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="N14EBE">
            <p id="id.2.1.1106.0.0" type="main">
              <s id="id.2.1.1106.2.0">
                <pb pagenum="96" xlink:href="037/01/207.jpg"/>
                <emph type="italics"/>
              ni tra il peſo, & la poſſanza ſoprapartienti, & molteplici ſopraparticolari, &
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              molteplici ſoprapartienti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="id.2.1.1107.0.0" type="main">
              <s id="id.2.1.1107.1.0">“Et dapoi le ſopraparticolari, & le ſotto ſopraparticolari furono dichiarate. </s>
              <s id="id.2.1.1107.2.0">Dal co
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              noſcimento del ſopraparticolare ſi intende ageuolmente il ſotto ſopraparticolare
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              che gli è oppoſto; pero che paragonando come è detto il 3. co'l 2. naſce il ſo­
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              praparticolare, & per lo contrario il 2. co'l 3. ſi produce il ſotto ſopraparticolare
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              per la forza di quella voce ſotto. </s>
            </p>
            <p id="id.2.1.1108.0.0" type="main">
              <s id="id.2.1.1108.1.0">“Hora reſta &c. </s>
              <s id="id.2.1.1108.2.0">Qui propone di trattare delle proportioni, che il peſo hà con la poſ
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              ſanza nel genere ſoprapartiente, & nel genere compoſto del molteplice ſoprapar
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              ticolare, & del molteplice ſoprapartiente. </s>
              <s id="id.2.1.1108.3.0">il genere ſo prapartiente è diuerſo dal
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              ſopraparticolare, che doue nel ſopraparticolare vna quantità contiene l'altra vna
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              ò più volte, & più parte, che può interamente numerare & l'vna, & l'altra: nel
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              ſoprapartiente contiene vna, ò più volte, & dauantaggio parte che non le puo­
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              te numerare, & miſurare perfettamente, come il cinque contiene il 3. vna volta,
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              & piu parte di eſſo, che è il 2. il quale non è miſura commune di ambidue loro,
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              & ſi denomina ſoprabipartiente terze, pero che contiene vna volta, & piu due
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              terze parti del contenuto. </s>
            </p>
            <p id="id.2.1.1109.0.0" type="main">
              <s id="id.2.1.1109.1.0">“Segue poi. </s>
              <s id="id.2.1.1109.2.0">Et le molteplici ſopraparticolari, che hò di ſopra moſtrato. </s>
              <s id="id.2.1.1109.3.0">Componen
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              do due generi inſieme il molteplice, & il ſopraparticolare naſce queſto moltepli­
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              ce ſopraparticolare, nelquale vna quantità contiene l'altra molte volte, & più par
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              te di eſſa, che è miſura commune di ambedue. </s>
              <s id="id.2.1.1109.4.0">La primiera ſua ſpetie è il 5. pa­
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              ragonato co'l due, che lo contiene due volte, & piu la metà di lui, cioè vno, mi­
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              ſura di ambedue. </s>
              <s id="id.2.1.1109.5.0">Chiamaſi queſta proportione doppia ſeſquialtera. </s>
              <s id="id.2.1.1109.6.0">Mettendo
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              parimente inſieme il genere molteplice co'l ſoprapartiente, ſi fa il molteplice ſo­
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              prapartiente, il quale è differente dal ſopradetto per riſpetto che in lui la maggior
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              quantità contiene la minore molte volte, & piu parte di eſſa, che non puote eſſe­
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              re loro miſura commune; la prima ſpetie del qual genere è come 8. à 3. peroche
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              l'otto contiene il 3. due volte, & piu parte di eſſo 3. cioè 2. che non gli puo miſu
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              rare ambidue, concioſia che il 2. non puo miſurare il 3. come fà l'otto per eſſere
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              queſti due numeri 8. & 3. tra ſe primi. </s>
              <s id="id.2.1.1109.7.0">& chiamaſi proportione doppia ſoprabi­
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              partiente. </s>
              <s id="id.2.1.1109.8.0">Vuole dunque l'autore andar inueſtigando le proportioni fra il peſo,
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              & la poſſanza ne i predetti generi ancora, come hà fatto ne gli altri. </s>
            </p>
            <p id="id.2.1.1110.0.0" type="main">
              <s id="id.2.1.1110.1.0">Da queſte poche coſe, lequali hò qui narrato per ageuolare l'intédimento de i voca­
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              boli pertinenti alle proportioni poſte da l'autore, ſi potrà facilmente con qual­
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              che ſtudio comprendere tutta la ſomma delle vltime dimoſtrationi della taglia,
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              nelle quali ſono queſti vocaboli di proportioni, quantunque in ogni loco quaſi
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              con gli eſſempi ſtesſi de' numeri ſiano dall'autore manifeſtate. </s>
            </p>
            <p id="id.2.1.1111.0.0" type="head">
              <s id="id.2.1.1111.1.0">PROPOSITIONE XXVI. </s>
            </p>
            <p id="id.2.1.1112.0.0" type="head">
              <s id="id.2.1.1112.1.0">PROBLEMA. </s>
            </p>
            <p id="id.2.1.1113.0.0" type="main">
              <s id="id.2.1.1113.1.0">Se vogliamo trouare la proportione ſoprapartiente, come ſe la
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              proportione, laquale hà il peſo alla poſſanza che ſoſtiene il pe
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              ſo ſarà ſoprabipartiente, come il cinque à tre. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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