# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068193:0210
# Permalink to this reading: https://leibnizlegible.com/page/00068193:0210?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 104v, page id 00068193:0210
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068193&page=210
# Source image: https://digitale-sammlungen.gwlb.de/content/00068193/jpgs/default/00000210.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
# Lines: 59 recognised, mean confidence 0.86
# 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.

ut
qui
A.
qu
ba
fr
De Mosu difformi seu accel. vel retard.
ri impares deinceps ab unitate:
Nam quadratorum 0. 1. 4. 9. 16. 25. etc. differentiae sunt
1. 3. 5. 7. 8. et. Et patet tempore A, F nercursum etse triangu
tum AICIS, ut I: tempore 1828 trapexium 1C15252C, quod et
qe
ut 3; tempore 2535 traperium 2C25353C, quod est ut 5; et ita
poprius.
Prop. 4.
Media temporis velocitas Carithmetica) in motuum
formiter secundum tempora accelerato seu qua latum unifor-
miter mobile tantundem longitudinis percurriset eodem tempo
re, quantum nunc percurrerat dicto motu accelerato est dimidia
ultimae velocitatis acceleratione quaesitae.
Hoc ett, si mobile per tempus A3F moveretur celcritate
uniformi 35G vel AH dimidia ynus 3J3C acquisitae tempore
A3S motu aequabiliter accelerato, tantundem longitudinis seu
spatis absolveret hac celeritate uniformi seu constante, quantum
nunc accelerata. Nam longitudo percursa celeritate AH tempo
re A3F repraesentatur rectangulo AA3S; et longitudo percursa
celeritatibus TC proportione temporum As crescentibus reprae
sentatur triangulo rectangulo A353C: (per prop. 8. cap. de Velocitate
muniversum). Ut autem sit rectangulum A A3F aequale trint
gulo A3B3C, oportet esse AA dimidiam iptius 353C.
Srop. 5.
Si acquisitae velocitates sint in ratione duplicata, triplo
cata ete aliteru multiplicata, temporum inde a quiete impent
rum longitudines percursae sunt (respective) in truplicata, quad
a
plicata, et generaliter unitate magis quam velocitates, multipli
cata temporum ratione.
Nam temporibus exirtentibus (Fiu.
eae AF7
)ut AS, partibus P.
tatibus et in duplicata ratione, seu ut quadrata ipsorum AS, liner
ACC erit parabola, cujus verta A, spatia autem percursa erun
t
In
Vi
ut
E+
tr
M
pro
bir
pon
na
se
et
ad
eas
est
tra