DelMonte, Guidubaldo, Mechanicorvm Liber

List of thumbnails

< >
141
141 		142
142
143
143 		144
144
145
145 		146
146
147
147 		148
148
149
149 		150
150
< >
page |< < of 288 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N13F6F">
            <pb xlink:href="036/01/148.jpg"/>
            <p id="id.2.1.145.4.0.0.0" type="head">
              <s id="id.2.1.145.5.1.1.0">PROPOSITIO IIII. </s>
            </p>
            <p id="id.2.1.145.6.0.0.0" type="main">
              <s id="id.2.1.145.6.1.1.0">Sit vectis AB, cuius fulcimentum ſit A; qui
                <lb/>
              bifariam diuidatur in D: ſitq; pondus C in D
                <lb/>
              appenſum; duæq; ſint potentiæ æquales in BD
                <lb/>
              pondus C ſuſtinentes. </s>
              <s id="id.2.1.145.6.1.2.0">Dico unamquamq; poten
                <lb/>
              tiam in BD ponderis C ſubtriplam eſſe. </s>
            </p>
            <p id="id.2.1.145.7.0.0.0" type="main">
              <s id="id.2.1.145.7.1.1.0">Quoniam enim altera
                <lb/>
              potentia eſt in D colloca
                <lb/>
              ta, & pondus C in eodem
                <lb/>
              puncto D eſt appenſum;
                <lb/>
              potentia in D partem
                <lb/>
              ponderis C ſuſtinebit ip­
                <lb/>
              ſi potentiæ D æqualem. </s>
              <s id="id.2.1.145.7.1.2.0">
                <lb/>
                <figure id="id.036.01.148.1.jpg" place="text" xlink:href="036/01/148/1.jpg" number="143"/>
                <lb/>
              quare potentia in B partem ſuſtinebit reliquam, quæ pars dupla erit
                <lb/>
              ipſius potentiæ in B; cùm pondus ad potentiam eandem habeat
                <lb/>
              proportionem, quam AB ad AD: & potentiæ in BD ſunt æqua­
                <lb/>
              les; ergo potentia in B duplam ſuſtinebit partem eius, quam ſuſti
                <lb/>
              net potentia in D. </s>
              <s id="id.2.1.145.7.1.2.0.a">diuidatur ergo pondus C in duas partes, qua
                <lb/>
              rum vna ſit reliquæ dupla; quod fiet, ſi in tres partes æquales EFG
                <lb/>
              diuiſerimus: tunc enim FG dupla erit ipſius E. </s>
              <s id="id.2.1.145.7.1.2.0.b">Itaq; potentia
                <lb/>
              in D partem E ſuſtinebit, & potentiam in B reliquas FG. </s>
              <s id="N14406">vtreq;
                <lb/>
              igitur inter ſe ſe æquales potentiæ in BD ſimul totum ſuſtinebunt
                <lb/>
              pondus C. </s>
              <s id="id.2.1.145.7.1.2.0.c">& quoniam potentia in D partem E ſuſtinet, quæ ter
                <lb/>
              tia eſt pars ponderis C, ipſiq; eſt æqualis; erit potentia in D ſub
                <lb/>
              tripla ponderis C. </s>
              <s id="N14413">& cùm potentia in B ſuſtineat partes FG, qua
                <lb/>
              rum potentia in B eſt ſubdupla; erit in B potentia vni partium FG,
                <lb/>
              putà G æqualis. </s>
              <s id="id.2.1.145.7.1.3.0">G verò tertia eſt pars ponderis C; potentia
                <lb/>
              igitur in B ſubtripla erit ponderis C. </s>
              <s id="id.2.1.145.7.1.3.0.a">Vnaquæq; ergo potentia in
                <lb/>
              BD ſubtripla eſt ponderis C. </s>
              <s id="N14423">quod demonſtrare oportebat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum