Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N19109">
            <pb pagenum="140" xlink:href="026/01/172.jpg"/>
            <p id="N197A1" type="main">
              <s id="N197A3">Hinc inuertenda eſt progreſſionis linea; </s>
              <s id="N197A7">quippe linea AE repræſen­
                <lb/>
              tat nobis progreſſionem motus accelerati, quæ fit in inſtantibus, & li­
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              nea FK progreſſionem motus, quæ fit in partibus temporis ſenſibilibus; </s>
              <s id="N197AF">
                <lb/>
              in illa primo inſtanti decurritur primum ſpatium AB, ſecundo tempore
                <lb/>
              æquali BC, tertio CD, quarto DE: </s>
              <s id="N197B6">in hac vero prima parte acquiritur
                <lb/>
              ſpatium FG ſecunda æquali primæ GH, tertia HI, quarta IK; </s>
              <s id="N197BC">igitur ſi ac­
                <lb/>
              cipiatur linea AE, progrediendo ab A verſus E, vel linea FK progre­
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              diendo ab F verſus K habebitur progreſſio motus naturaliter accelerati; </s>
              <s id="N197C4">
                <lb/>
              ſi verò accipiatur EA, vel KF, progrediendo ſcilicet ab E verſus A, vel à
                <lb/>
              K verſus F, erit progreſſio motus violenti naturaliter retardati; </s>
              <s id="N197CB">vt con­
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              ſtat ex præcedèntibus Theorematis; & quemadmodum progreſſio acce­
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              lerationis in inſtantibus finitis fit iuxta ſeriem iſtorum numerorum 1.2.
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              3.4. in partibus verò temporis ſenſibilibus iuxta ſeriem iſtorum 1.3.5.7.
                <lb/>
              ita fit omninò progreſſio retardationis in inſtantibus iuxta hos nume­
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              ros 4.3.2.1. in partibus temporis ſenſibilibus iuxta hos 7.5. 3. 1. </s>
            </p>
            <p id="N197DA" type="main">
              <s id="N197DC">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              28.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N197E8" type="main">
              <s id="N197EA">
                <emph type="italics"/>
              Motus violentus durat tot inſtantibus ſcilicet æquiualentibus quot ſunt ij
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              gradus impetus quibus violentus ſuperat innatum,
                <emph.end type="italics"/>
              v.g. ſit vnus gradus im­
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              petus innati; </s>
              <s id="N197F9">producantur 5. gradus violenti, quorum ſinguli ſint æqua­
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              les innato etiam
                <expan abbr="æquiualẽter">æquiualenter</expan>
              , motus durabit 4. inſtantibus etiam æqui­
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              ualenter id eſt 4. temporibus, quorum ſingula erunt æqualia primo in­
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              ſtanti motus naturalis, probatur, cum ſingulis inſtantibus æqualibus de­
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              ſtruatur vnus gradus; certè 4. inſtantibus durat motus. </s>
            </p>
            <p id="N19809" type="main">
              <s id="N1980B">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              29.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N19817" type="main">
              <s id="N19819">
                <emph type="italics"/>
              Si accipiantur ſpatia æqualia in hac progreſſione retardationis, eſt inuerſa
                <lb/>
              illius, quàm tribuimus ſuprà accelerationi, aſſumptis ſcilicet ſpatiis æqualibus; </s>
              <s id="N19821">
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              tum ſi accipiantur ſpatia æqualia prime ſpatie quod decurritur prime inſtan­
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              ti metus naturalis, tum ſi accipiantur ſpatia æqualia date ſpatie quod in par­
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              te temporis ſenſibili percurritur
                <emph.end type="italics"/>
              ; </s>
              <s id="N1982D">quippe quemadmodum in progreſſione
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              accelerationis decreſcunt tempora; </s>
              <s id="N19833">ſic in progreſſione retardationis
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              creſcunt, aſſumptis ſcilicet ſpatiis æqualibus; quare ne iam dicta hic re­
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              petam, conſule quæ diximus lib.2. de hac progreſſione. </s>
            </p>
            <p id="N1983B" type="main">
              <s id="N1983D">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              30.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N19849" type="main">
              <s id="N1984B">
                <emph type="italics"/>
              Hinc instantia initio huius metus ſunt minora ſicut initio motus naturalis
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              ſunt maiora; </s>
              <s id="N19853">& ſub finem in motu violente ſunt maiora, in naturali ſunt mi­
                <lb/>
              nora
                <emph.end type="italics"/>
              ; </s>
              <s id="N1985C">quia ſcilicet hic acceleratur, ille retardatur: </s>
              <s id="N19860">igitur velo­
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              citas accelerati creſcit; </s>
              <s id="N19866">igitur ſi accipiantur ſpatia æqualia, decreſcit tem­
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              pus; </s>
              <s id="N1986C">at verò velocitas retardati decreſcit, igitur aſſumptis ſpatiis æquali­
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              bus, creſcit tempus; </s>
              <s id="N19872">igitur ſi accipiatur ſpatium, quod percurritur primo
                <lb/>
              inſtanti huius motus, & deinde alia huic æqualia; </s>
              <s id="N19878">haud dubiè, cum ſe­
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              cundo inſtanti motus ſit tardior, ſitque aſſumptum æquale ſpatium; haud
                <lb/>
              dubiè inquam inſtans ſecundum erit maius primo, & tertium ſecundo,
                <lb/>
              atque ita deinceps. </s>
            </p>
          </chap>
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