DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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<
archimedes
>
<
text
>
<
body
>
<
chap
id
="
N10019
">
<
p
id
="
N1196C
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type
="
main
">
<
s
id
="
N11A1D
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<
pb
xlink:href
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077/01/050.jpg
"
pagenum
="
46
"/>
tes ex determinatis diſtantijs determinatas quo〈que〉 habeant
<
lb
/>
grauitates; ſi ex dato puncto æ〈que〉ponderare debent. </
s
>
<
s
id
="
N11A25
">Quòd
<
lb
/>
ſi in hoc caſu datum fuerit punctum C, ex quo pondera AB
<
lb
/>
ex æqualibus diſtantijs CA CB ę〈que〉ponderare debeant: o
<
lb
/>
porteret, vt pondera AB (ex demonſtratis) ſemper eſſent æ
<
lb
/>
qualia.
<
expan
abbr
="
Quoniã
">Quoniam</
expan
>
<
expan
abbr
="
autẽ
">autem</
expan
>
<
expan
abbr
="
quomodocũ〈que〉
">quomodocun〈que〉</
expan
>
ſint pondera, hoc eſt; ſi
<
lb
/>
ue pondus A maius, ſiue minus fuerit, quàm B, manent, ſi
<
lb
/>
igitur dixerimus, ergo pondus A ponderi B ę〈que〉ponderat;
<
lb
/>
eſſet omnino inconueniens. </
s
>
<
s
id
="
N11A41
">cùm ex ijsdem diſtantijs
<
expan
abbr
="
eidẽ
">eidem</
expan
>
<
expan
abbr
="
põ
">pom</
expan
>
<
lb
/>
deri pondus quandoquè maius, quandoquè minus ę〈que〉pon
<
lb
/>
derare non poſſit; vt in hoc caſu accidere poteſt. </
s
>
<
s
id
="
N11A4F
">Quocirca
<
lb
/>
nec propriè dici poſſunt pondera, ſiue in libra AB, ſiue ex
<
lb
/>
diſtantijs CA CB conſtituta eſſe. </
s
>
<
s
id
="
N11A55
">Vndè ne〈que〉 Archimedis
<
lb
/>
propoſitiones in hoc caſu ſunt intelligendę quandoquidem
<
lb
/>
in his propriè quærit ponderum, magnitudinumquè æ〈que〉
<
lb
/>
ponderationes. </
s
>
<
s
id
="
N11A5D
">ne〈que〉 enim in hac quarta demonſtratione in
<
lb
/>
hoc caſu potuiſſet Archimedes abſurdum oſtendere, ſi C
<
expan
abbr
="
nõ
">non</
expan
>
<
lb
/>
eſt grauitatis centrum magnitudinis ex AB compoſitæ, ſit
<
lb
/>
E. facta igitur ex E ſuſpenſione, magnitudines æquales AB
<
lb
/>
ex in æqualibus diſtantijs EA EB ę〈que〉ponderabunt. </
s
>
<
s
id
="
N11A6B
">quod
<
lb
/>
fieri non poteſt. </
s
>
<
s
id
="
N11A6F
">non enim hoc eſt abſurdum; cùm pondera
<
lb
/>
ex E ſuſpenſa
<
expan
abbr
="
maneãt
">maneant</
expan
>
idcirco quando linea AB eſt
<
expan
abbr
="
horizõ
">horizom</
expan
>
<
lb
/>
ti erecta; propriè ad rem noſtram minimè pertinet. </
s
>
<
s
id
="
N11A7D
">Ex dictis
<
lb
/>
igitur ſemper valet conſe〈que〉ntia, hoc punctum horum pon
<
lb
/>
derum centrum eſt grauitatis, ergo ſi ex hoc ſuſpendantur,
<
expan
abbr
="
põ
">pom</
expan
>
<
lb
/>
dera ę〈que〉ponderant. </
s
>
<
s
id
="
N11A89
">non autem è conuerſo. </
s
>
<
s
id
="
N11A8B
">niſi quando ar
<
lb
/>
gumentatio ſumitur ſemper ex recta linea, quæ centra graui
<
lb
/>
tatis magnitudinum coniungit, & quando hęc linea non eſt
<
lb
/>
<
arrow.to.target
n
="
fig22
"/>
<
lb
/>
horizonti erecta. </
s
>
<
s
id
="
N11A98
">hac enim
<
lb
/>
ratione quocun〈que〉 modo
<
lb
/>
recta linea ſe habeat, ſem
<
lb
/>
per ſequitur idem. </
s
>
<
s
id
="
N11AA0
">Vt ſi li
<
lb
/>
nea AB fuerit, ſiue
<
expan
abbr
="
nõ
">non</
expan
>
fue
<
lb
/>
rit horizonti æquidiſtans,
<
lb
/>
ipſius medium C centrum
<
lb
/>
erit grauitatis magnitudi
<
lb
/>
nis ex magnitudinibus AB æqualibus compoſitę. </
s
>
<
s
id
="
N11AB0
">vnde ſequi</
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>