DelMonte, Guidubaldo, Le mechaniche

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    <archimedes>
      <text id="id.0.0.0.0.3">
        <body id="id.2.0.0.0.0">
          <chap id="N106DF">
            <p id="id.2.1.201.0.0" type="main">
              <s id="id.2.1.201.8.0">
                <pb xlink:href="037/01/046.jpg"/>
                <emph type="italics"/>
              mouerſi ſolamente fin ad S. </s>
              <s id="id.2.1.201.9.0">Et ſe di nouo moſtraſſero vna portione della ſceſa da S
                <lb/>
              in A, & coſi ſucceßiuamente eſſere piu diritta della ſceſa eguale del peſo oppoſto;
                <lb/>
              ſempre ſeguirà, che la bilancia SI andarà piu da preſſo ad AB, ma non
                <expan abbr="dimostre­rãno">dimostre­
                  <lb/>
                ranno</expan>
              giamai che per
                <lb/>
              uenga in AB. </s>
              <s id="id.2.1.201.10.0">Se
                <lb/>
              dunque vogliono di
                <lb/>
              moſtrare, che la
                <expan abbr="bilãcia">bilan
                  <lb/>
                cia</expan>
              DE ritorni in
                <lb/>
              AB, egli è neceſſa­
                <lb/>
              rio, che preſupponga
                <lb/>
              no, che la ſceſa del
                <lb/>
              peſo da D in A
                <expan abbr="prẽda">pren
                  <lb/>
                da</expan>
              di diretto la quan
                <lb/>
              tità della linea tira­
                <lb/>
              ta dal punto D ad
                <lb/>
              AB ad angoli ret­
                <lb/>
              ti; & coſi, ſe para­
                <lb/>
              goneremo le ſceſe e­
                <lb/>
              guali di DA AN
                <lb/>
              fra loro, lequali
                <expan abbr="prẽdono">pren
                  <lb/>
                dono</expan>
              di diretto OC
                <lb/>
              CT, accaderà, che
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.037.01.046.1.jpg" xlink:href="037/01/046/1.jpg" number="28"/>
                <lb/>
                <emph type="italics"/>
              il peſo iſteſſo ſarà in D graue egualmente, come in A. </s>
              <s id="id.2.1.201.11.0">Ma ſe le portioni ſolamente
                <lb/>
              piglieremo da DA, ſarà piu graue in A, che in D. </s>
              <s id="id.2.1.201.12.0">Adunque dalla diuerſità ſo­
                <lb/>
              lamente del modo del conſiderare, auerrà, che il peſo medeſimo ſarà & piu graue,
                <lb/>
              & piu leggiero; & non per la natura della coſa. </s>
              <s id="id.2.1.201.13.0">Di piu la preſuppoſta loro non
                <lb/>
              afferma, che il peſo ſecondo il ſito ſia piu graue, quanto nel ſito medeſimo il principio
                <lb/>
              della ſua diſceſa è meno obliquo. </s>
              <s id="id.2.1.201.14.0">La preſupposta dunque di ſopra addotta, cioè che
                <lb/>
              ſecondo il ſito il peſo è piu graue quanto nell'iſteſſo ſito meno obliqua è la diſceſa, non
                <lb/>
              ſolamente non ſi puote concedere à modo alcuno, per le coſe, che habbiamo dette;
                <lb/>
              ma anco percioche non è coſa difficile il dimoſtrare tutto l'oppoſto, cioè il peſo medeſi
                <lb/>
              mo in eguali circonferenze quanto meno obliqua è la diſceſa, iui meno grauare.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="id.2.1.203.0.0" type="main">
              <s id="id.2.1.203.1.0">
                <emph type="italics"/>
              Siano come prima le circonferenze AL AM tra loro eguali; & ſia il punto L vici
                <lb/>
              no ad F, & congiungaſi LM, la quale ſarà à piombo di AB & LX ſarà anco
                <lb/>
              eguale ad XM. </s>
              <s id="id.2.1.203.2.0">Dapoi preſſo ad M tra M & G ſia preſo come ſi vuole, il pun
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="note48"/>
                <emph type="italics"/>
              to P, & ſia fatta la circonferenza PO eguale alla circonferenza AM, ſarà il
                <lb/>
              punto O preſſo ad A. </s>
              <s id="id.2.1.203.3.0">& ſiano congiunte le linee CL, CO, CM, CP, OP
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="note49"/>
              </s>
              <s id="N11983">
                <emph type="italics"/>
              & dal punto P tiriſi la PN a piombo di OC. </s>
              <s id="id.2.1.203.4.0">& percioche la circonferenza
                <lb/>
              AM è eguale alla circonferentia OP; ſarà l'angolo ACM eguale all'angolo
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="note50"/>
                <emph type="italics"/>
              OCP, & l'angolo CXM retto eguale al retto CNP, ſarà anco il reſtante angolo
                <lb/>
              XMC del triangolo MXC eguale al reſtante NPC del triangolo PCN.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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