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# 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 531, page id 779782283:0617
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L AB. V. DE RESISTENTIA CORPORNM
vio; hinc si cxlindrocum longitu- dubie si asTumacur funis ciuldem
dines, ee diametri batium sinE pro- balis, cum priore, sed mille pedes
portionales, id est li vna diametee
est ad aliam, ve lonoicudo ad lon-
sicudinem, cylindri line in ratione
eriplicata, id est ve cubi diamerio-
rum, vel longicudinum; de quia
haec propolicio non parum vlui
esse porest, in aliqua figura, in gra-
ciam erronum explicanda est: (IF V. 9.
Eig. 24. Cylindrus LC; a alius LB; cerre
Cab. 2. diamerer MB, est ad diametrum
KC, ve longicudo LM, ad longi.
cndinem LK; de Cylindeus LC, eAt
ad cxlindrum LB, in Parione cri-
PlICaTA LR LM; Sic enim LN, cius-
dem diamerri, cum LB; de lonoi-
cudinis, cum LC; est ad LC in du-
plicata RNI, KC; veI LM, LK; nam
LM est ad LR, VEKH, ad HC; igi-
cus eadem eAt duplicara LM, LK; de
KII, KC; igicur cylindrus L N es
2d L C, in duplicaTa LM, LR; Sed
L. N es ad LB, VELR, ad LM; igi-
EUE LC, ad LB, in compolIEa, ex
duplicata RL, NIL; _ Cx RL, ad
ML; Sed haec est eriplicata, VE CON-
Aac ex terminis; cubus enim est ad
cubum, in compolica ex ratione la-
TeruM, e ex coruundem duplicara:
igitur exlindri proporrionales Cunt
in ratione criplicara dinmeerorum,
vel longicudinum; igieur ex pon-
Longus; pondus huius, erir ad pon-
dus B, inrarione millecapla, per
Prop. 19. igicur pondus Funis, mille
Pedes lonsi, ett aequale ponderi A.
re constar ex terminis; igicur ( a
Pondere A, Funis B FraNGIEUL; CCPEO
Funis mille pedes longus proprio
Pondere FrangCEUE; Per PFOP. 15.
quod dixi de fune, de omni cplin-
dio, materix durae, cirra censionem
considerata, v. 9. de plumbeo, Fer-
ieo, ricreo, dec. dictum censeatur.
PROP. ZX III.
Omnes funes, eiusdem materiae, quo
propriopondere franguatur, sunt cius
dem loncicudinis. lcet sint dinersae
crassiudinis, vel basis: Sic enim
quilibet funis A, qui proprio pon-
dere frangatur, sc alius quilibet B.
quadruplo crastior, ciuidem ma-
ceriae, ex longirudinis; dico, quod
B proprio pondere Frangetur; quod
Facile demonstro; quia ve lc habee
ris ponderis Funis A, ad ciusdem
relistentiam, ita se habet vis pon-
deris Funis B, ad relistentiam cius.
dem; cum enim funis B pondus.
tancumdem crelcar, supra pondus
funis A, quantum crescie resistencia
Funis B, supra resistentiam Funis A-
dera corumdem exlindrorum, (unt cerre eadem est rario ponderis B, ac
is eadem rarione criplicata.
PROP. X X IL
Daro pondere, cuius vi, datus fu-
nis frangitur; invenire loneiudinem
funis, ejusdem basis, qui proprio
pondere francatur: Sic dacum pon-
relistentiam B, _ ponderis A, 2d
relictentiam A; ve Patet ex terminisi
Si enim duas quantirates, per eam-
dem mulciplices, cadem IMaMCE prO
Porrio, quod autem Funis B ean-
cumdem crelcat pondus, quaneuir
relistentia, parer; quia pondus cy-
dus A, cuius vi dacus Funis B, vnum lindri B, est ad pondus cylindri A.
pedem longus, Fcansitur; sirque recylindens B, ad cylindrum A;
pondus appentum A, ad pondus aequi cxlindri ciusdem longicudi-
funis, in casione mislecupla; haud nis, Cune re bales, re perspicuura
2
etes