Fabri, Honoré, Tractatus physicus de motu locali, 1646

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            <p id="N19C00" type="main">
              <s id="N19C17">
                <pb pagenum="145" xlink:href="026/01/177.jpg"/>
              conſtat ex dictis; igitur rationes ictuum non ſunt, vt rationes ſegmen­
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              torum integri ſpatij. </s>
            </p>
            <p id="N19C24" type="main">
              <s id="N19C26">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              47.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N19C32" type="main">
              <s id="N19C34">
                <emph type="italics"/>
              Vt in praxi determinentur rationes ictuum
                <emph.end type="italics"/>
              ; </s>
              <s id="N19C3D">aſſumatur progreſſio Gali­
                <lb/>
              lei in AF, ita vt ſi prima parte temporis ſenſibili percurratur ſpatium
                <lb/>
              FE 9 partium æqualium; </s>
              <s id="N19C45">ſecunda percurratur ED. 7. partium, tertia
                <lb/>
              DC 5. quarta CB 3; </s>
              <s id="N19C4B">quinta BA 1. hoc poſito facilè erit determinare
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              rationes ictuum; </s>
              <s id="N19C51">nam in deſcenſu ictus ſunt vt velocitates, & hæ vt tem­
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              pora; </s>
              <s id="N19C57">igitur ſi AB percurritur in dato tempore, & AC in duobus prio­
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              ri æqualibus; </s>
              <s id="N19C5D">certè ictus in deſcenſu AC eſt duplus ictus in deſcenſu
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              AB; in AD triplus, &c. </s>
              <s id="N19C63">Igitur in aſcenſu ictus in F erit quintuplus,
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              ictus in E quadruplus in D triplus, &c. </s>
              <s id="N19C68">igitur ictus ſunt in ratione dupli­
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              cata ſpatiorum facto ſpatij initio à ſummo puncto A. </s>
            </p>
            <p id="N19C6E" type="main">
              <s id="N19C70">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              48.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N19C7C" type="main">
              <s id="N19C7E">
                <emph type="italics"/>
              Hinc cognitis viribus, quibus corpus graue proijcitur ad datam altitudi­
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              nem, cognoſci poſſunt vires, quibus ad aliam quamcumque proijciatur
                <emph.end type="italics"/>
              ; </s>
              <s id="N19C89">v. g.
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              proiiciatur corpus graue ad altitudinem 48. pedum; </s>
              <s id="N19C92">vires ſunt iis æqua­
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              les, quas acquirit in deſcenſu eiuſdem altitudinis 48. pedum; </s>
              <s id="N19C98">ſit alia di­
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              ſtantia 100. pedum; haud dubiè vires neceſſariæ ad motum hunc violen­
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              tum ſunt æquales iis, quas acquireret in deſcenſu 100. pedum per Th.
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              40. atqui ita ſe habent vires acquiſitæ in deſcenſu 48. pedum ad vires
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              acquiſitas in deſcenſu 100. vt v.g. 48. ad v.g. 100. id eſt ferè vt 7.
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              ad 10. </s>
            </p>
            <p id="N19CAB" type="main">
              <s id="N19CAD">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              49.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N19CB9" type="main">
              <s id="N19CBB">
                <emph type="italics"/>
              Cognitis etiam ſpatiis cognoſcetur tempus
                <emph.end type="italics"/>
              ; </s>
              <s id="N19CC4">ſit enim decurſum idem ſpa­
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              tium 48. pedum motu violento ſurſum; </s>
              <s id="N19CCA">idque v. g. tempore 2. ſecundo­
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              rum, quod ferè cum experientia conſentit; </s>
              <s id="N19CD4">ſit aliud ſpatium 100. tempus
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              primi motus eſt ad tempus ſecundi vt v. g. 48. ad v. g. 100. quia ſpatia
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              ſunt vt quadrata temporum; </s>
              <s id="N19CE4">igitur tempora vt radices 4. hinc vires ſunt
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              in ratione temporum; </s>
              <s id="N19CEA">quia vt temporibus æqualibus acquiruntur æqua­
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              lia velocitatis momenta in motu naturali, ita & deſtruuntur æqualia in
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              motu violento, quæ omnia conſtant; igitur ictus ſunt vt vires, vires vt
                <lb/>
              tempora, tempora denique, vt radices
                <expan abbr="q.">que</expan>
              ſpatiorum. </s>
            </p>
            <p id="N19CF8" type="main">
              <s id="N19CFA">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              150.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N19D06" type="main">
              <s id="N19D08">
                <emph type="italics"/>
              In vltimo contactu motus violenti nullus eſt ictus, v. g. mobile projectum
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              ſurſum
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                <emph type="italics"/>
              per lineam
                <emph.end type="italics"/>
              FA
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              nullam percuſſionem infligeret in
                <emph.end type="italics"/>
              A; </s>
              <s id="N19D23">probatur
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              quia non tendit vlteriùs; </s>
              <s id="N19D29">igitur non impeditur eius motus à ſuperficie
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              corporis terminati ad punctum A; igitur nullum impetum in eo produ­
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              cit, qui tantùm producitur ad tollendum impedimentum per Th.44.l.1.
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              igitur nullum ictum infligit, qui tantùm infligitur per impetum, vt
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              conſtat. </s>
            </p>
            <p id="N19D35" type="main">
              <s id="N19D37">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              51.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N19D43" type="main">
              <s id="N19D45">
                <emph type="italics"/>
              Ex his ſatis facilè comparari poſſunt rationes percuſſionis,
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              quæ infliguntur </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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