Fabri, Honoré, Tractatus physicus de motu locali, 1646

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    <archimedes>
      <text>
        <body>
          <chap id="N1C940">
            <p id="N1CAFE" type="main">
              <s id="N1CB15">
                <pb pagenum="197" xlink:href="026/01/229.jpg"/>
              ſum, AB, ſit planum inclinatum AE duplum AB; </s>
              <s id="N1CB1E">certè vbi mobile ex A
                <lb/>
              peruenit in E per planum AE, diſtat æquè à centro, ac ſi eſſet in B; </s>
              <s id="N1CB24">ſup­
                <lb/>
              pono enim perpendiculares omnes deorſum eſſe parallelas per poſtula­
                <lb/>
              tum; </s>
              <s id="N1CB2C">igitur non acceſſit propiùs ad centrum confecto ſpatio AE, quàm
                <lb/>
              confecto AB; </s>
              <s id="N1CB32">igitur impeditur in plano AE in ea proportione, in qua
                <lb/>
              AB eſt minor AE, nam haud dubiè AE eſt maior AB, ſit autem dupla v.g.
                <lb/>
              igitur impeditur non quidem totus motus ſed ſubduplus; </s>
              <s id="N1CB3B">in plano verò
                <lb/>
              AD impeditur iuxta cam proportionem in qua AB eſt minor AD, nec
                <lb/>
              enim aliunde poteſt impediri, cum ſcilicet impediatur tantùm, quia im­
                <lb/>
              peditur linea ad quam ab ipſa natura determinatus eſt per Th.2. v. g.li­
                <lb/>
              nea deorſum AB; </s>
              <s id="N1CB49">quippè lineæ comparantur inter ſe v.g. AE cum AB,
                <lb/>
              nam impedimentum lineæ AE in eo tantùm poſitum eſt, quòd difficiliùs
                <lb/>
              per illam quàm per AB ad
                <expan abbr="cẽtrum">centrum</expan>
              feratur mobile, quod certum eſt, cum
                <lb/>
              imperimentum petatur a difficultate; </s>
              <s id="N1CB59">atqui difficultas motus, qui fit per
                <lb/>
              lineam AE in eo tantùm eſt, quòd ſit maius ſpatium conficiendum, igi­
                <lb/>
              tur quò maius ſpatium eſt, maior difficultas eſt; igitur quò maior linea
                <lb/>
              eſt, maius impedimentum eſt. </s>
            </p>
            <p id="N1CB63" type="main">
              <s id="N1CB65">Adde quod vel impedimenti proportio petitur ab angulis vel à Tan­
                <lb/>
              gentibus, vel à ſecantibus; </s>
              <s id="N1CB6B">nihil enim aliud adeſſe poteſt; </s>
              <s id="N1CB6F">igitur per Ax.
                <lb/>
              3. poteſt tantùm impediri ab his; </s>
              <s id="N1CB76">ſed proportio impedimenti non poteſt
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              eſſe ab angulis; </s>
              <s id="N1CB7C">quod probatur primò, quia ſi ego quæram à te in qua
                <lb/>
              proportione motus per AE eſt tardior motu per AB; </s>
              <s id="N1CB82">dices in ea, in qua
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              angulus EAB eſt maior nullo angulo, quod eſt ridiculum: </s>
              <s id="N1CB88">Equidem di­
                <lb/>
              ceres motum per AD eſſe velociorem motu per AE in ea proportione,
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              in qua angulus EAB eſt maior angulo BAD, quod tamen falſum eſt; </s>
              <s id="N1CB90">eſſet
                <lb/>
              enim ferè duplò maior, quod repugnat
                <expan abbr="experimẽtis">experimentis</expan>
              omnibus; </s>
              <s id="N1CB9A">at ſi
                <expan abbr="accipiã">accipiam</expan>
                <lb/>
              angulum BA, qui ſit tantùm vnius gradus ſeu minuti, ſitque EAB angu­
                <lb/>
              lus 60. grad. ſi velocitas motus per AI eſſet ad velocitatem motus per
                <lb/>
              AE vt angulus EAB ad angulum BAI, motus per AI eſſet ſexagecuplò
                <lb/>
              velocior, quàm per AE, quod eſt abſurdum: Diceret fortè aliquis in to­
                <lb/>
              to angulo 90. GAB diſtribui huius impedimenti motum v.g. ſi angulus
                <lb/>
              BAI ſit 1.grad. </s>
              <s id="N1CBB2">motus per AI amittit tantùm (1/90) ſui motus; ſi angulus D
                <lb/>
              AB circiter 40.grad. </s>
              <s id="N1CBB8">motus per AD amittit tantùm (40/90), & per AE (60/90); cum
                <lb/>
              ſit angulus BAE 60. grad. igitur motus per AB eſt ad motum per AE
                <lb/>
              vt 3.ad 1. quod omnibus experimentis repugnat. </s>
            </p>
            <p id="N1CBC2" type="main">
              <s id="N1CBC4">Secundò probatur, quia ſi fiat inclinata proximè accedens ad AG v.
                <lb/>
              g.4′.& aſſumatur alia accedens 3′. </s>
              <s id="N1CBCA">differentia anguli erit tantùm 2′. </s>
              <s id="N1CBCD">cum
                <lb/>
              tamen differentia longitudinis plani ſeu ſecantis huius, & illius, ſit ma­
                <lb/>
              xima, vt conſtat ex canone ſinuum, igitur non imminueretur motus in
                <lb/>
              plano inclinato ratione impedimenti contra Th.4. quis enim neget eſſe
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              maximum impedimentum motus tantum ſpatium, quod
                <expan abbr="conficiendũ">conficiendum</expan>
              eſt. </s>
            </p>
            <p id="N1CBDC" type="main">
              <s id="N1CBDE">Tertiò, omnia experimenta conſentiunt huic Theoremati, & repu­
                <lb/>
              gnant huic propoſitioni quæ petitur ab angulis; </s>
              <s id="N1CBE4">adde quod angulus ni­
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              hil prorſus facit ad motum, ſed linea ſeu ſpatium; denique hoc ipſum eſt
                <lb/>
              quod ab omnibus Mechanicis vulgò ſupponitur perinde quaſi prima </s>
            </p>
          </chap>
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    </archimedes>
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