Fabri, Honoré, Tractatus physicus de motu locali, 1646

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    <archimedes>
      <text>
        <body>
          <chap id="N270EE">
            <pb pagenum="443" xlink:href="026/01/479.jpg"/>
            <figure id="id.026.01.479.1.jpg" xlink:href="026/01/479/1.jpg" number="37"/>
            <p id="N2AA64" type="main">
              <s id="N2AA66">
                <emph type="center"/>
              APPENDIX QVARTA.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N2AA6D" type="main">
              <s id="N2AA6F">
                <emph type="center"/>
                <emph type="italics"/>
              DE PRINCIPIO PHYSICO
                <lb/>
              Rationis duplicatæ Phyſicæ.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N2AA7C" type="main">
              <s id="N2AA7E">VIx credi poteſt quam multis effectibus naturalibus hæc
                <lb/>
              duplicata ratio affigatur, aliquos curſim indicabo vt ve­
                <lb/>
              rum germanumque illius principium ſtatuatur. </s>
            </p>
            <p id="N2AA85" type="main">
              <s id="N2AA87">1. In motu recto naturaliter accelerato, decurſa ſpatia
                <lb/>
              ſunt in ratione duplicata temporum, id eſt vt temporum
                <lb/>
              quadrata; dixi in motu recto, tùm eo, qui fit deorſum in perpendiculo,
                <lb/>
              tùm eo, qui fit in plano inclinato. </s>
            </p>
            <p id="N2AA91" type="main">
              <s id="N2AA93">2. Si iaciantur lapides inæqualis ponderis à potentia toto niſu agente
                <lb/>
              & eodem arcu, lapides ſunt in ratione duplicata inflictorum ictuum. </s>
            </p>
            <p id="N2AA98" type="main">
              <s id="N2AA9A">3. Si impingantur ſudes inæquales eodem brachiorum arcu, pondera
                <lb/>
              ſunt in ratione duplicata ictuum. </s>
            </p>
            <p id="N2AA9F" type="main">
              <s id="N2AAA1">4. Si malleus impingatur diuerſo arcu ab eadem potentia, arcus ſunt
                <lb/>
              in ratione duplicata ictuum. </s>
            </p>
            <p id="N2AAA6" type="main">
              <s id="N2AAA8">5. Si ex tubis erectis eiuſdem cauitatis æqualique foramine fluat aqua,
                <lb/>
              longitudines tuborum ſunt in ratione duplicata quantitatum aquæ, quæ
                <lb/>
              ex tubis æquali tempore fluunt. </s>
            </p>
            <p id="N2AAAF" type="main">
              <s id="N2AAB1">6. Similiter ſi ex ſiphonibus fluat aqua æquali foramine, longitudines
                <lb/>
              ſiphonum ſunt in ratione duplicata quantitatum aquæ, &c. </s>
              <s id="N2AAB6">vt ſuprà. </s>
            </p>
            <p id="N2AAB9" type="main">
              <s id="N2AABB">7. Si chordæ tenſæ eiuſdem longitudinis appendantur inæqualia pon­
                <lb/>
              dera, hæc ſunt in ratione duplicata ſonorum in ratione acuti & grauis. </s>
            </p>
            <p id="N2AAC0" type="main">
              <s id="N2AAC2">8. Si chordæ tenſæ ſint eiuſdem longitudinis & diuerſæ craſſitiei, ba­
                <lb/>
              ſes ſunt in ratione duplicata ſonorum permutando. </s>
            </p>
            <p id="N2AAC7" type="main">
              <s id="N2AAC9">9. Lumen ita propagatur vt lumina propagata ſub eodem angulo, &
                <lb/>
              cono ſint in ratione duplicata diſtantiarum permutando. </s>
            </p>
            <p id="N2AACE" type="main">
              <s id="N2AAD0">10. Idem dico prorſus de propagatione ſonorum, immò auſim dicere
                <lb/>
              toti rei ſonorum familiariſſimam eſſe hanc rationem duplicatam. </s>
            </p>
            <p id="N2AAD5" type="main">
              <s id="N2AAD7">11. In funependulis res eſt clariſſima; nam longitudines ſunt in ratio­
                <lb/>
              ne duplicata temporum quibus vibrationes perficiuntur. </s>
            </p>
            <p id="N2AADD" type="main">
              <s id="N2AADF">12. Non eſt omittendum quod in humana voce obſeruatur pro ratio­
                <lb/>
              ne grauis & acuti, ſcilicet niſus eſſe in ratione duplicata
                <expan abbr="ſonorũ">ſonorum</expan>
              . </s>
              <s id="N2AAE8">Omitto
                <lb/>
              infinita ferè alia quæ huic rationi duplicatæ ſubſunt, ſed iam principia
                <lb/>
              phyſica his effectibus quibus ineſt hæc ratio duplicata, tribuamus. </s>
            </p>
            <p id="N2AAEF" type="main">
              <s id="N2AAF1">Primum caput & vndecimum hoc principio nituntur, eadem cauſa
                <lb/>
              æquali tempore æqualem effectum producit vnde illud; corpus graue
                <lb/>
              æqualibus temporibus æqualia acquirit velocitatis momenta, de quo lib.
                <lb/>
              2. Ex hoc principio demonſtrauimus in partibus temporis ſenſibilibus
                <lb/>
              ſpatia eſſe temporum quadrata. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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