Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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Corollarium.
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<
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">Hinc manifeſta ratio, cur funependulum poſt vibrationem deſcenſus
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non perueniat in aſcenſu ad tantam altitudinem; </
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<
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id
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">nec eſt quod aliqui di
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cant aëra interceptum efficere, ne ad æqualem altitudinem aſcendat,
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cùm aër non minùs reſiſtat deſcenſui, quàm aſcenſui; quod quomodo
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fiat, iam alibi explicuimus. </
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Theorema
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20.
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Maioris vibrationis aſcenſus imminuitur in maiori proportione, quàm mi
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noris
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; </
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<
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id
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">certa experientia, cuius ratio eſt, quia in arcu ſuperiore plùs im
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petus deſtruitur, in inferiore minùs; </
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<
s
id
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N23FFD
">igitur plùs ſpatij detrahitur maiori
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vibrationi, quàm minori, ſcilicet in aſcenſu; </
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<
s
id
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N24003
">hæc ratio demonſtratiua eſt,
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quia quò minùs impetus deſtruitur ſingulis inſtantibus, plùs ſpatij ac
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quiritur, vt conſtat ex planis inclinatis; </
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>
<
s
id
="
N2400B
">ſit enim in eadem figura pla
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num inclinatum DO, & verticale DA; </
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<
s
id
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N24011
">imprimatur impetus mobili ex D,
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certè cum eodem impetu aſcendet per DA & per DO, vt demonſtraui
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mus cum de planis inclinatis; </
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>
<
s
id
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N24019
">igitur ſingulis inſtantibus minùs impetus
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in DO deſtruitur, quàm in DA; </
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>
<
s
id
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N2401F
">vnde maius ſpatium conficitur; </
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<
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id
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N24023
">eſt enim
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DO maior DA: </
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<
s
id
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N24029
">ita prorſus accidit in arcu aſcenſus funependuli; </
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<
s
id
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N2402D
">ſit enim
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arcus aſcenſus DH æqualis arcui deſcenſus oppoſiti; </
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>
<
s
id
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N24033
">certè tantillùm im
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petus deſtruetur; </
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>
<
s
id
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N24039
">igitur arcus aſcenſus ferè accedet ad A; </
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>
<
s
id
="
N2403D
">ſi vetò arcus
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deſcenſus ſit æqualis DL, plùs impetus deſtruetur in aſcenſu; igitur ar
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cus aſcenſus habebit minorem proportionem ad DL, quàm prior ad DH,
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& hæc eſt veriſſima ratio luculentiſſimi experimenti, quod ferè omnibus
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notum eſt. </
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Theorema
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21.
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Si proijciatur mobile per ipſum perpendiculum DA cum eo impetu, quo
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ex D feratur in A motu naturaliter retardato; </
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<
s
id
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N24061
">certè cum eodem impetu fere
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tur in O per DO, & per arcum DLO:
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probatur quia ex A in D, vel ex O
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in D ſiue per chordam OD, ſiue per arcum OHD æqualis impetus ac
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quiritur per Lemma 11. ſed cum eodem impetu, quo ex A fertur in D.
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vel ex O in D motu naturaliter accelerato, ex D ferri poteſt in A vel in
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O: </
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>
<
s
id
="
N24072
">dixi cum eodem impetu, ita vt tot gradus impetus concurrant ad aſ
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cenſum, quot ad deſcenſum; </
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>
<
s
id
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N24078
">ſi enim aliquis gradus concurrens ad deſ
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cenſum, non concurreret ad aſcenſum; </
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<
s
id
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">haud dubiè non perueniret mo
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bile ad
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abbr
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eãdem
">eandem</
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altitudinem; quod autem æquale ſpatium reſpondeat
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aſcenſui, & deſcenſui ſuppoſito æquali impetu, iam demonſtratum eſt ſu
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prà l. 3. & 5. ſed iam examinandæ ſunt proportiones huius deſtructio
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nis impetus in maioribus, & minoribus vibrationibus. </
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<
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Theorema
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22.
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<
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Poteſt determinari in qua parte arcus deſinat motus ſurſum in aſcenſu
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vibrationis, ſi cognoſcatur ad quam altitudinem ferretur mobile per ipſum
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perpendiculum
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; </
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<
s
id
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">fit cum punctum infimum D, ſitque in pendule ille impe
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tus, haud dubiè per arcum ferretur in
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, ducatur
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">α</
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>
Q parallela AO; </
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<
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">haud </
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