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

List of thumbnails

< >
81
81 		82
82
83
83 		84
84
85
85 		86
86
87
87 		88
88
89
89 		90
90
< >
page |< < of 207 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N10019">
            <p id="N17843" type="main">
              <s id="N178BF">
                <pb xlink:href="077/01/199.jpg" pagenum="195"/>
                <emph type="italics"/>
              in puncto B. ſi autem hoc, est vt AF ad DG potentia,
                <emph.end type="italics"/>
                <arrow.to.target n="marg384"/>
                <lb/>
                <emph type="italics"/>
              ſic FB ad BG longitudine, hoc est MN ad NO.
                <lb/>
              vt autem MN ad NO longitudine, itaest MN ad Nx potentia.
                <emph.end type="italics"/>
                <lb/>
              quandoquidem treslineæ MN NX NO ſunt proportio­
                <lb/>
              nales.
                <emph type="italics"/>
              vt igitur AF ad DG potentia, ita est MN ad N X
                <emph.end type="italics"/>
                <arrow.to.target n="marg385"/>
                <lb/>
                <emph type="italics"/>
              potentia. </s>
              <s id="N178F6">quare, & longitudine in eadem ſunt proportione
                <emph.end type="italics"/>
              ; vt ſcili
                <lb/>
              cet AF ad DG, ita MN ad NX.
                <emph type="italics"/>
              ſieist ita〈que〉 cubus ex AF
                <emph.end type="italics"/>
                <arrow.to.target n="marg386"/>
                <lb/>
                <emph type="italics"/>
              ad cubum ex DG, ita cubus ex MN ad cubum ex NX. Verùm
                <emph.end type="italics"/>
                <arrow.to.target n="marg387"/>
                <lb/>
                <emph type="italics"/>
              vt cubus ex AF adcubum ex DG, ſic portio ABC ad portio­
                <lb/>
              nem DBE.
                <emph.end type="italics"/>
              vtigitur cubus ex MN ad cubum ex NX, ita
                <lb/>
              portio ABC ad portionem DBE.
                <emph type="italics"/>
              ſicut autem cubus ex MN
                <lb/>
              ad culum ex Nx, ita MN ad NT.
                <emph.end type="italics"/>
              cùm ſint quatuor lineæ
                <lb/>
              MN NX NO NT in continua proportione. </s>
              <s id="N17925">ac propterea
                <lb/>
              eritportio ABC ad portionem DBE, vt MN ad NT.
                <lb/>
                <emph type="italics"/>
              Quare & diuidendo frustum ADEC ad portionem DBE eſt, vt
                <emph.end type="italics"/>
                <arrow.to.target n="marg388"/>
                <lb/>
                <emph type="italics"/>
              MT ad NT.
                <emph.end type="italics"/>
              Quia vero, vt factum fuit, ità eſt MT ad TN,
                <lb/>
              vt FH ad IR, eſt verò FH ipſius FG tresquintæ, erit fru­
                <lb/>
              ſtum ADEC ad portionem DBE, vt FH ad IR
                <emph type="italics"/>
              hoc est
                <lb/>
              tres quintæ ipſius GF ad IR. & quoniam ſolidum baſim habens qua­
                <lb/>
              dratum ex AF, altitudinem verò lineam compoſitam ex dupla ipſius
                <lb/>
              DG, & ipſa AF, ad cubum ex AF proportionem habet,
                <emph.end type="italics"/>
              quam ſo
                <lb/>
              lidi altitudo ad altitudinem cubi, ſiquidem ſunt in eadem ba
                <lb/>
              ſi. </s>
              <s id="N1794E">tàm emm ſolidum, quàm cubus baſim habet quadratum
                <lb/>
              ex AF. idcirco ſolidum baſim habens quadratum ex AF,
                <lb/>
              altitudinem verò lineam compoſitam ex dupla ipſius DG, &
                <lb/>
              ipſa AF ad cubum ex AF eam proportio nem habebit,
                <emph type="italics"/>
              quam
                <emph.end type="italics"/>
                <lb/>
              ſolidi altitudo,
                <emph type="italics"/>
              dupla,
                <emph.end type="italics"/>
              ſcilicet
                <emph type="italics"/>
              ipſius DG cumlinea AF
                <emph.end type="italics"/>
              ad alci­
                <lb/>
              tudinem cubi, hoc eſt
                <emph type="italics"/>
              ad FA.
                <emph.end type="italics"/>
              Atverò quoniam oſtenſum eſt
                <lb/>
              ita eſſe AF ad DG, vt MN ad NX, eritconuertendo DG
                <lb/>
              ad AF, vt NX ad MN, & antecedentium dupla, hoc eſt du
                <lb/>
              pla ipſius DG ad AF, vt dupla ipſius NX ad MN. & com­
                <lb/>
              ponendo dupla ipſius DG cum AF ad AF, vt dupla
                <arrow.to.target n="marg389"/>
                <lb/>
              NX cum MN ad MN.
                <emph type="italics"/>
              Quare & vt
                <emph.end type="italics"/>
              ſolidum baſim habens
                <lb/>
              quadratum ex AF, altitudinem verò lineam compoſitam ex
                <lb/>
              dupla ipſius DG cum AF ad cubum ex AF, ita
                <emph type="italics"/>
              dupla ipſius NX
                <lb/>
              cum linea NM ad NM. est autem
                <emph.end type="italics"/>
              cubus ex AF adcubum
                <lb/>
              ex DG, vt cubus ex MN ad cubum ex NX, vt oſtenſum eſt, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum