Commandino, Federico
,
Liber de centro gravitatis solidorum
,
1565
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<
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id
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s.000199
">Itaque quoniam duæ lineæ Kl, lm ſe ſe tangentes, duabus
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lineis ſe ſe tangentibus ab, bc æquidiſtant; nec ſunt in e o
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dem plano: angulus klm æqualis eſt angulo abc: & ita an
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gulus lmk, angulo bca, & mkl ipſi cab æqualis probabi
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tur. </
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<
s
id
="
s.000200
">triangulum ergo klm eſt æquale, & ſimile triangulo
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lb
/>
abc. quare & triangulo def. </
s
>
<
s
id
="
s.000201
">Ducatur linea cgo, & per ip
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lb
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ſam, & per cf ducatur planum ſecans priſma; cuius & paral
<
lb
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lelogrammi ae communis ſectio ſit opq.</
s
>
<
s
id
="
s.000202
"> tranſibit linea
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lb
/>
fq per h, & mp per n. </
s
>
<
s
id
="
s.000203
">nam cum plana æquidiſtantia ſecen
<
lb
/>
tur à plano cq, communes eorum ſectiones cgo, mp, fq
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lb
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ſibi ipſis æquidiſtabunt. </
s
>
<
s
id
="
s.000204
">Sed & æquidiſtant ab, kl, de. </
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>
<
s
id
="
s.000205
">an
<
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/>
<
arrow.to.target
n
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marg27
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guli ergo aoc, kpm, dqf inter ſe æquales ſunt: & ſunt
<
lb
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æquales qui ad puncta akd conſtituuntur. </
s
>
<
s
id
="
s.000206
">quare & reliqui
<
lb
/>
reliquis æquales; & triangula aco, Kmp, dfq inter ſe ſimi
<
lb
/>
<
arrow.to.target
n
="
marg28
"/>
<
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lia erunt. </
s
>
<
s
id
="
s.000207
">Vt igitur ca ad ao, ita fd ad dq: & permutando
<
lb
/>
ut ca ad fd, ita ao ad dq.</
s
>
<
s
id
="
s.000208
">eſt autem ca æqualis fd. </
s
>
<
s
id
="
s.000209
">ergo &
<
lb
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ao ipſi dq.</
s
>
<
s
id
="
s.000210
"> eadem quoque ratione & ao ipſi Kp æqualis
<
lb
/>
demonſtrabitur. </
s
>
<
s
id
="
s.000211
">Itaque ſi triangula, abc, def æqualia &
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/>
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figure
id
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xlink:href
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number
="
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<
lb
/>
ſimilia inter ſe
<
expan
abbr
="
aptẽtur
">aptentur</
expan
>
,
<
lb
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cadet linea fq in lineam
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lb
/>
<
arrow.to.target
n
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marg29
"/>
<
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cgo. </
s
>
<
s
id
="
s.000212
">Sed &
<
expan
abbr
="
centrũ
">centrum</
expan
>
gra
<
lb
/>
uitatis h in g
<
expan
abbr
="
centrũ
">centrum</
expan
>
ca
<
lb
/>
det. </
s
>
<
s
id
="
s.000213
">
<
expan
abbr
="
trãſibit
">tranſibit</
expan
>
igitur linea
<
lb
/>
fq per h: & planum per
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lb
/>
co & cf
<
expan
abbr
="
ductũ
">ductum</
expan
>
per
<
expan
abbr
="
axẽ
">axem</
expan
>
<
lb
/>
gh ducetur:
<
expan
abbr
="
idcircoq;
">idcircoque</
expan
>
li
<
lb
/>
neam mp
<
expan
abbr
="
etiã
">etiam</
expan
>
per n
<
expan
abbr
="
trã
">tran</
expan
>
<
lb
/>
ſire neceſſe erit. </
s
>
<
s
id
="
s.000214
">Quo
<
lb
/>
niam ergo fh, cg æqua
<
lb
/>
les ſunt, &
<
expan
abbr
="
æquidiſtãtes
">æquidiſtantes</
expan
>
:
<
lb
/>
<
expan
abbr
="
itemq;
">itemque</
expan
>
hq, go; rectæ li
<
lb
/>
neæ, quæ ipſas
<
expan
abbr
="
cõnectũt
">connectunt</
expan
>
<
lb
/>
cmf, gnh, opq æqua
<
lb
/>
les æquidiſtantes
<
expan
abbr
="
erũt
">erunt</
expan
>
.</
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>
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