Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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326
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026/01/360.jpg
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detrahetur HK quadruplum MN; </
s
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<
s
id
="
N24562
">nam ſicut idem impetus concurrens
<
lb
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duobus temporibus addit quadruplum ſpatium propter motum accele
<
lb
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ratum; </
s
>
<
s
id
="
N2456A
">ita ſi non concurrat duobus temporibus, deerit ſpatium qua
<
lb
/>
druplum illius quod deeſſet, ſi tantùm vno tempore non concurreret; </
s
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<
s
id
="
N24570
">
<
lb
/>
igitur aſcenſus maioris funependuli erit OH; </
s
>
<
s
id
="
N24575
">igitur OH, ON erunt vi
<
lb
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brationes ſimiles; </
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>
<
s
id
="
N2457B
">igitur ſi deſcendat AG ex H, & AO ex N, vibrationes
<
lb
/>
aſcenſus ſecundi erunt adhuc ſimiles propter
<
expan
abbr
="
cãdem
">eandem</
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rationem; </
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<
s
id
="
N24585
">igitur
<
lb
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& vibrationes tertij aſcenſus, quarti, quinti, atque ita deinceps; </
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>
<
s
id
="
N2458B
">igitur tot
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lb
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erunt vibrationes maioris, quot minoris per ſe, ſi prima vtriuſque vi
<
lb
/>
bratio ſit ſimilis: dixi per ſe; nam per accidens ratione funis ferè ſemper
<
lb
/>
accidit mutari iſtum ordinem vibrationum. </
s
>
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<
p
id
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N24595
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type
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<
s
id
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N24597
">Præterea, cùm impetus, quo pendulum maius aſcendit per GK,
<
lb
/>
ſit duplus illius, quo minus aſcendit per OM, cùm in ſingulis punctis
<
lb
/>
aſcenſus OM, & ſingulis aſcenſus GK deſtruatur impetus; </
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>
<
s
id
="
N2459F
">cum GK ſit
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lb
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quadruplum OM; </
s
>
<
s
id
="
N245A5
">certè in ſingulis punctis GK impetus deſtruitur ſub
<
lb
/>
duplus illius, qui in ſingulis punctis OM deſtruitur; ſi enim æqualis; </
s
>
<
s
id
="
N245AB
">igi
<
lb
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tur impetus per GK eſſet quadruplus impetus per OM; </
s
>
<
s
id
="
N245B1
">ſi minor ſubdu
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lb
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plo v. g. ſubquadruplus; </
s
>
<
s
id
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N245BB
">igitur impetus per GK eſſet æqualis impetui
<
lb
/>
per OM; </
s
>
<
s
id
="
N245C1
">ſed eſt tantum duplus; </
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>
<
s
id
="
N245C5
">igitur ſubduplus deſtruitur in ſingulis
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lb
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punctis, igitur in æquali punctorum GK numero, ſubduplus tantùm im
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petus deſtrueretur; </
s
>
<
s
id
="
N245CD
">in duplo punctorum numero, æqualis, in quadruplo
<
lb
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punctorum numero, duplus; </
s
>
<
s
id
="
N245D3
">deſtruitur autem in ſingulis punctis GK
<
lb
/>
ſubduplus; quia ſubduplum tantùm tempus reſpondet ſingulis punctis G
<
lb
/>
K illius temporis, quod reſpondet ſingulis punctis OM. </
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Corollarium
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1.
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<
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">Primò colligo, ſolutionem primi dubij propoſiti ſuprà, ita vt non iam
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dubium, at certum omninò ſuperſit. </
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Corollarium
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2.
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</
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<
s
id
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N24602
">Secundò colligo, ſolutionem ſecundi dubij, ſi enim funependulum P
<
lb
/>
G demittatur ex PR & AG ex AT; </
s
>
<
s
id
="
N24608
">haud dubiè plures erunt vibrationes
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lb
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penduli PG, quàm AG; </
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>
<
s
id
="
N2460E
">quia tot eſſent AG, quot PG, ſi AG demittere
<
lb
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tur ex AD; </
s
>
<
s
id
="
N24614
">ſed plures ſunt vibrationes funependuli AG demiſſi ex AD,
<
lb
/>
quàm eiuſdem ex AT; </
s
>
<
s
id
="
N2461A
">ergo plures funependuli PG demiſſi ex PR,
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quàm AG demiſſi ex AT; vnde ſoluitur prima pars dubij ſecundi, </
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Corollarium
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3.
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</
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<
s
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">Tertiò colligo, ſolutionem ſecundæ partis eiuſdem dubij; </
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<
s
id
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N24635
">ſi enim A
<
lb
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O demittatur ex AB, & AG ex AS; </
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>
<
s
id
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N2463B
">ita arcus GS ſit æqualis arcui OB; </
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>
<
s
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N2463F
">
<
lb
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certè erunt plures vibrationes AO, quàm AG, vt patet ex dictis; quod
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ſpectat ad tertium dubium, illud ipſum ſoluemus paulò pòſt. </
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Corollarium.
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4.
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</
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<
s
id
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">Quartò ſi demittatur funependulum AG ex AV, vt deſcendat in A
<
lb
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G, ſitque clauus horizonti parallelus in P, non aſcendet ſegmentum PG
<
lb
/>
in PR, vt vult Galileus; </
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>
<
s
id
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">quia AV non aſcenderet in AT, quod ipſe ſup-</
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