Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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minùs quidem qua proportione motus eſt tardior, & ſi ſpatium AC ma
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jus eſt ſpatio AE in ca proportione in qua motus per AE eſt velocior; </
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pauciores partes ſpatij AE augent motum, ſed plùs ſingulæ, & plures
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ſpatij AC augent motum, ſed minùs ſingulæ; </
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<
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">ſed cum ſint plures in ea
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dem proportione, in qua minùs augent; certè plures quarum ſingulæ mi
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nùs augent, ſimul ſumptæ æqualiter augent, v.g. ſint AC 4. partes, & AE
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2. ſingulæ AE augeant motum vt 4. & ſingulæ AC vt 2. quia in ca pro
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portione minùs augent in qua 2. ſunt ad 4. certè 2. ſimul ſumptæ augent
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motum vt 8. & 4. ſimul ſumptæ etiam vt 8. quæ dicta ſunt in gratiam
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Geometrarum, ſed meliùs adhuc ex dictis patebit. </
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Theorema
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21.
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Hinc aqualis eſſet ictus ab eodem mobili poſt motum per AE. AF. AC.
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AG.
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quia eſſet acquiſitus æqualis impetus; igitur eſſet æqualis ictus,
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quod certè mirabile eſt. </
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Theorema
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22.
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Hinc poteſt determinari ſpatij quæcunque petita proportio ad ſpatium da
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tum
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; </
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<
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">v. g. ſit ictus inflictus à mobili decurſa perpendiculari AE: </
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qualem ictum ſed confecto ſpatio duplo; </
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qualem ictum ſed confecto ſpatio triplo, accipe AG triplam AE. </
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Theorema
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23.
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Tempora quibus percurruntur ſpatia planorum ſunt vt planorum longitu
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dines,
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v.g.tempus quo percurritur planum inclinatum AC eſt ad tempus
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quo percurritur perpendicularis AE, vt AC ad AE; </
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<
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id
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">probatur, cùm enim
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mobile in C & in E habeat æqualem impetum ſeu velocitatem per Th.
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20. certè cùm motus in AC ſit ſubduplus v.g. motus in AE, eſt enim
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vt AE ad AC per Th.6. igitur cum ſubduplo motu æquali tempore ac
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quiritur ſubduplus impetus; </
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<
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id
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">igitur tempore duplo æqualis impetus; </
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">at
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qui tempus motus per AC eſt ad tempus motus per AE vt AC ad AE,
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ideſt duplum; </
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<
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">adde quod ſi æqualis impetus eſt in C & in E; </
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<
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">igitur æqua
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lis in D & in B, ſed AB eſt ad BC vt AD ad DE; </
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<
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">igitur ſi creſcit impe
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tus per partes ſubduplas in AC, neceſſariò creſcit per partes duplas in
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ſpatio, atque in tempore; </
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<
s
id
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">cùm enim motus ſit ſubduplus, tarditas eſt ſub
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dupla; </
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<
s
id
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">igitur acquiritur in AC ſpatium AB ſubduplum AE eo tempore,
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quo percurritur AE, ſi enim accipiantur æqualia tempora, ſpatia ſunt vt
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motus; </
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<
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">ſed motus per AC eſt ſubduplus; </
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<
s
id
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">igitur ſpatium AB eſt ſubdu
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plum AE; </
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<
s
id
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">ſed tempore æquali conficit BC triplum AB, igitur tota AC
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eſt dupla AE; </
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<
s
id
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">ſed percurritur tempore duplo; </
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<
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id
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">igitur tempora ſunt vt
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lõgitudines
">longitudines</
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planorum; </
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<
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">ſed clariùs, & breuiùs illud demonſtro; </
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">In ea pro
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portione erit maius tempus per AC quàm per AE, in qua minor eſt
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motus per AC quàm per AE; </
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<
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">ſi enim motus per AF eſſet ad motum per
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AE vt AF ad AE, certè æquali tempore AF & AE percurrerentur; </
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<
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qua proportione motus per AF eſt minor, tempus eſt maius; </
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<
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enim additur tempori, quantum detrahitur motui; igitur tempora ſunt </
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