Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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<
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202
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lo CF, retineatur pondus B ne ſcilicet deorſum cadat; </
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<
s
id
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N1CF83
">tùm ſubtrahatur
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pondus trianguli CAD; nunquid fortè altera manus ſuſtinebit tantùm
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ſubduplum ponderis B? & altera ſubduplum? </
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<
s
id
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N1CF8B
">igitur vt habeatur quod
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ſuſtinet ſuppoſita dextra v.g. debet ſubſtrahi, quod ſuſtinet ſiniſtra, ſed
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quod ſuſtinet ſiniſtra, eſt vt ipſa potentia, id eſt vt CA ad CD; igitur
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tota CD repræſentat totum pondus, ſegmentum CF partem ponderis
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quæ competit potentiæ E, FD verò partem quæ ſuſtinetur à pla
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no CF. </
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>
</
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<
p
id
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type
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<
s
id
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N1CF9E
">Hinc facilè poſſet determinari quota pars ponderis incubet plano,
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ſit enim planum inclinatum AC, perpendiculum AB, accipiatur AB
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æqualis AB, ſitque AC tripla AB, duæ tertiæ ponderis incubant plano
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ſi verò ſit horizontale planum, totum pondus grauitat in illud; </
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>
<
s
id
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N1CFA8
">nulla eſt
<
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enim perpendicularis, ſi ſit perpendiculare planum, nihil prorſus gra
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lb
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uitat; </
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>
<
s
id
="
N1CFB0
">quia nulla eſt inclinata, & quò propiùs accedit planum inclina
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tum ad horizontalem plùs grauitat pondus in illud, minùs verò; quò
<
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propiùs accedit ad perpendicularem. </
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>
</
p
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<
p
id
="
N1CFB8
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type
="
main
">
<
s
id
="
N1CFBA
">Hinc eſſet oppoſita ratio grauitationis, & motus, in plano inclinato; </
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>
<
s
id
="
N1CFBE
">
<
lb
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nam quò plùs eſt grauitationis minùs eſt motus, quò plùs motus, minùs
<
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grauitationis; </
s
>
<
s
id
="
N1CFC5
">quando verò planum inclinatum eſt duplum perpendicu
<
lb
/>
culi vt planum CFD, tunc
<
expan
abbr
="
tantũdem
">tantundem</
expan
>
detrahitur de grauitatione in
<
lb
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planum quantùm de motu in eodem plano; </
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>
<
s
id
="
N1CFD1
">ideſt vtrique ſubduplum,
<
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ſi verò vt in plano ADC perpendiculum eſt ſubtriplum plani, detrahun
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tur de motu 2/3 & de grauitatione 1/3, idem dico de aliis, quæ certè omnia
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ex veris principiis phyſicis conſequi videntur, quò enim plus grauitat
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mobile in planum, plùs ſuſtinetur; </
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>
<
s
id
="
N1CFDD
">quò plùs ſuſtinetur, plùs impeditur il
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lius motus; </
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>
<
s
id
="
N1CFE3
">ſed hoc repugnat communi Mechanicorum ſententiæ, qui
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cenſent grauitationem in planum inclinatum eſſe ad grauitationem in
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horizontale, vt Tangens eſt ad ſecantem, quæ ſit linea plani inclinati,
<
lb
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v.g. vt AB ad CD, quod certè omnes ſupponunt, ſed minimè
<
expan
abbr
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demon-ſtrãt
">demon
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ſtrant</
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, ſi quid video ſaltem phyſicè; </
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<
s
id
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N1CFF5
">nec enim illud nemonſtrant propriè ex
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eo quòd pondus in extremitate libræ affixum habeat diuerſa momenta
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iuxta rationem Tangentium ad ſecantes, v.g. in ſecunda figura Th.5.
<
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pondus in D eſt ad pondus in C vt BA ad DA, quod veriſſimum eſt, &
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ſuprà demonſtrauimus; </
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>
<
s
id
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N1D003
">quippe hoc pertinet ad rationem momenti, non
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verò grauitationis in planum; </
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<
s
id
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">adde quod affixum eſt pondus vecti; </
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<
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id
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">igi
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tur vectis ſuſtinet totum illius pondus; </
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>
<
s
id
="
N1D013
">vtrùm verò ſi pondus in plano
<
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inclinato veluti in vecte moueatur pondus quo grauitat in planum ſit
<
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ad pondus quo grauitat in horizontali vt Tangens ad ſecantem, certè
<
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non demonſtrant; </
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>
<
s
id
="
N1D01D
">attamen ita res prorſus ſe habet; quare fit. </
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Theorema
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16.
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Grauitatio ponderis in planum inclinatum eſt ad grauitationem eiuſdem
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in planum horizontale, vt Tangens, vel horizontalis ad ſecantem, vel incli
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natam,
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quod demonſtro. </
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<
s
id
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">Primò ſit planum inclinatum GD, pondus in-</
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