Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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434
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026/01/468.jpg
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<
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Scholium.
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<
p
id
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type
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<
s
id
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N2A25E
">Obſeruabis non deeſſe fortè aliquos, quibus centrum grauitatis Py
<
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ramidos difficile inuentu videatur; </
s
>
<
s
id
="
N2A264
">quare in eorum gratiam facilem de
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monſtrationem ſubijcio; </
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<
s
id
="
N2A26A
">ſit enim pyramis EFBA, cuius baſis ſit trian
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gularis EFB; </
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>
<
s
id
="
N2A270
">ducatur EC diuidens bifariam FB, ſitque DC 1/3 totius
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lb
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EC, centrum grauitatis baſis EFB eſt D, per Sch.Th.2. ducatur AD, id
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lb
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eſt axis pyramidos, per communem definitionem; </
s
>
<
s
id
="
N2A278
">quippe axis eſt recta
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ducta à vertice ad centrum grauitatis baſis oppoſitæ; </
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>
<
s
id
="
N2A27E
">ducatur AC, diui
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dens BF bifariam æqualiter; </
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>
<
s
id
="
N2A284
">aſſumatur GC, 1/3 AC, ducatur EG, hæc
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eſt axis, vt patet ex dictis; </
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>
<
s
id
="
N2A28A
">aſſumatur autem triangulum AEC, ſitque HO
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lb
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K maioris claritatis gratia, ſintque gemini axes HL, OI, centrum py
<
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ramis eſt in OI & in HL; igitur in M; </
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>
<
s
id
="
N2A292
">ſed ML eſt 1/4 totius LH, quod
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ſic demonſtro; </
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>
<
s
id
="
N2A298
">triangula PIM, OLM ſunt æquiangula; </
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>
<
s
id
="
N2A29C
">igitur propor
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tionalia; </
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>
<
s
id
="
N2A2A2
">itemque duo HIN, & HKO; </
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>
<
s
id
="
N2A2A6
">igitur vt HK ad KO, ita HI ad
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IN; </
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>
<
s
id
="
N2A2AC
">ſed HI continet 2/4 HK, per hypotheſim; </
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>
<
s
id
="
N2A2B0
">igitur IN continet 2/3 KO; </
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>
<
s
id
="
N2A2B4
">
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lb
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igitur IN eſt æqualis LO; </
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<
s
id
="
N2A2B9
">igitur vt IP eſt ad LO, ita PM ad ML; ſed
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lb
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PI eſt ad LO vt 2. 2/3 ad 8. id eſt vt 3. ad 9. nam ſit OK 12. IN æqualis
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/>
LO eſt 8.igitur PM eſt ad ML, vt 3. ad 9. vel vt 1. ad 3. igitur ſit HL
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12. PL erit 4. igitur PM 1. ML 3. igitur ML eſt 1/4 LH, quod erat
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demonſtrandum. </
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>
</
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<
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id
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type
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">
<
s
id
="
N2A2C7
">Si verò pyramidos baſis ſit quadrilatera, vel polygona, diuidi poteſt in
<
lb
/>
plures, quarum baſis ſit trilatera; quare in omni pyramide facilè de
<
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monſtratur centrum grauitatis ita dirimere axem, vt ſegmentum verſus
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baſim ſit 1/4 totius. </
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>
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type
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Theorema
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type
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28.
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Determinari poteſt centrum percuſſionis coni mixti, cuius baſis ſit portio
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ſuperficiei ſphæræ, cuius centrum ſit in apice coni
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type
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; </
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<
s
id
="
N2A2EC
">quia vt ſe habet triangu
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lum Iſoſceles ad conum, ita ſe habet ſector ſub eodem angulo ad prædi
<
lb
/>
ctum conum mixtum, vt patet; </
s
>
<
s
id
="
N2A2F4
">quia vt conus ille rectus formatur a trian
<
lb
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gulo circa ſuum axem circumacto, ita & mixtus formatur à ſectore circa
<
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/>
ſuum axem circumuoluto; </
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>
<
s
id
="
N2A2FC
">igitur vt ſe habet diſtantia inter centrum vel
<
lb
/>
apicem trianguli, circa quem voluitur, & centrum percuſſionis eiuſdem
<
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/>
ad diſtantiam inter eoſdem terminos in cono recto, ita ſe habet diſtan
<
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tia inter eoſdem terminos in ſectore, ad diſtantiam inter eoſdem termi
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nos in prædicto cono mixto; </
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>
<
s
id
="
N2A308
">ſed cognoſcuntur ex dictis ſuprà tres pri
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mi termini huius proportionis; igitur cognoſci poteſt quartus, igitur
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/>
determinari centrum percuſſionis, quod erat demonſtrandum. </
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>
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id
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type
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Corollarium.
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</
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<
p
id
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N2A31E
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type
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<
s
id
="
N2A320
">Colligo primò, ex his facilè cognoſci poſſe centrum percuſſionis ſe
<
lb
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ctoris ſphæræ, nam vt ſe habet conus rectus ad pyramidem, ita ſe habes
<
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/>
prædictus conus mixtus ad ſectorem, ſub eodem ſcilicet angulo. </
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>
</
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<
p
id
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N2A327
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type
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<
s
id
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N2A329
">Colligo ſecundò, etiam poſſe cognoſci centrum percuſſionis eiuſdem
<
lb
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ſectoris circumacti, non tantùm circa centrum ſphæræ, ſed circa radium; </
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"/>
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