Ceva, Giovanni, Geometria motus, 1692

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            <p type="main">
              <s id="s.000191">
                <pb pagenum="16" xlink:href="022/01/022.jpg"/>
              geneſes GHKL, YZ 43. & ſit pariter HI ad IK, vt ſegmen­
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              tum ABFE ad EFCD. </s>
              <s id="s.000192">Sit ſimiliter Z
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              ad
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              4 vt ſeg­
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              mentum NPQV ad VQRT, ductiſque applicatis IM, QV,
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              manifeſtum eſt, vt velocitas AB æqualis eſt velocitati GH,
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              ſic EF æqualem fore ipſi IM; nam quia ſpatium
                <expan abbr="tranſactũ">tranſactum</expan>
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              iuxta imaginem ABFE ad ſpatium tranſactum imagine
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                <arrow.to.target n="marg39"/>
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              EFCD eſt vt illa ad hanc imaginem, nempe vt HI ad IK,
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              erit mobile inſtanti F in puncto I, & ideo inibi erit veloci­
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              tas eadem, quam habet mobile inſtanti F, ſcilicet æquales
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              erunt EF, IM. </s>
              <s id="s.000193">Eodem modo erunt æquales QV,
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              2, &
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              ſunt etiam æquales NP, YZ, ergo ſicut ſe habet AB ad EF,
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              ita erit GH ad MI, & vt eſt NP ad
                <expan abbr="Vq.">Vque</expan>
              ita erit YZ ad 2
                <gap/>
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              Præterea concipiatur figura OPRSXO ſimilis ipſi ABCD,
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              ſcilicet ſit CB ad PR vt AB ad OP, vel (cum ſint BF ad
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              FC ita PQ ad QR, vt EF ad homologam XQ, erit ſeg­
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              mentum ABFE ad ſibi ſimile ſegmentum OPQX in dupli­
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              cata ratione laterum homologorum EF ad XQ, & item in
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                <expan abbr="eadẽ">eadem</expan>
              duplicata ratione erunt interſe ſimilia
                <expan abbr="ſegmẽta">ſegmenta</expan>
              EFCD
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              ad XQRS, ſed cum etiam OPQX ſegmentum ad NPQV,
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              & XQRS ad ſegmentum VQRT ſint in eadem ratione
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              eiuſdem QX ad QV, erit ex æquali ſegmentum ABFE ad
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              ſegmentum NPQV, vt ſegmentum EFCD ad VQRT, &
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              permutando, ſegmentum ABFE ad ſegmentum EFCD ha­
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              bebit eandem rationem, ac ſegmentum NPQV ad VQRT
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              ſcilicet erit HI ad IK vt Z
                <gap/>
              ad
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              4, ob idque conſtat ge­
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              neſium applicatas vnius proportionales eſſe applicatis al­
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              terius, quare ſimiles motus erunt, qui fiunt iuxta imagines
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              velocitatum propoſitas. </s>
            </p>
            <p type="margin">
              <s id="s.000194">
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                <emph type="italics"/>
              Pr.
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              2.
                <emph type="italics"/>
              huius.
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              </s>
            </p>
            <p type="main">
              <s id="s.000195">
                <emph type="center"/>
              PROP. VIII. THEOR. VIII.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000196">SPatia, quæ curruntur ſimilibus motibus ſunt in ratione
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              compoſita temporum, & homologarum velocitatum,
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              inter quas ſunt extremæ, aut primæ. </s>
            </p>
          </chap>
        </body>
      </text>
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