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; </s>
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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; </s>
              <s id="N1D463">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. </s>
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              Theorema
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              21.
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            <p id="N1D483" type="main">
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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. </s>
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            <p id="N1D492" type="main">
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              Theorema
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              22.
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              </s>
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              Hinc poteſt determinari ſpatij quæcunque petita proportio ad ſpatium da­
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              tum
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              ; </s>
              <s id="N1D4AD">v. g. ſit ictus inflictus à mobili decurſa perpendiculari AE: </s>
              <s id="N1D4B5">vis æ­
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              qualem ictum ſed confecto ſpatio duplo; </s>
              <s id="N1D4BB">accipe AC duplam AE: vis æ­
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              qualem ictum ſed confecto ſpatio triplo, accipe AG triplam AE. </s>
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            <p id="N1D4C2" type="main">
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              Theorema
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              23.
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              </s>
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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; </s>
              <s id="N1D4DF">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; </s>
              <s id="N1D4EE">igitur tempore duplo æqualis impetus; </s>
              <s id="N1D4F2">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; </s>
              <s id="N1D4FA">adde quod ſi æqualis impetus eſt in C & in E; </s>
              <s id="N1D4FE">igitur æqua­
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              lis in D & in B, ſed AB eſt ad BC vt AD ad DE; </s>
              <s id="N1D504">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; </s>
              <s id="N1D50C">cùm enim motus ſit ſubduplus, tarditas eſt ſub­
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              dupla; </s>
              <s id="N1D512">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; </s>
              <s id="N1D51A">ſed motus per AC eſt ſubduplus; </s>
              <s id="N1D51E">igitur ſpatium AB eſt ſubdu­
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              plum AE; </s>
              <s id="N1D524">ſed tempore æquali conficit BC triplum AB, igitur tota AC
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              eſt dupla AE; </s>
              <s id="N1D52A">ſed percurritur tempore duplo; </s>
              <s id="N1D52E">igitur tempora ſunt vt
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                <expan abbr="lõgitudines">longitudines</expan>
              planorum; </s>
              <s id="N1D537">ſed clariùs, & breuiùs illud demonſtro; </s>
              <s id="N1D53B">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; </s>
              <s id="N1D543">ſi enim motus per AF eſſet ad motum per
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              AE vt AF ad AE, certè æquali tempore AF & AE percurrerentur; </s>
              <s id="N1D549">igitur
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              qua proportione motus per AF eſt minor, tempus eſt maius; </s>
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                <expan abbr="tantũdem">tantundem</expan>
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              enim additur tempori, quantum detrahitur motui; igitur tempora ſunt </s>
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