# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068160:0070
# Permalink to this reading: https://leibnizlegible.com/page/00068160:0070?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 10, 7
# Folio 35v, page id 00068160:0070
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 34r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068160&page=70
# Source image: https://digitale-sammlungen.gwlb.de/content/00068160/jpgs/default/00000070.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 96 lines, status machine
# Lines: 96 recognised, mean confidence 0.82
# 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: the recognised lines in reading order, one per line.

ergo Cn - Gt Ergo
condrarius et
sit ABAX, et BC, y.
jam calculo quaeramus pA
p tat
et _X, v=eV et,
B: BC :: dx: cy jam Cg = Y - X
et N et QN =  - P9. jam PQ = y - p. Et fint q N - V- y + p
Ergo habemus: r - X :: V - y + p: dx: dy = seu fiet
imenre rdys xdu .: nde y du + p d∞ Y - xyA = V
ese 
r- X ) + y -  ( fB ee
) ipli pR et t
D at explicata
AXMocutrat LTis. detem ese M5)
portignale () et D debent Y et psic
et y per
assumi, ut aequatio fiat identica F Alioqui quaesitum impossi
ergo 
bile est. Sunt autem  temporum incrementa. Vel
Fdy  g p = B. Hinc tempora tota seu svax sunt
am
s (xdus +sud PX. nan sat bis 1CPpC
et hoc = PL2C + ICL2C, 1C vel IC. H. P. q2C. 1C - )C. H. P- 2C8
vel jam C. H. P. g. 2C. 1C = Sydx (se 1C1B. 2B. 16, 1C) + 2C 2B. R - B R. p
seu jam ZC. 2B. R = (7) in r -() 1BR. P = p. s Y ( Y - X
eu
1Ci H. P = sy)C
X y - P in Y-B: Z et 269. P-
X(X) in (y) P : 2 Ergo
seu-
p. 2C. 1C =
Ergo denique
ydx (seu 1CB. 2B. 2L. 1C) 4(y) in r- (X) - p em r - X
= y - p in r (X) : r - (X) in (y)- B: 2
v ax seu tmpon =  x + (y) (- (x)() (- PB + pX (L rs + Lsps
Epr () e) ry (+ Ap ( (3) C L pex)
suax seutem = (ydx + r. (9) -y ∞ p () - X  L (X) (3) - y
seu tempus = Sidx +Y r - (). (1G = B. (X) X =
super est ut quantitatem conatus centrif peti vel
centri fugi investigemus. Necesse est eum respectu impetus
tam quae respectu conatus no motus jam concepti est infinite parva
Nempe curva erC3C contrario ordine evoloe Intelligatur, situs evoluta
VV, et per V ducatur V V parallela ipsi BC, et per 3C, ipsa
3CK eidem parallelu, quae est  conatum exprimis
centrifunum, respectu conatus concepti rC. K
ubi apporret yc pK esse infinité parva respectu 2CK
et infinities infinité parvam pC. nam IV.2V sunt
Eo etiCrC= x 2C, K sunt homogenedt, ut et 1V2V
et 1VW. ab 3C.X est ad 1VW ut 2C36 ad 2C 1k seu
ut infinite para aderdinarium,
itaque jam
3CH; 2C3C:: WNV: +C. V (unde patet sumlis 1V. W semper
aequalibus, fore summar conatuum centrifetorum seu ipsarum F3CK,
ut logarithmos arcuum evolutorum XC.. G
jam ratio 1V.  ad 1V2V
Ita habetur: per s ducatur paralleta ipsi curvam tangenti in C, seu
ipsi 2C2V et per V ducatur parallela ipsi CP (quae est 1V W continuata)
et itenon recta tangens curvam evolatione ipsis CC descriptam in Y
(quae erit ipsa 2VIV continuala) occurrentes ipsi per–
et fet (V i e 1IV. I: 1V2V::
auno valorem, V. 1. fiet;
3C. H. C3C..
rgo vires centri pelae (vel centrifugae ie astone granitatis ec sevitatis, sunt inter
remlutorum curvael
P ductae, illavi f haecui G.
radiorum sec
IV. F : IV. G.
Ergo substituendo
112  VVCIVG. CY
ter in gpopsionalion divetesquidem 
notectu et ergevolatione tesci
rectarum
a b recipinis adt
et
et PH
 adia
rx sy seu
y- P ax
iCRCi
Eugo restans at2HL  
geXK erit-
loqudcilineo
quadril
hecat
obiter
4.
es
deus
et sit BBC
cerperdia
in ad tangentem
etr ilyptilu
standem angulus dest res
eF= C et
Nique C erit = VG