DelMonte, Guidubaldo, Le mechaniche

List of thumbnails

< >
121
121 		122
122
123
123 		124
124
125
125 		126
126
127
127 		128
128
129
129 		130
130
< >
page |< < of 270 > >|
    <archimedes>
      <text id="id.0.0.0.0.3">
        <body id="id.2.0.0.0.0">
          <chap id="N14EBE">
            <pb xlink:href="037/01/150.jpg"/>
            <p id="id.2.1.823.0.0" type="head">
              <s id="id.2.1.823.1.0">PROPOSITIONE VIII. </s>
            </p>
            <p id="id.2.1.824.0.0" type="main">
              <s id="id.2.1.824.1.0">Siano due leue AB CD diuiſe in due parti eguali EF, i ſo­
                <lb/>
              ſtegni delle quali ſiano AC, & ſia appiccato il peſo G ne'
                <lb/>
              punti EF all'vna, & l'altra leua, ſi fattamente, che dall'vno,
                <lb/>
              & l'altro peſi egualmente: & ſiano tre poſſanze eguali in BD
                <lb/>
              E che ſoſtenghino il peſo G. </s>
              <s id="id.2.1.824.2.0">Dico, che ciaſcuna delle det­
                <lb/>
              te poſſanze ſeparatamente è vn quinto del peſo G. </s>
            </p>
            <p id="id.2.1.825.0.0" type="main">
              <s id="id.2.1.825.1.0">
                <emph type="italics"/>
              Percioche il peſo G ſta appiccato in EF, & ſono le tre poſſanze in EBD egua­
                <lb/>
              li: però la poſſanza di E ſoſterrà la parte ſolamente del peſo G, che ſarà eguale
                <lb/>
              ad eſſa poſſanza di E, ma
                <lb/>
              le poſſanze di BD ſoſterran
                <lb/>
              no la parte reſtante, & la
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="note233"/>
                <emph type="italics"/>
              parte, che è da B ſoſtenu­
                <lb/>
              ta, ſarà il doppio di eſſo: ma
                <lb/>
              la parte ſoſtenuta da D ſa­
                <lb/>
              rà ſimilmente il doppio di eſ
                <lb/>
              ſo D per cauſa della pro­
                <lb/>
              portione di BA verſo AE,
                <lb/>
              & di DC verſo CF. </s>
              <s id="id.2.1.825.2.0">Con
                <lb/>
              cioſia dunque, che le poſſan­
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="note234"/>
                <emph type="italics"/>
              ze di BD ſiano eguali, ſa­
                <lb/>
              ranno anche (per quel che di
                <lb/>
              ſopra è detto) le parti del pe
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.037.01.150.1.jpg" xlink:href="037/01/150/1.jpg" number="144"/>
                <lb/>
                <emph type="italics"/>
              ſo G, lequali ſono ſoſtenute dalle poſſanze di BD, fra loro eguali, & ogni vna
                <lb/>
              ſarà il doppio di quella tal parte, che è ſoſtenuta dalla poſſanza di E. </s>
              <s id="id.2.1.825.3.0">Diuidaſi
                <lb/>
              dunque il peſo G in tre parti, delle quali due ſiano fra loro eguali, & di più ogni
                <lb/>
              vna di loro ſeparatamente ſia il doppio dell'altra terza parte, ilche accaderà, ſe
                <lb/>
              in cinque parti eguali HKLMN ſarà diuiſo: percioche la parte compoſta di due
                <lb/>
              parti KL è il doppio della parte H, & la parte ancora di MN è ſimilmen­
                <lb/>
              te il doppio della parte iſteſſa H. </s>
              <s id="id.2.1.825.4.0">Per laqual coſa anche la parte KL ſarà egua­
                <lb/>
              le alla parte MN. </s>
              <s id="id.2.1.825.5.0">Ma ſoſtenga la poſſanza di E la parte di H; & la poſſan
                <lb/>
              za di B le parti di KL: & la poſſanza di D le parti MN; adunque le tre
                <lb/>
              poſſanze eguali poſte in BDE ſoſterranno tutto il peſo G: & ogn'vna delle
                <lb/>
              poſſanze di BD ſoſterrà il doppio di quel che ſoſtiene la poſſanza di E. </s>
              <s id="id.2.1.825.6.0">Però
                <lb/>
              eſſendo che la poſſanza di E ſoſtenga la parte di H, laquale è la quinta parte del
                <lb/>
              peſo G, & ſia ad eſſo eguale, ſarà la poſſanza di E vn quinto del peſo G. </s>
              <s id="N15A13">&
                <lb/>
              percioche la poſſanza di B ſoſtiene le parti di KL, lequali ſono il doppio & del­
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum