus acceerabitus
in ergo considerandum est velut partes axis; vis
in quonoce momento temporis expreita velut differentiae
Pone corpus aliququod grave descendere in aecta AF
dc primum perpurrece AB.  spatium minus
F in tempore FG, erat spatia in
vis acquisita in quolibet nomento temporis,
velut ordinatae;
spatia percursa uit spitia poctiones
figura ausem est seu
y Y va-y
frgura 8. Hcrentiam seu viriu simplit
X. maximo
(9)  X - 2yX
 2yX.. 4
l- f1.
E X (+ais a Cy
-4 sa BX + 2y.
Oy (1) = say
X B a - y Ego
2yAX. 2y1 y + La - y; ou y a-y
ou y 7 a- 9. ou 29 7 a.
Z1V2aZ-Z
fe dazC
+co - fcz ...  pat 
A Bco  cot
2Z5 co +a.
2H aZ
a -Z + Vra Z - Z  Cd. Ergo 2aZ. Z p, ∞ +Z - a 
c + 2c07 = 2a, + Z - 2 a7 + a2. Ego
Z +Haq .fco + s C0.
Cor +ZCd DZ + co rDa.. Z + Sia. 27 a
(DC Z senz. Z l raz. Z p7 a - 1a2 +7
+Z+ a HV3l.
= 2aZ - a 0 Z
pa2. X n5 (trase ae ce 3a f a Bea n cerir
a, sive Z +2
et q - eaz 2aZ- Z Y 2a B3= 3a. a
Ergo 8a3- 3a772a
8a t3 5a
Entsi + 6a ofi to H