Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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<
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s.000644
">SIT fruſtum pyramidis ae, cuius maior baſis triangu
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lum abc, minor def: & oporteat ipſum plano, quod baſi
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æquidiſtet, ita ſecare, ut ſectio ſit proportionalis inter
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triã
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gula abc, def. </
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<
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id
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s.000645
">Inueniatur inter lineas ab, de media pro
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portionalis, quæ ſit bg: & à puncto g erigatur gh æquidi
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ſtans be,
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abbr
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ſecansq;
">ſecansque</
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>
ad in h: deinde per h ducatur planum
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baſibus æquidiſtans, cuius ſectio ſit triangulum hkl. </
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<
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id
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s.000646
">Dico
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triangulum hKl proportionale eſſe inter triangula abc,
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id.023.01.069.1.jpg
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def, hoc eſt triangulum abc ad
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triangulum hKl eandem habere
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proportionem, quam
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expan
abbr
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triãgulum
">triangulum</
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>
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hKl ad ipſum def. </
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<
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Quoniã
">Quoniam</
expan
>
enim
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marg76
"/>
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lineæ ab, hK æquidiſtantium pla
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norum ſectiones inter ſe æquidi
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ſtant: atque æquidiſtant bk, gh:
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n
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marg77
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linea hk ipſi gb eſt æqualis: & pro
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pterea proportionalis inter ab,
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de. </
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>
<
s
id
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s.000648
">quare ut ab ad hK, ita eſt hk
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ad de. </
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>
<
s
id
="
s.000649
">fiat ut hk ad de, ita de
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ad aliam lineam, in qua ſit m. </
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>
<
s
id
="
s.000650
">erit
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ex æquali ut ab ad de, ita hk ad
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/>
<
arrow.to.target
n
="
marg78
"/>
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m. </
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>
<
s
id
="
s.000651
">Et quoniam triangula abc,
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hKl, def ſimilia ſunt;
<
expan
abbr
="
triangulũ
">triangulum</
expan
>
<
lb
/>
<
arrow.to.target
n
="
marg79
"/>
<
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/>
abc ad triangulum hkl eſt, ut li
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nea ab ad lineam de:
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expan
abbr
="
triangulũ
">triangulum</
expan
>
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/>
<
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n
="
marg80
"/>
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autem hkl ad ipſum def eſt, ut hk ad m. </
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>
<
s
id
="
s.000652
">ergo triangulum
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abc ad triangulum hkl eandem proportionem habet,
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/>
quam triangulum hKl ad ipſum def. </
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>
<
s
id
="
s.000653
">Eodem modo in a
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liis fruſtis pyramidis idem demonſtrabitur.</
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16. unde
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cimi</
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34. primi</
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9. huius
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corol.</
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20. ſexti</
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11. quinti</
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<
s
id
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">Sit fruſtum coni, uel coni portionis ad: & ſecetur plano
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per axem, cuius ſectio ſit abcd, ita ut maior ipſius baſis ſit
<
lb
/>
circulus, uel ellipſis circa diametrum ab; minor circa cd. </
s
>
<
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/>
<
s
id
="
s.000660
">Rurſus inter lineas ab, cd inueniatur proportionalis be:
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& ab e ducta ef æquidiſtante bd, quæ lineam ca in f ſecet, </
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