DelMonte, Guidubaldo, In duos Archimedis aequeponderantium libros Paraphrasis : scholijs illustrata

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    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N163BC" type="main">
              <s id="N163CE">
                <pb xlink:href="077/01/165.jpg" pagenum="161"/>
              niam figuræ, ipforum què centra inter ſe coaptari poſſunt. </s>
              <s id="N163D8">vt
                <lb/>
              omnibus figuris rectilineis ęqualibus, & ſimilib^{9} accidere po­
                <lb/>
              teſt. </s>
              <s id="N163DE">Hoc tamé contingere poſſe in parabolis, vt AKB BLC, vi
                <lb/>
              detur in
                <expan abbr="cõueniés">conueniés</expan>
              .
                <expan abbr="Nã">Nam</expan>
              quamuis AKB BLC ſint æquales, & ſint
                <lb/>
                <expan abbr="etiã">etiam</expan>
              ſimiles; non ſunt tamen ſimiles ea ſi militudine, vt ſuntre
                <lb/>
              ctilineæ figuræ; vtantea diximus. </s>
              <s id="N163F1">Quod etiam
                <expan abbr="perſpicuũ">perſpicuum</expan>
              fit ex
                <lb/>
              hoc, quia non ſemper coaptari poreiſt portio AKB
                <expan abbr="cũ">cum</expan>
              portio­
                <lb/>
              ne BLC.
                <expan abbr="nõ">non</expan>
              .
                <expan abbr="n.">enim</expan>
              ſemper recta linea BC erit æqualisipſi BA;
                <expan abbr="neq́">ne〈que〉</expan>
              ;
                <lb/>
              ſectionis linea BLC ſectionis lineę BKA ęqualis exiſtet.
                <expan abbr="Cũ">Cum</expan>
                <expan abbr="nõ">non</expan>
                <lb/>
              ſemper AC, & quæ ſuntipſi AC æquidiſtates ad rectos ſint an
                <lb/>
              gulos diametro BD. ſi.n. </s>
              <s id="N16419">ęquidiſtantes lineę diametro fuerint
                <lb/>
              perpendiculares, tunc AB BC inter ſe ęquales eſſent;
                <expan abbr="portioq́">portio〈que〉</expan>
              ;
                <lb/>
              AKB
                <expan abbr="cũ">cum</expan>
              portione BLC coaptari poſſet: ſecùs autem minimè.
                <lb/>
              Quare centra grauiratis HI lineas KFLG in eadem proportio
                <lb/>
              ne ſecare minimèſupponi poſſe videtur; tùm exijs, quæ dicta
                <lb/>
              ſunt; tú quia hoc oſtendet Archimedes in ſeptima propoſitio
                <lb/>
              ne. </s>
              <s id="N1642F">quòd ſi adhuc non eſt
                <expan abbr="demõſtratú">demonſtratú</expan>
              ,
                <expan abbr="nõ">non</expan>
              poteſt
                <expan abbr="quoq́">quo〈que〉</expan>
              ; ſuppo
                <lb/>
              ni; præſertim cùm ſit demonſtrabile. </s>
              <s id="N1643F">ac propterea
                <expan abbr="demõſtra-tio">demonſtra­
                  <lb/>
                tio</expan>
              nullam videturvim haberead
                <expan abbr="oſtendendũ">oſtendendum</expan>
              , quod propoſi­
                <lb/>
              tú fuit. </s>
              <s id="N1644D">Huic
                <expan abbr="tamẽ">tamen</expan>
              occurri poſſevidetur
                <expan abbr="cũ">cum</expan>
              Eutocio in exphca
                <lb/>
              tione huiusloci dicendo, hoc ſupponere Archimedé, quia por
                <lb/>
              tiones AKBBLC ſuntęquales, quarú diametri KFLG ſunt ę­
                <lb/>
              quales, &
                <expan abbr="ęquidiſtãtes">ęquidiſtantes</expan>
              , quæ ſimiliter diuiduntur à punctis HI;
                <lb/>
              vnde erit kG ad HF, vt LI ad IG. ex quibus colligit HF ipſi IG
                <lb/>
                <expan abbr="æqualẽ">æqualem</expan>
              eſſe; ac propterea HG
                <expan abbr="parallelogrãmũ">parallelogrammum</expan>
              exiltere. </s>
              <s id="N1646C">Quæ
                <expan abbr="tñ">tnm</expan>
                <lb/>
              reſponſio
                <expan abbr="nõ">non</expan>
              eſt Eutocio digna. </s>
              <s id="N16478">cùm ex dictis
                <expan abbr="nõ">non</expan>
              ſit omninò
                <lb/>
              demonſtratiua, vtres mathematicę
                <expan abbr="requirũt">requirunt</expan>
              ; quapropter omit
                <lb/>
              tenda eſt.hac.n.rationeſupponitur centra HI lineas KFLG in
                <lb/>
              eadem proportione ſecare.quod nullo modo ſupponi poteſt.
                <lb/>
              Quare dici poterit, & fortaſle rectiùs, quòd vis demonſtratio­
                <lb/>
              nis videtur in hoc eſſe conſtituta, vt ſupponatur puncta HI
                <expan abbr="v-bicunq́">v­
                  <lb/>
                bicun〈que〉</expan>
              ; eſſe poſſe in lineis KFLG; ita vt ſiue ducta HI fuerit,
                <lb/>
              ſiue etiam non fuerit ipſi FG æquidiſtans, demonſtratio
                <expan abbr="tamẽ">tamen</expan>
                <lb/>
              ſuam ſemper habebit vim,
                <expan abbr="idẽq́">iden〈que〉</expan>
              ; concludet. </s>
              <s id="N1649E">Nam ex
                <expan abbr="præcedẽ">præcedem</expan>
              .
                <lb/>
              ti patet centra grauitatis portionum AKB BLC eſſe in lineis
                <lb/>
              KF LG; hoceſt inter puncta KF, & LG.
                <expan abbr="ſupponãturitaq́">ſupponanturita〈que〉</expan>
              ;
                <expan abbr="cẽ-tra">cen­
                  <lb/>
                tra</expan>
              grauitatis
                <expan abbr="portionũ">portionum</expan>
              AKB BLC eſſe puncta HI
                <expan abbr="vbicũq́">vbicun〈que〉</expan>
              ; </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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