Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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<
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id
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s.000644
">SIT fruſtum pyramidis ae, cuius maior baſis triangu
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lb
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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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abbr
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triã
">trian</
expan
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gula abc, def. </
s
>
<
s
id
="
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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lb
/>
ſtans be,
<
expan
abbr
="
ſecansq;
">ſecansque</
expan
>
ad in h: deinde per h ducatur planum
<
lb
/>
baſibus æquidiſtans, cuius ſectio ſit triangulum hkl. </
s
>
<
s
id
="
s.000646
">Dico
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lb
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triangulum hKl proportionale eſſe inter triangula abc,
<
lb
/>
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figure
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id.023.01.069.1.jpg
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xlink:href
="
023/01/069/1.jpg
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number
="
61
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lb
/>
def, hoc eſt triangulum abc ad
<
lb
/>
triangulum hKl eandem habere
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lb
/>
proportionem, quam
<
expan
abbr
="
triãgulum
">triangulum</
expan
>
<
lb
/>
hKl ad ipſum def. </
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>
<
s
id
="
s.000647
">
<
expan
abbr
="
Quoniã
">Quoniam</
expan
>
enim
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lb
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arrow.to.target
n
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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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/>
<
arrow.to.target
n
="
marg77
"/>
<
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linea hk ipſi gb eſt æqualis: & pro
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lb
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pterea proportionalis inter ab,
<
lb
/>
de. </
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>
<
s
id
="
s.000648
">quare ut ab ad hK, ita eſt hk
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lb
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ad de. </
s
>
<
s
id
="
s.000649
">fiat ut hk ad de, ita de
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lb
/>
ad aliam lineam, in qua ſit m. </
s
>
<
s
id
="
s.000650
">erit
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lb
/>
ex æquali ut ab ad de, ita hk ad
<
lb
/>
<
arrow.to.target
n
="
marg78
"/>
<
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/>
m. </
s
>
<
s
id
="
s.000651
">Et quoniam triangula abc,
<
lb
/>
hKl, def ſimilia ſunt;
<
expan
abbr
="
triangulũ
">triangulum</
expan
>
<
lb
/>
<
arrow.to.target
n
="
marg79
"/>
<
lb
/>
abc ad triangulum hkl eſt, ut li
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lb
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nea ab ad lineam de:
<
expan
abbr
="
triangulũ
">triangulum</
expan
>
<
lb
/>
<
arrow.to.target
n
="
marg80
"/>
<
lb
/>
autem hkl ad ipſum def eſt, ut hk ad m. </
s
>
<
s
id
="
s.000652
">ergo triangulum
<
lb
/>
abc ad triangulum hkl eandem proportionem habet,
<
lb
/>
quam triangulum hKl ad ipſum def. </
s
>
<
s
id
="
s.000653
">Eodem modo in a
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liis fruſtis pyramidis idem demonſtrabitur.</
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>
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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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s.000659
">Sit fruſtum coni, uel coni portionis ad: & ſecetur plano
<
lb
/>
per axem, cuius ſectio ſit abcd, ita ut maior ipſius baſis ſit
<
lb
/>
circulus, uel ellipſis circa diametrum ab; minor circa cd. </
s
>
<
lb
/>
<
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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>
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