# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/779782283:0160
# Permalink to this reading: https://leibnizlegible.com/page/779782283:0160?run=74
# Title: [Physica, Id Est, Scientia Rerum Corporearum, In Decem Tractatus Distributa] Physica, Id Est, Scientia Rervm Corporearvm, In Decem Tractatvs Distribvta (shelfmarks Leibn. Marg. 7:1-2; ZEN Leibn. Marg. 7:1-2)
# Folio 74, page id 779782283:0160
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=779782283&page=160
# Source image: https://digitale-sammlungen.gwlb.de/content/779782283/jpgs/default/00000160.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 88 lines, status machine
# Lines: 88 recognised, mean confidence 0.89
# 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.

518. 4.
PE RSTCA TRACZAEES T
darumnon cenlarum vel aeque ten- tio eric eadem relocitas, exitque
Parum longicudines, lune in ratione
lubduplicara criangulorum, isirui
lunere rempora; ergo vicistim cem-
Pora Cunc ve praedictae longieu-
dines, quod crar demonstrandum.
C OR OZ L.
Flinc colligo primo, Posse chor-
dam cenlam ira Lecari, re Leomen-
Eum, vel duplo cicius, vel criplo,
_C. reducatuE, quam roca ChOEda;
v. 8. Volo Legmencum, quod duplo
citiis reducatur, (r chorda censa
AF, Secetur aequalicer bitariam in
I. Tegmencum LA, duxlo cirius re-
ducetur; ( rero lecetur in R, IF2 VE
AR, SIE Z. EOTIUS AF, CeGIEMEIIZ
AR, qua duplo cicius rediICetUE;
acque ica in omni data ratione.
Secundo ita pocest lecari chorda.
tenta AF, re tempora reductionis
segmeatorum, sinc in qualibeera-
tione daca; nempe (i in eadem r2
tione dinidatus chordes; nam FeIM-
voca lunc ve legmeura, si Legmenta
Cunc aeque tenta.
PROP. LLLAIIL
Si sint duae cordae aeque tensa, i
aequalis longicudinis, que primo mon
Fig. 5. do reducantur reductio maioris fit per
plures velocitaris gradus: Nemipe (IC
AF, longicudo chordae maioris, et
TeMPUS, SIE AB, primus otadus re-
locitacis, quam habet initio extre-
mum punetum F, Cerre cotum Erian-
sulum ABF, repeaelentat velocita-
rem, in illa reductione acquisitam
ab entremo puncto, per PrOP. 64.
sic aurem DF, longicudo minoris
chordae vel tempus, quae sic lubdu-
plaprioris, de aeque tenla; certe
cumi Cupponatur eadem vis morrix,
Primus sradus DM, aequalis AI5,
tocumque crianguluIm DMF. RCPER
Centat velocitarem acquilicam in
illa reductione; igieuL EOE TUNE NO-
quin est aequadis vis censionis, inin
a2 velocitaris crementa, quor lunt
puncta in AF, e in DE, Ced lune
plura in AF, quam in DF; quis hoc
negec; igitur plura cremenca, 1gi-
cur per plures velociraris oradus tt
reductio inaioris, quod erac demon.
Arandum.
DROD. LZXZVIIF
In reductione chordarum diversae
lonciendinis, es eiusdem tensionis, ab
extremo puncto acquiritur maior ve-
locitas, in reductione maioris, quam
minoris. Probatur sic enim en-
Cura maioris chordae AF, vel
temporis minoris vero D F; ve- Lig: s
locitas acquisica, in reductione
maioris, LepEaTeNEAEUE PeF ErIAN.
sulum AFB; acgnilica verd in re-
ductione minoris, per criangulu
DME, quod est minus priore; nam
est. ciusdem alcicudinis, ee minoris
DalL.5 .
Veloertates acquistia ad calieno
puncto in reductione chordarum in-
aequalium, es aeque tensarum. sunt ve
loncitudines excessuum: vel tempo–
rum. Sic enim triangulum AEB, LC-Fig. 5..
praelentans relocitarem in redu-
ctione maioris acquisita; _L DMF,
repralentans acquilica in reductio-
ne minOris; trianoulUI ABE, est
ad criangulUI DMF, ve basIS AF,
ad basim DF, Cunc enim eiusdem al-
ticudinis, (od illae bales lune velon.
gicudines chordarum vel exceltuus
vel cemporum ex hypochel; isieur
relocirares CuME rE longicudines
praedi
L R. C   L 22- 22LL ab