Varro, Michael, De motv tractatvs
page |< < of 64 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="044/01/035.jpg" pagenum="27"/>
                <expan abbr="partiũ">partium</expan>
                <expan abbr="illarũ">illarum</expan>
                <expan abbr="proportionẽ">proportionem</expan>
                <expan abbr="ſeruabũt">ſeruabunt</expan>
              . </s>
              <s>Sit
                <expan abbr="exẽpli">exempli</expan>
              gratia
                <lb/>
              linea AB, quæ in puncto C in datam rationem ſecta
                <lb/>
              ſit, puta vt pars AC quadrupla ſit ad partem CB, mo­
                <lb/>
              ueatúrque circa centrum C, punctum A deſcribet cir
                <lb/>
              culum
                <expan abbr="quadruplũ">quadruplum</expan>
              ad illum quem B
                <lb/>
              deſcribet. </s>
              <s>Eſt enim
                <expan abbr="eadẽ">eadem</expan>
              ratio in cir­
                <lb/>
              culo diametri ad
                <expan abbr="diametrũ">diametrum</expan>
              , quæ eſt
                <lb/>
              circunferentiæ ad
                <expan abbr="circunferentiã">circunferentiam</expan>
              (vt
                <lb/>
              alibi demonſtrauimus.) Hac igitur
                <lb/>
              ratione A puncti motus quadruplus
                <lb/>
                <figure id="id.044.01.035.1.jpg" xlink:href="044/01/035/1.jpg" number="3"/>
                <lb/>
              erit ad puncti B
                <expan abbr="motũ">motum</expan>
              . </s>
              <s>Si verò ponamus AD
                <expan abbr="perpen-dicularẽ">perpen­
                  <lb/>
                dicularem</expan>
              eſſe, & linea AB illi primùm
                <expan abbr="coincidẽs">coincidens</expan>
              circa
                <lb/>
              punctum C, moueatur donec A ad D perueniat: tum
                <lb/>
                <expan abbr="eodẽ">eodem</expan>
              momento B perueniet ad E: motum igitur erit
                <lb/>
              A in linea
                <expan abbr="perpẽdiculari">perpendiculari</expan>
              tota circuli maioris diame­
                <lb/>
              tro, quæ eſt AD:B verò in
                <expan abbr="eadẽ">eadem</expan>
              linea, minoris
                <expan abbr="tãtùm">tantùm</expan>
                <lb/>
              circuli diametro
                <expan abbr="motũ">motum</expan>
              erit, quę eſt BE. </s>
              <s>Atqui diame
                <lb/>
              ter AD quadrupla eſt ad BE, quia ex hypotheſi
                <expan abbr="ſemi-diametrorũ">ſemi­
                  <lb/>
                diametrorum</expan>
                <expan abbr="illorũ">illorum</expan>
                <expan abbr="circulorũ">circulorum</expan>
              proportio eſt, vt 4 ad 1.
                <lb/>
              Motus igitur
                <expan abbr="pũcti">puncti</expan>
              in linea A
                <expan abbr="perpẽdiculari">perpendiculari</expan>
              ad
                <expan abbr="motũ">motum</expan>
                <lb/>
                <expan abbr="pũcti">puncti</expan>
              B quadruplus erit:
                <expan abbr="Idẽ">Idem</expan>
              dicetur ſi in data aliqua
                <lb/>
              alia ratione ſecta ſit linea AB.
                <expan abbr="Demõſtratũ">Demonſtratum</expan>
              igitur eſt
                <lb/>
              quomodo fieri poſſit vt rectæ lineę extrema
                <expan abbr="ſecũdũ">ſecundum</expan>
                <lb/>
                <expan abbr="datã">datam</expan>
                <expan abbr="rationẽ">rationem</expan>
              moueantur. </s>
              <s>Si igitur illis extremis duæ
                <lb/>
              vires applicentur,
                <expan abbr="mouebũtur">mouebuntur</expan>
                <expan abbr="eodẽ">eodem</expan>
              ipſo motu: ergo
                <lb/>
              ſecundum datam vel propoſitam rationem. </s>
              <s>Quod
                <lb/>
              aſſumptum erat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>