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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 101, page id 779782283:0187
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sie
L. IB. II. DE COMPRESSO ET PENSO:
1OI
cularis, A AFC, est aquilaLCrUM; SeoMenEO AC, v. 9. L, e ducatuE
hoc posito, re AI, est 2d IC 5 ita ULEI, Parallela AB, SCCAE PFOPOI
AV, est ad VE; Ced vE AV, est ad
VI. ICA VL. a LVO, VE PaTeE ex Fu-
clide; igitur AV, non est ad VC;
in Fatione AL, ad IC, seu quod idem
est in satione AV ad VE, Sed in 12-
tione duplicata AV, ad VI, vel AL,
ad LC; igitur punctum L, nOn KC-
dic in V: praeterea chorda AFC, est
masis centa, quam AEC,; VE
PaTCE; nam AFC, Facit maiorem
quanticarem, quam AFC; 1gi
cur maiorem censionem; Led
quando chorda AFC, reducituI,
punctum L. redic in V; ve Cupra Fu-
se demonstracum ett; igitur quan-
do chorda AIC, reducitur, cum
AI SE minus cenCa, CerEO L, NON
redic in V, nec lupra V; ve enim
hoc ACret, ALC deberet esse
magis centa, quam AFC, isicur in
Eta V.
PROD. CLV
Determinari possunt, in chorda non
tensa sineula puncta, quibus respon-
dent singula chorda tensae; posiris jeg-
mentis tensionis inaequalibus: Sic enim
non centa AD, centa ACD; CCo-
menca centionis inaqualia ACD;
allumacur CB, ae qualis C A, cum du-
CatUE AB; CerrC DB, es aequalis
ACD; igirur Ei a singulis punctis
rectae DB, ducantur rectae paralle-
lx AB, v. 8. IEFL, FC, GF, ad qua-
lica puncta cerminabuncur: sic enim
punctum C, v. 8. a quo ducta (IC.
FC, pacallela AB, CeKEE VEAF, est
ad FD, Ita BC, vel AC, ad CD, Cx.
Euclide; isicur C, redic In P; G, in
E, ecc. nempe legmenca proportio-
nalia corius BD, relpondent prO.
portionalibus cOrins AD; de (1
altumacur quodtibec punctu int
Tionalicer BC; AC, AE, VE paTCE CX
Fuclide, igicur decerminari poltune
Singula puncta, dc.
PROP. CLVI.
Nullum punctum chorda aeque
tensae, redie in chordae non tensa pro-
prium locum per lineam perpendicu.
larem, nisi sermenta chorda tensa
sine aequalia: Sic enim chorda tensa
ACF, ec nO cen (a AF; AINE AC, CF, TI8. 12
Cegmenta aequalia, punctum C.
dum reducitur chorda, redit in O
per lincam CO, perpendicularem
in AE, re Supra Fuse demonstracum
eAt; aC VeTO SInE SCTIENTa ADE,
inaqualia, e aeque cenla; dico quod
Dnon redic in F, Pet DF, perpen-
diculorem; redeat enim, (i tieri p0-
cest; ducacur AB, parallela DF; ill2
etiam exir perpendicularis; igieur
DB, esc aqualis DA; nempC FB,
est aequalis EOTI EDA, PCF PEOP. 155
ee constat ex hypochesi; Ced hoc
dici non porest; quia FC, de CB,
icemque C A, aequales Supponun-
tur; igitur criangulu ACB, est
ilolceles; igitur habet duos angu-
l0s ad balim aquales; (cilicet CAB,
CBA; aequi SI DA, essec aequalis
DB, triangulum DAB, eslet ilosce
les isitur angulus VBA, est aequa-
lis angulo DAB, vet CAB, id est
pars, tori; quod dici non pocest;
igitur linea DF, non Porest elle per-
pendicularis in AF, quod erac de
ab.
ais usons t onite aDen
datur otrestensionis impressae, erunt
aquales extensine, incensive vero et
10
t o
idlem, vel aequale pondus, chor-