Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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tempore deſtruitur totus impetus; </
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<
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<
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id
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">certè im
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petus totus non deſtruitur per LC, eo tempore, quo ex F aſcenderet in
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C, ſed pro rata, id eſt in ratione FC ad LC, quæ ſit ſubdupla v.g. igitur
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impetus deſtruitur tantùm ſubduplus; </
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<
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">igitur eo tempore, quo ex F aſcen
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dit in C, ex L aſcendet in K, ita vt LM æquali FC addatur MK æqua
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lis EB; eſt autem EB ſubdupla CA vel EF. </
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<
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">Similiter ſit perpendicu
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lum FG, & inclinata HF tripla FG; </
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<
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">aſſumatur FC æqualis FG, item
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que HO æqualis GF; </
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<
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id
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">certè eo tempore, quo perpendiculari detrahitur
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totus impetus, detrahitur tantùm ſubtriplum per inclinatam HF; </
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<
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">igitur
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aſſumatur ER ſubtripla EF; </
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">& addatur OP æqualis FR: </
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<
s
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">dico quod eo
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tempore, quo ex G aſcendit in F, ex H aſcendit in P; </
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<
s
id
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">quippe aſcenderet
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in O, ſi eo tempore totus impetus deſtrueretur, & in S ſi nullus; </
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<
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id
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">igitur
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in P, ſi ſubtriplus tantùm deſtruatur, deſtruitur porrò ſubtriplus, quia vis
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impetus innati per FH eſt tantùm ſubtripla eiuſdem per FG; </
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<
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id
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">atqui de
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ſtruitur tantùm ab impetu innato, quæ omnia certiſſimè conſtant; Ex
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quo habes tempora eſſe vt lineas. </
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Theorema
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42.
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Hinc poteſt dici quo tempore conficiatur tota inclinata ſurſum ſcilicet eo
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tempore quo inclinata deorſum percurritur.
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v.g, CL dupla CF percurritur
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tempore duplo illius, quo percurritur CF; </
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<
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id
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">igitur mobile proiectum ex
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L in C percurrit LC eodem tempore aſcendendo, quo percurrit EL de
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ſcendendo; ſed percurrit EL deſcendendo eodem tempore, quo percur
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rit perpendicularem quadruplam CF, vt ſuprà diximus. </
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Theorema
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43.
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Hinc nunquam in inclinata ſurſum proiectum mobile acquirit duplum ſpa
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tium illius quod acquirit idem proiectum in verticali ſurſum,
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v. g. ex H pro
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iectum nunquam acquiret in HF duplum ſpatium GF, poſito quòd ex
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G proiiciatur tantùm in F dato tempore, ſitque eadem potentia per HF.
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Probatur, quia ſemper deſtruitur aliquid impetus iuxta proportionem
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FG ad FH per Th.40. ſed ſi nullus deſtruitur impetus, duplum ſpatium
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conficit; </
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<
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id
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">igitur ſi aliquid deſtruitur, duplum ſpatium non conficitur: po
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teſt tamen propiùs in infinitum ad duplum accedere. </
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Theorema
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44.
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Hinc erecta perpendiculari
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FC,
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ductaque horizontali
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FL,
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productaque
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in infinitum, ſi ex quolibet illius puncto eleuetur planum inclinatum termina
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tum ad
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C,
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eadem potentia que ex
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F
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in
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C
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mobile proiiciet, etiam ex quolibet
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puncto deſignato in horizontali proiiciet in
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C
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per planum inclinatum
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; quod
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probatur per Th. 38. </
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Theorema
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45.
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Ex his etiam probatur proiici ex
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L
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in
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C
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ab ea potentia, quæ ex
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F
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proiicit in
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C; </
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>
<
s
id
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">cum enim primo tempore proiiciat ex L in K (ſuppono enim LC
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eſſe quadruplam KC) certè ſecundo conficit tantùm KC; </
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<
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id
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">eſt enim mo
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tus violentus ſurſum retardatus inuerſus motus deorſum accelerati; </
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<
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