DelMonte, Guidubaldo
,
Mechanicorvm Liber
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<
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">PROPOSITIO. VI. </
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<
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">Pondera æqualia in libra appenſa eam in gra
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uitate proportionem habent; quam diſtantiæ, ex
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quibus appenduntur.
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<
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">Sit libra BAC ſuſpenſa ex puncto A; & ſecetur AC vtcunq;
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lb
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in D: ex punctis autem DC appendantur æqualia pondera EF.
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</
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<
s
id
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id.2.1.57.3.1.1.0.a
">Dico pondus F ad pondus E eam in grauitate proportionem ha
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bere, quam habet diſtantia CA ad diſtantiam AD. </
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<
s
id
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">fiat enim vt
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CA ad AD, ita pondus F ad aliud pondus, quod ſit G. </
s
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<
s
id
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id.2.1.57.3.1.1.0.c
">Dico pri
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múm pondera GF ex puncto C ſuſpenſa tantùm ponderare, quan
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tùm pondera EF ex punctis DC. </
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<
s
id
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id.2.1.57.3.1.1.0.d
">Secetur DC bifariam in H, &
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lb
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ex H appendantur vtraq; pondera EF. </
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<
s
id
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">ponderabunt EF ſimul
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ſumpta in eo ſitu, quantùm ponderant in DC. ponatur BA
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arrow.to.target
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note108
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æqualis AH, ſeceturq; BA in K, ita vt ſit KA æqualis AD:
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deinde ex puncto B appendatur pondus L duplum ponderis F,
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lb
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hoc eſt æquale duobus ponderibus EF, quod quidem æqueponde
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rabit ponderibus EF in H appenſis, hoc eſt appenſis in DC. </
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>
<
s
id
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id.2.1.57.3.1.1.0.e
">
<
expan
abbr
="
Quoniã
">Quoniam</
expan
>
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lb
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igitur, vt CA ad AD, ita eſt pondus F ad pondus G; erit compo
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lb
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nendo vt CA AD ad AD, hoc eſt vt Ck ad AD, ita ponde
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ra
<
arrow.to.target
n
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note109
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FG ad pondus G. </
s
>
<
s
id
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">ſed cùm ſit, vt CA ad AD, ita F pon
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dus ad pondus G; erit conuertendo, vt DA ad AC, ita pondus
<
arrow.to.target
n
="
note110
"/>
<
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G ad pondus F; & conſequentium dupla, vt DA ad duplam ipſius
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AC, ita pondus G ad duplum ponderis F, hoc eſt ad pondus
<
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L. </
s
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<
s
id
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">Quare vt Ck ad DA, ita pondera EF ad pondus G; & vt </
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</
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