Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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Theorema
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33.
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Hinc ratio hypotheſeos primæ,
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cùm enim conſtet hic motus ex accelera
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to & retardato, eius linea eſt curua per Th.20. non tamen eſt Parabola,
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vt conſtat ex eodem Th.20. Vnde reiicies Galileum, qui vult lineam mo
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tus proiecti per horizontalem in aëre libero eſſe Parabolam. </
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Theorema
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34.
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In hoc motu retardatur in maiori proportione violentus quàm acceleretur
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natur alis
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; </
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<
s
id
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">probatur, non in minore, quia plùs impetus adderetur quàm de
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traheretur; igitur maior eſſet in fine motus quàm initio, igitur maior
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ictus contra hyp.;. </
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<
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">non in æquali, quia ſemper eſſet æqualis ictus con
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tra hyp.3.& contra Th.29. </
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Theorema
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35.
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Hinc plùs detrahitur impetus quàm addatur,
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type
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"/>
quia ſcilicet detrahitur
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pro rata, vt dicemus infrà; at verò cùm acceleretur tantùm naturalis
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iuxta rationem motus, & motus ſit iuxta rationem plani, minùs accele
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ratur quàm ſi caderet mobile perpendiculariter deorſum. </
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Theorema
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36.
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Hinc ratio clara cur ſit minor ictus in ſine huius motus
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type
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; </
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<
s
id
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">quia ſcilicet eſt
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minùs impetus, quia plùs detractum eſt quàm additum; </
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>
<
s
id
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N1AD35
">nec eſt quod
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tribuant hanc retardationem medio; </
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<
s
id
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">quippe aër non plùs reſiſtit motui
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violento quàm naturali; </
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<
s
id
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">ſed id quod detrahitur ab aëre corpori graui, v.
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g. pilæ plumbeæ eſt inſenſibile, vt fatentur omnes; igitur idem
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abbr
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dicen-dū
">dicen
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dum</
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eſt de motu violento & mixto, hinc hoc ipſum etiam fieret in vacuo. </
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Theorema
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37.
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"/>
Impetus naturalis concurrit ad hunc motum
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type
="
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"/>
; probatur, quia alioquin
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eſſet rectus contra hyp. </
s
>
<
s
id
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">3. prætereà poteſt concurrere; </
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>
<
s
id
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">nec enim ſunt li
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neæ determinationum oppoſitæ; igitur concurrit per Th.137.l.1. </
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Theorema
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38.
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<
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Si impetus naturalis non concurreret ad hunc motum, proiectum moueretur
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per lineam horizontalem rectam, vt conſtat, motu æquabili
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; poſito quod non
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retardaretur in horizontali, eodem modo moueretur quo in verticali
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ſurſum, quæ omnia conſtant ex dictis ſuprà. </
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Theorema
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39.
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Patest vtrimque deſcribi linea curua huius motus
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; </
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<
s
id
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">ſit enim mobile pro
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jectum ex E per horizontalem EI
<
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eã
">eam</
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>
ſcilicet velocitate, quam acquiſiuiſ
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ſet motu naturaliter accelerato deſcendendo ex A in E; </
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>
<
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<
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abbr
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ſitq́ue
">ſitque</
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AB ſpa
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tium acquiſitum primo inſtanti deſcenſus; BC duplum, CD triplum, &c. </
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<
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<
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iuxta progreſſionem arithmeticam, ſit EI æqualis EA, diuidatur que eo
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dem modo in 4. ſpatia vt diuiſa eſt EA; </
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<
s
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">aſſumpta EO æqualis AB, ducan
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tur FN. GM. HL. IK. parallelæ EV; </
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<
s
id
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">aſſumatur OP æqualis OE, & PQ,
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quæ ſit ad OE, vt OE ad hypothenuſim ſeu planum inclinatum EN, aſ-</
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