Baliani, Giovanni Battista, De motv natvrali gravivm solidorvm et liqvidorvm

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    <archimedes>
      <text>
        <body>
          <chap type="bk">
            <pb xlink:href="064/01/072.jpg"/>
            <subchap1 n="8" type="proposition">
              <p type="head">
                <s id="s.000505">PROPOSITIO VIII.</s>
              </p>
              <subchap2 n="8" type="statement">
                <p type="main">
                  <s id="s.000506">Si lineae perpendicularis, & inclinata ab eo­
                    <lb/>
                  dem puncto digressae, per quas idem grave
                    <lb/>
                  naturaliter ducatur, secentur a recta norma­
                    <lb/>
                  lis ad inclinatam; impetus in punctis sectionis,
                    <lb/>
                  sunt ut portiones linearum intra sectiones.</s>
                </p>
              </subchap2>
              <figure id="id.064.01.072.1.jpg" xlink:href="064/01/072/1.jpg" number="41"/>
              <subchap2 n="8" type="proof">
                <p type="main">
                  <s id="s.000507">Sint rectae AB perpendicularis, & AC quomo­
                    <lb/>
                  documque; inclinata per quas grave naturaliter
                    <lb/>
                  ducatur, sectae a BD normali ad AC declinantem.</s>
                </p>
                <p type="main">
                  <s id="s.000508">Dico impetum in B ad impetum in D esse ut AB
                    <lb/>
                  ad AD.</s>
                </p>
                <p type="main">
                  <s id="s.000509">Fiat BE dupla AB mensura impetus in B, & DF
                    <lb/>
                  dupla AD mensura impetus in D
                    <arrow.to.target n="marg131"/>
                  .</s>
                </p>
                <p type="margin">
                  <s id="s.000510">
                    <margin.target id="marg131"/>
                  Per 10. sexti.</s>
                </p>
                <p type="main">
                  <s id="s.000511">Quoniam grave ducitur per AB AD eodem
                    <lb/>
                  tempore
                    <arrow.to.target n="marg132"/>
                  . Ducitur etiam sine ope gravitatis eo­
                    <lb/>
                  dem tempore per spatia aequalia ipsis BE, DF
                    <arrow.to.target n="marg133"/>
                    <lb/>
                  & proinde BE, DF sunt ut impetus in B & D
                    <arrow.to.target n="marg134"/>
                  .</s>
                </p>
                <p type="margin">
                  <s id="s.000512">
                    <margin.target id="marg132"/>
                  Per 18. Quinti.</s>
                </p>
                <p type="margin">
                  <s id="s.000513">
                    <margin.target id="marg133"/>
                  Per 16. Quinti.</s>
                </p>
                <p type="margin">
                  <s id="s.000514">
                    <margin.target id="marg134"/>
                  Per pr. huius.</s>
                </p>
                <p type="main">
                  <s id="s.000515">At BE, DF sunt ut AB, AD per constr. quip­
                    <lb/>
                  pe earum duplae. </s>
                  <s id="s.000516">Igitur AB, AD sun t ut im­
                    <lb/>
                  petus in B & D
                    <arrow.to.target n="marg135"/>
                  quod, etc.</s>
                </p>
                <p type="margin">
                  <s id="s.000517">
                    <margin.target id="marg135"/>
                  Per cor. 3. huius.</s>
                </p>
              </subchap2>
              <subchap2 type="corollary">
                <p type="head">
                  <s id="s.000518">Corollarium</s>
                </p>
                <p type="main">
                  <s id="s.000519">Impetus sive velocitas in B ad impetum in D
                    <lb/>
                  est ut AC ad AB.</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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