Lorini, Buonaiuto , Le fortificationi, old version (312 p.), 1609

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="031/01/206.jpg" pagenum="198"/>
              faranno trecento, come ſi diſſe eſſere il peſo, e ſe in F, ſarà ſettantacinque, & in G, di libre cento,
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              & in H, di cento cinquanta. </s>
              <s>Ma eſſendo in D, ſarà trecento, eguale al peſo, come ſi propoſe. </s>
            </p>
            <p type="head">
              <s>PROPOSITIONE.</s>
            </p>
            <p type="main">
              <s>Si può vſare la lieua in vn'altro modo, cioè che in vna eſtremità ſia il ſoſtegno, e
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              nell'altra la forza, & il peſo attaccato in qual ſi voglia luogo, tra la forza, & il ſo­
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              ſtegno, nel qual caſo, la forza al peſo hà la medeſima proportione, che la diſtanza
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              trail ſoſtegno e'l peſo a tutta la lieua. </s>
            </p>
            <p type="main">
              <s>Come per eſſempio ſia la
                <lb/>
              lieua BA, il cui ſoſtegno
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              A, enell'altra eſtremità B,
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              la forza, & il peſo D, che ſia
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              appiccato nel punto C, di­
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              co che ſe tutta la lieua AB,
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              ſarà due volte maggiore
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              della AC, la metà della
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              forza poſta in B, ſoſterrà
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              il peſo; e parimente ſe eſſo
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              peſo ſarà appiccato in E,
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              di modo che la linea BA, fuſſe tripla della diſtanza AE, baſteria la terza parte della forza; e ſimil­
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              mente eſſendo BA, ſei volte maggiore di AD, la ſeſta parte della forza poſta in B, ſoſterrà l'iſteſ­
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              ſo peſo, benche di più la grauezza della lieua. </s>
            </p>
            <figure id="id.031.01.206.1.jpg" xlink:href="031/01/206/1.jpg" number="154"/>
            <p type="head">
              <s>COROLARIO.</s>
            </p>
            <p type="main">
              <s>Di quì ſi fà manifeſta la cagione del problema di Ariſtotele, quando due perſone portano vn peſo
                <lb/>
              legato a vna ſtanga, che ſopra le ſpalle dell'vno, e dell'altro ſi poſi, cioè quello che hauerà il peſo più
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              vicino, durerà tanto più fatica dell'altro, che l'hauerà più lontano, quanto ſarà la diſtanza dal centro
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              del peſo alla poſſanza che lo ſoſtenta, come per eſſempio, ripigliando la medeſima figura ſupponia­
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              mo, che la ſtanga, ouer lieua AB, poſi ſopra le due ſpalle ne'punti BA; cioè che il ſoſtegno A, ſia
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              vna ſeconda poſſanza eguale alla B. </s>
              <s>E perche la diſtanza BA, è doppia alla AC, la forza in A,
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              eſſendo il peſo D, attaccato in C, ſarà la metà di eſſo peſo, come anco ſarà all'altra parte B. </s>
              <s>E però
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              tutto verrà a eſſere egualmente ſoſtenuto dalle due ſpalle BA; Ma ſe poi eſſo peſo fuſſe attaccato
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              nel punto E, e che la diſtanza BA, ſia tripla alla AE, con la terza parte ſolo della forza poſta in
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              B, ſi douerà ſoſtentare: e così verrà a durare il doppio più fatica la A, ſi come è la diſtanza BE,
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              doppia della EA. </s>
              <s>Finalmente ſe il peſo fuſſe appiccato in D, eſſendo BA, cinque volte maggio­
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              re di AD, i cinque ſeſti rimanenti toccheranno alla ſpalla A, & alla B, vn ſeſto ſolo, che ſarà egua
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              le alla detta diſtanza BD, cioè cinque volte maggiore della DA; dal che finalmente concludere­
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              mo, che portandoſi il peſo con vna ſtanga ſopra le ſpalle di due huomini per vna ſtrada piana, l'vno
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              porterà ſempre più fatica dell'altro a proportione della diſtanza, che ſarà tra il centro del peſo D,
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              alla poſſanza che lo douerà ſoſtentare, che biſognaua moſtrare. </s>
            </p>
            <p type="main">
              <s>Ma ſe il propoſto peſo fuſſe dalle due poſſanze ſoſtentato, & portato per vna ſtrada non piana, ma
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              erta ouero in pendere, l'effetto ſaria molto contrario, benche dalle ragioni, & dimoſtrationi Ma­
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              tematiche ciò non ſia approbato, perche ſi confonderebbe il tutto, poi che il Matematico per fare le
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              ſue dimoſtrationi certe, & vere, ſuppone ſempre ciò fare con le ſemplice linee aſtratte dalla
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              materia, e che la grauezza del peſo, ſia ſoſtentata ſopra al piano dell'Orizonte, doue non poſſa acca­
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              dere alcuna di quelle diuerſità, che apporta il moto, & peſo de i corpi materiali, & i ſiti ſtrauaganti,
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              attendendo ſolo al fondamento della ragione, dal che ne dipende eſſere le dimoſtrationi Matemati­
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              che, nel primo grado di verità: ma perche con la ſcienza, è neceſſario la pratica nelle coſe materiali,
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              con lequali ſi elequiſcono l'opere reali, e maſſime le machine per leuare peſi, & altro, doue in cam­
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              bio di linee biſogna ſeruirſi de'traui di legno, & con ferramenti di peſo ſtrauaganti, come s'e detto,
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              & ſi dirà, & non hauendo coſi fatta pratica, con la ſcienza ſola ſi potranno bene diſegnare eſſe ma­
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              chine in carta con le ſue chiare dimoſtrationi, ma venendoſi poi a fare l'opera, l'effetto ſarà molto di­
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              uerſo, e ſolo per la diuerſità della materia, & non che le dimoſtrationi già fatte poſſino fallare, e per
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              confermatione di tale diuerſità, e maſſime de ſiti per doue ſi deue traſportare il peſo, proporremo, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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