# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/779782283:0647
# Permalink to this reading: https://leibnizlegible.com/page/779782283:0647?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 561, page id 779782283:0647
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=779782283&page=647
# Source image: https://digitale-sammlungen.gwlb.de/content/779782283/jpgs/default/00000647.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 87 lines, status machine
# Lines: 87 recognised, mean confidence 0.92
# 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.

PIB. V. DE RESISTEN PIA COREORVM. 56I
cata diamerrorum, permurando, rum: Nempe omnis relistentia, vel
per proP. 49. COF. 1. Sed relistentiae, est a balI, vel à longicudine, seu
racione balis, lunc in eriplicara dia- breuirare rectis; Cunc enim resi-
mecrorum balIS, PeF PFOP. 49. PEX-
terea momenea ratione longicudi-
nis, Cune ve longicudines, Ve patce
ex dictis, praelerrim prop. 24. atqui
resistentiae rarione rectis, TunE VE
Longicudines, permurando; per prop.
24. num. 10. igieur resistentiae cy-
LindEOLIm TUNE DE MOMCNEA PEF-
mucando; _ vicisIm IOIMEHCA, VE
relictentia permurando; praelcin-
dendo Scilicet ab auomento ino-
menti, quod a maiori pondere pro-
cedat.
DROP. LV
Tiinc praescindendo ab auemento
momenti, quod est à maiori ponde-
re, vel cylindri, vel appenso; resi-
stentiae sunt in cylindris diversae dia-
metri, es loncitudinis, in composita,
ex triplicata diamerrorum, non per-
mucando; es ex simplici ratione lon-
sicudinum permutando: Ouia mo-
menca Cune inhis, praescindendo
Ccilicet ab inaequalitare ponderis, in
racione compolica ex rriplicata dia-
metcorum permutando; ex ex sim-
Plici lonsicudinum non permuran-
do; Sed FesISeNEIX CUNE VE MOMIEN-
ca permurando, ve constar; ve aurem
haec ratio compolita habeacur, sine
dux linca, ve cubi diaMCFEOLIIM;
ducantur illa in longicudines, per-
mucando; rehistentix, ireinque mo-
menta, erune ve rectangula, Tub his
laceribus contenta; pari modo ha-
bebitur ratio compolica, ex rripli-
caca, de alia duplicata.
PROP. LV
Resistentiae cylindrorum similium,
sunt in ratione duplicara diametro-
Sencia, rarione rectis, re lonoitu-
dines, permucando; de ratione ba-
S5, circularis scilicer, in eriplicara
diametrorum; igitur cum longieu-
do, sic ad lonsicudinem, re diame-
cer, ad diameerum, in cylindris si-
milibus, vel proportionalibus; ce
Sistentiae Cune in ratione compolita,
ex criplicata diametrorum, non per-
inutando, e ex rarione carumdem,
permutando; igitur maioris resi
Rentia, est ad relictentiam minoris
ratione ba(IS, ve cubus maioris dia-
metri ad cubum minoris; aE vero
ratione rectis, ve diamerer minor,
ad maiorem; igicur hc compenla-
eio, e Hc duplicara, ex eriplicata;
V. 5. SInECD, CO, Cplindri pro- Fi8. 28.
Portionales; relistentia lune in com- T ab. 2.
Polica, ex criplicara diametrorum
CA, CB, X ex ratione simplici C A,
CB, permutando, sic autem CA,
dupla CB; criplicata cA =. rario
vero diaerrorum =. PeRIUTeEuE
=. COIPONAEuIF =. vel =. vides du-
plicatam diamerrorum =. pari mo-
do sine cylindri similes CL, C6, sic
CA, cripla CL, racio diametrorum
est =. PermUTCTuT,. eriplicata ve-
ro diameceorum =. Componatur,
=7. vel 2. vides duplicacam diame-
trorum; cario est, quia si non Ae-
tet permutario, e maior diaeter
duceretur in Cuum cubum, minor
reco, in luum, per compolicionem,
haberetur cario quadruplicata dia-
metcorum; cum aurem AaE perMU-
cario, e ducacur maior diamerer,
in minorem cubum, minor in ma
iorem; regreditur rario ad dupli-
cacam; ioitur relistentia eplindro-
rum similium, Cune in duplicata
BBbb diame