# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068096:0004
# Permalink to this reading: https://leibnizlegible.com/page/00068096:0004?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 1
# Folio 2v, page id 00068096:0004
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068096&page=4
# Source image: https://digitale-sammlungen.gwlb.de/content/00068096/jpgs/default/00000004.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 92 lines, status machine
# Lines: 92 recognised, mean confidence 0.87
# 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.

Mods desolmiuandi punctum
lineae isochoae BD in quod cadens
grave sd uta si corp celeritate
dedescendendi, inde porro
descendat in ata uni frmiter
Cy = v. Ergo d Gdy - 3 d
de
3 dv
= 3y ~ PX
2u
WX
PW ax di jm d.
PW - dv + d7 1 = 1 + 37 = 1+ 2
ic.
sit paraboloetes quadrato Cubica BD, imi respondet altitudo AB siv et 
QAB sit latus rectum, et grave iad ens ix AB et in B ionans pergere increment
huoporis ME, tendet porro incremento temporis eode. sit aliud grare.
cadens ex altitudine NP, in eandem carvam BdP, videndum nn
continume possit motum in eadem recta BDPE. imrementum,
in AB sumatur AR = Np, erit incrementum temporis; post lapsam
liberum ex A vel AB,ut diff. A5 seu ut TV. ducatur
tungens PIV, et aut incrementu temporis quo corpus
et ipsi E L in Z, et debet esse Z Y ad TV, ut P h ad Id
hoc est in parobbolvende Bd P, debet punctum
pumitatem ut iproducatur YE donec iisi
Aco iccuriat in co demittatur inde 1d P in BE7)
e
1 +:
4C
4C
v. =. AR = AB = BR
4c
B1
seu V ad gC. ut AR - AB ad AB
et eut V seu Ax quaesita
cines BB
at 4C seu 4 lateri recti est ipsa
allitudo AB nun latus rectum est 4Z AB
duns
debet esse Ecyptans ad TV determmnato
per altitudinem AR ut PW ad WX id est data
LV (non VE est onstans) inveniri debel punctum p
ubi pro ad lox postutatu habeant radnem
poMelior erit constructio si duae prratela
horrfonti ducantur non per A et B, sed per F et B
ita loco VE, sumatur BE, et langens in S sect
BE in V, et Fk in 
cujus. 4 sunt A dant AB. Ergo Y
et est es demissa perpendicutaris ipsi BE occurrat
inf jam Dis ita indagtibimus Tangens
srp producta occuiret Axi, in A, et AA = AR
jam triangula LR ARS et _OV sunt similia
Ergo PW: WVX:: BE. AR: RS. AB jam BE
jam BE =  AB et R5 = Y AR.
Ergo PW: WX:: +AR: AAB seu in subduplicata
ratione altitudintue datae An ad altitu vertici 
D= BR. Ergo. corpus pe ex altitudine
A ladens in jochionam lineo b BD,
in ea porro descenidet uniformiter
idque praevideri poterat sine omnibus istis ratiocimis
omnique calculo, nam  ex ipsa constinctione
corpus ddeniat in D per ABD
ex D porro descendet uniformiter; jam ead idem fit
ligine lineae sin
ergo D V est ad RS ut FB ad DR seu ut AB id A
ERgo DV = RS. AB: AR. jam 
PW: WX :: BE: DV. 
WX dv. -. . 9v 4c + 9u = 8G
et
2
de
 lum nsquo ulis sese an set
ad deter minundam rationem plo: nX
seu v = 2 ly = et
et dy
WWX
dv
su
si audecunque eadem celcritate perveniat ad idem puanctum D
pervenit autem ad D eadem geleritate modo descendut ex
vel obliaua rectam vel invor
lexam
quae
descendendo pervenne ad D
lsochiona lineae inservit AB.
T BE vpaesentit tempus intreneula
temporis perpetum seu unforme
BDP, et fV incrementu
ervenien
quo corpus in pp
libere descenderelendit, ergo
gebet esse