Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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<
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id
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N1C940
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<
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pagenum
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232
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xlink:href
="
026/01/264.jpg
"/>
<
p
id
="
N1EBDE
"
type
="
main
">
<
s
id
="
N1EBE0
">Obſeruaſti iam vt puto motum per Arcum TBE eſſe inuerſum vul
<
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garis funependuli; </
s
>
<
s
id
="
N1EBE6
">quippe in illo motuum incrementa initio ſunt mino
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lb
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ra, & ſemper creſcunt; at verò in hoc initio ſunt maiora, & ſemper de
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creſcunt. </
s
>
</
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<
p
id
="
N1EBEE
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type
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<
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N1EBF0
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<
emph
type
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center
"/>
<
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type
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italics
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Theorema
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100.
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</
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</
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<
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<
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type
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Poſſunt determinari vires, quæ ſuſtinere poſſunt datum pondus collocatum̨
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emph.end
type
="
italics
"/>
<
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<
emph
type
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italics
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in arcu erecto ATE
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type
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italics
"/>
: </
s
>
<
s
id
="
N1EC0D
">quippe ad ſuſtinendum pondus in T nullæ vires
<
lb
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requiruntur, ad ſuſtinendum in E æqualis potentia ponderi requiritur; </
s
>
<
s
id
="
N1EC13
">
<
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at verò potentia, quæ ſuſtinet in 5. ſe habet ad æqualem vt A 7.ad AE,
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in 4.vt A Z.ad AE, in B vt A
<
foreign
lang
="
grc
">δ</
foreign
>
ad AE, in D vt AH ad AE, in X vt AF ad
<
lb
/>
AE; </
s
>
<
s
id
="
N1EC20
">denique in E vt AE ad AE; ratio eſt, quia potentia debet eſſe pro
<
lb
/>
portionata momento ponderis, ſeu motus, ſed motus in B.v.g.per BE eſt
<
lb
/>
ad motum qui fit per perpendicularem vt A
<
foreign
lang
="
grc
">δ</
foreign
>
ad AB vel AE, igitur po
<
lb
/>
tentia quæ impedit hunc motum, id eſt quæ ſuſtinet pondus in B eſt ad
<
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illam quæ ſuſtinet in E vt A
<
foreign
lang
="
grc
">δ</
foreign
>
ad AE. </
s
>
</
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>
<
p
id
="
N1EC35
"
type
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">
<
s
id
="
N1EC37
">Debet autem ſuſtineri pondus vel per Tangentem ductam ad punctum
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lb
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B vel ipſi parallelam in certo dumtaxat funiculo, vt fit in trochleis; vnde
<
lb
/>
ſi ſemicirculus A 2.E ſit trochlea, & pondus pendeat ex E,
<
expan
abbr
="
adhibeaturq;
">adhibeaturque</
expan
>
<
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potentia trahens in A, debet eſſe æqualis ponderi, ſed de trochleis fusè
<
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lib. 11. </
s
>
</
p
>
<
p
id
="
N1EC47
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type
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">
<
s
id
="
N1EC49
">Hinc etiam facilè determinari poteſt quomodo deſtruatur impetus,
<
lb
/>
ſi proiiciatur globus per arcum EBT ſurſum; </
s
>
<
s
id
="
N1EC4F
">nam in eadem proportione
<
lb
/>
deſtruetur in aſcendendo, qua acceleratur deſcendendo; </
s
>
<
s
id
="
N1EC55
">neque eſt hîc
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lb
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ſingularis difficultas; </
s
>
<
s
id
="
N1EC5B
">quemadmodum enim in deſcenſu ſemper accele
<
lb
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ratur per incrementa inæqualia iuxta rationem explicatam; </
s
>
<
s
id
="
N1EC61
">ita in aſcen
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ſu ſemper retardatur per detractiones inæquales; </
s
>
<
s
id
="
N1EC67
">in deſcenſu quidem per
<
lb
/>
incrementa initio minora, & maiora ſub finem; in aſcenſu è contrario
<
lb
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per detractiones initio maiores ſub finem minores. </
s
>
</
p
>
<
p
id
="
N1EC6F
"
type
="
main
">
<
s
id
="
N1EC71
">Hinc denique determinari poteſt quantùm corpus grauitet in toto
<
lb
/>
arcu TBE; </
s
>
<
s
id
="
N1EC77
">in E nihil grauitat, in T totum grauitat; igitur grauitatio in
<
lb
/>
T, ſeu tota eſt ad grauitationem in E, vt TA ad nihil, in 5. verò vt AT
<
lb
/>
ad AT, in 4. vt AT ad AA, in B vt AT ad AS, atque ita deinceps, quæ
<
lb
/>
conſtant ex dictis. </
s
>
</
p
>
<
p
id
="
N1EC81
"
type
="
main
">
<
s
id
="
N1EC83
">Inſuper obſerua corpus graue incumbens arcui TBE, per varias lineas
<
lb
/>
poſſe pelli, vel trahi, de quibus idem prorſus dicendum eſt, quod dictum
<
lb
/>
eſt in Th.5. & Sch.Th.16. </
s
>
</
p
>
<
p
id
="
N1EC8A
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type
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main
">
<
s
id
="
N1EC8C
">Adde quod omiſimus, ſed facilè ex dictis lib. 1. intelligi poteſt, im
<
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petum qui producitur in acceleratione motus per planum inclinatum
<
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eſſe imperfectiorem ex duplici capite; primò ratione minoris temporis,
<
lb
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quo producitur ex ratione maioris vel minoris inclinationis, ſeu longi
<
lb
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tudinis. </
s
>
<
s
id
="
N1EC98
">v.g. ſit planum inclinatum AC; </
s
>
<
s
id
="
N1EC9E
">certè cum poſt motum per A
<
lb
/>
E, & per AB ſit æqualis ictus vel impetus; </
s
>
<
s
id
="
N1ECA4
">& cùm tempus quo deſcendit
<
lb
/>
per AE ſit duplum temporis, quo deſcendit per AB; </
s
>
<
s
id
="
N1ECAA
">certè ſingulis inſtan
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lb
/>
tibus, quibus durat motus per AC, producitur impetus ſubduplus tan-</
s
>
</
p
>
</
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