Vitruvius Pollio, I dieci libri dell?architettura, 1567

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        <body>
          <chap>
            <subchap1>
              <p type="main">
                <s id="s.002353">
                  <pb pagenum="106" xlink:href="045/01/114.jpg"/>
                  <figure id="id.045.01.114.1.jpg" xlink:href="045/01/114/1.jpg" number="20"/>
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                no ſono ſei, et le loro conuerſe ſei, però dodici ſono inutili. </s>
                <s id="s.002354">Adunque
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                tutti i modi ſi utili, come inutili ſono quaranta otto. </s>
                <s id="s.002355">Soppoſto
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                adunque il primo modo, cioè che la proportione che è tra a el b. ſia
                  <lb/>
                composta delle proportioni che ſono tra c, et d. et tra e, et f. io dimo­
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                strerò il ſecondo, che è compoſto della iſteſſa, che è trac. </s>
                <s id="s.002356">et. </s>
                <s id="s.002357">f. et tra,
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                e. et d. percheio ponerò tra c, et f. la proportione di d, et e. doue la
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                proportione tra c, et f. ſarà compoſta delle proportioni, che ſono tra
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                c, & d. & tra d, & c. & trae. </s>
                <s id="s.002358">& f. perilche ne ſeguita, che le pro­
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                portioni che ſono tra e, & f. & tra e, & d. ſaranno composte delle
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                proportioni che ſono trac, & d. tra d, & e. & tra e. & f. & trae.
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                </s>
                <s id="s.002359">& d. Male proportioni che ſono tra c, & d. trad. </s>
                <s id="s.002360">& e. et tra e. et
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                d. compongono quella, che è tra e. et d. per la terza propoſitio­
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                ne. </s>
                <s id="s.002361">poſti d, et c. tra c. et d. adunque e. à d. et c. ad f. ſono ſi come c.
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                à d. et a. ad f. ma la proportione, che è tra a. et b. è compoſta delle
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                proportioni che ſono tra e. et d. et tra e, et f. adunque la proportione
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                tra a, et b. ſarà composta delle proportioni, che ſono tra c. & f. et
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                tra e. et d. che ſono le poſte nella concluſione.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="s.002362">
                  <emph type="italics"/>
                Il terzo modo è, che anche la proportione tra a, et c. ſarà compoſta della proportione di b, à
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                d. et di c. ad f. ilche è manifeſto, perche poſto b. tra a. et c. la proportione che è tra a. et c. ſarà
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                compoſta da quella, che è tra a. et b. tra b. et c. ma la proportione, che è tra a, et b. ſi compo­
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                ne di c. et d. et di e. et f. ſecondo il ſuppoſto da noi. </s>
                <s id="s.002363">adunque a, à c. è fa ta di b. et c. et
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                et di c. et d. et die, et f. ma b, à c. et c. à d. compongono la b. à d. trapoſto il c. tra b. et e. </s>
                <s id="s.002364">
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                Adunque la proportione, che è tra a, et c. è compoſta di b. et d. et di e. et f.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="s.002365">
                  <emph type="italics"/>
                Il quarto modo procede dal terzo, ſi come il ſecondo dal primo. </s>
                <s id="s.002366">poſti tra b, & f. commune­
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                mente d. & e. & coſi tutti i modi pari, con i loro diſpari ſi collegano, per iſchiſare il repetere
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                la iſteſſa uia.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="s.002367">
                  <emph type="italics"/>
                Il quinto modo è che la proportione di a, ad e. è compoſta di b, ad f. & di c. à d. perche po­
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                ſto b. tra a, & e. ſi fa l'argomento del terzo. </s>
                <s id="s.002368">perche lo a. ad e. è compoſto dello a. al b. & del b.
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                allo e. ma lo a. al b. è compoſto dell' e. al f. & del c. al d. perche coſi hauemo poſto. </s>
                <s id="s.002369">adunque a,
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                ad e. ſi compone di b. à c. & die. </s>
                <s id="s.002370">ad f. & di c. </s>
                <s id="s.002371">à d. ma b. ad e. & e. ad f. compongono b. ad f. tra­
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                poſto e. tra b, & f. adunque la proportione tra a. & e. è compoſta delle proportioni, che ſono
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                tra b. & f. & tra c, & d.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="s.002372">
                  <emph type="italics"/>
                Il ſeſto modo ſi caua dal quinto, per lo argomento del ſecondo, trapoſto f. & c. tra b. & d.
                  <emph.end type="italics"/>
                  <emph type="italics"/>
                Il ſettimo compone la proportione di b, à d. delle proportioni di à. </s>
              </p>
              <p type="main">
                <s id="s.002373">a c. & di f. ad e. perche
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                eſſendo compoſto a. b. di c. à d. & die. </s>
                <s id="s.002374">ad f. ne ſegue per la quarta proportione, che la proportio­
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                ne tra b, & a. ſarà compoſta di d. & c. & di f. & e. poſto adunque a. tra b. & d. la proportio­
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                ne, che è tra b, & d. ſarà fatta di b. & a. & di a, & d. ma b, & a. è compoſto di d. & c. et di f.
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                & e. adunque la proportione di b. à d. ſarà compoſta di tre proportioni. </s>
                <s id="s.002375">cioè di a, à d. di d, à
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                c. & di f. ad e. </s>
                <s id="s.002376">Ma la a, à d. & la d. à c. compongono quella, che è tra a. & c. trappoſto
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                d. tra a, & c. adunque la proportione di b. à d. ſarà composta delle proportioni di a, à c. &
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                di f. ad e. ilche era il propoſito.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="s.002377">
                  <emph type="italics"/>
                L'ottauo modo. </s>
                <s id="s.002378">ſi come preſupoſto il primo ſi caua il ſecondo, coſi per lo iſteſſo argomento
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                ſi caua l'ottauo i ſuppoſti, & prouati ne i precedenti, posto in mezo di a. & e. e. & f.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="s.002379">
                  <emph type="italics"/>
                Il nono. </s>
                <s id="s.002380">ſimilmente la proportione di b, ad e. ſarà compoſta delle proportioni di a. ad e. & di
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                d. à c. perche b ad a, è compoſto di d. à c. & di f. ad e. trapposto a. tra b. & f. ſarà la pro­
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                portione tra b, & f. compoſta di b. ad a. & di a. ad f. & però b, ad f. ſarà compoſta di a. ad f.
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                & di f. ad e. & di d. à c. ma a. ad f. & f. ad e. compongono a. ad e. adunque b. & f. è com­
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                poſta di a. & e. & di d. & c.
                  <emph.end type="italics"/>
                  <emph type="italics"/>
                Il decimo. </s>
              </p>
            </subchap1>
          </chap>
        </body>
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    </archimedes>
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