DelMonte, Guidubaldo
,
In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata
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archimedes
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<
chap
id
="
N10019
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<
pb
xlink:href
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077/01/092.jpg
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pagenum
="
88
"/>
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N131E6
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type
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6.& 7
<
emph
type
="
italics
"/>
poſt
<
lb
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huius.
<
emph.end
type
="
italics
"/>
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</
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<
p
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N131F3
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type
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head
">
<
s
id
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N131F5
">SCHOLIVM.</
s
>
</
p
>
<
p
id
="
N131F7
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type
="
main
">
<
s
id
="
N131F9
">In hac propoſitione ſupponit Archimedes dari poſſe pun
<
lb
/>
cta in triangulis ſimilib^{9} ſimiliter poſita, qd
<
expan
abbr
="
quidẽ
">quidem</
expan
>
ſieri poſſe
<
lb
/>
oſtendimus in ſcholijs ſeptimi poſtulati. </
s
>
<
s
id
="
N13203
">Præterea idem vide
<
lb
/>
tur Archimedes in triangulis demonſtrare, quod in ſexto po
<
lb
/>
ſtulato vniuerſaliter in figuris ſuppoſuit. </
s
>
<
s
id
="
N13209
">Nam ſi centra gra
<
lb
/>
uitatis ſupponuntur in ſimilibus figuris eſſe ſimiliter poſita;
<
lb
/>
& in ſimilibus triangulis quo〈que〉 erunt ſimiliter poſita. </
s
>
<
s
id
="
N1320F
">In
<
lb
/>
ter hęc tamen maxima eſt differentia, nam in poſtulato inquit,
<
lb
/>
centra grauitatum in ſimilibus figuris eſſe ſimiliter poſita; cu
<
lb
/>
ius quidem conuerſum, nempè puncta in ſimilibus figuris ſi
<
lb
/>
militer poſita eſſe ipſarum centra grauitatis, eſt falium. </
s
>
<
s
id
="
N13219
">quod
<
lb
/>
eſt quidem manifeſtum abſ〈que〉 alio exemplo. </
s
>
<
s
id
="
N1321D
">ac propterea
<
lb
/>
Archimedes hoc in loco inquit, ſi duo erunt punſta in ſimi
<
lb
/>
libus triangulis ſimiliter poſita, & alterum ipſorum fuerit
<
expan
abbr
="
cẽ-trum
">cen
<
lb
/>
trum</
expan
>
grauitatis. </
s
>
<
s
id
="
N13229
">& alterum quo〈que〉
<
expan
abbr
="
cẽtrum
">centrum</
expan
>
grauitatis exiſtet.
<
lb
/>
Vnde propoſitio hęc potiùs eſt conuerſa poſtulati, quàm
<
lb
/>
eadem. </
s
>
</
p
>
<
p
id
="
N13233
"
type
="
main
">
<
s
id
="
N13235
">Ob demonſtrationem autem nouiſſe oportet, quòd ſi pun
<
lb
/>
ctum G fuerit in linea DN, tuncanguli EDG EDN eſſent in
<
lb
/>
terſe ęquales, ac propterea demonſtratio nihil abſurdi conclu
<
lb
/>
deret. </
s
>
<
s
id
="
N1323D
">In hoc autem caſu oſtendendum eſſet, angulum EFG
<
lb
/>
ipſi EFN ęqualem eſſe, vel FEG ipſi FEN. quæ quidem eo
<
lb
/>
dem prorſus modo oſtendentur. </
s
>
<
s
id
="
N13243
">comparando nempè angu
<
lb
/>
los EFG EFN angulo BCH; angulos verò FEG FEN ipſi
<
lb
/>
CBH. Quòd ſi G fuerit in alio ſitu, vt in triangulo EDN,
<
lb
/>
tuncanguli FDG FDN oſtendentur ęquales. </
s
>
<
s
id
="
N1324B
">& ita in alijs
<
lb
/>
caſibus, vbicun〈que〉 ſcilicet fuerit punctum G, ſemper ali
<
lb
/>
quod inuenietur huiuſmodi abſurdum. </
s
>
<
s
id
="
N13251
">quæ quidem omni
<
lb
/>
nò fieri non poſſunt. </
s
>
</
p
>
</
chap
>
</
body
>
</
text
>
</
archimedes
>