Vitruvius Pollio, I dieci libri dell?architettura, 1567

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            <subchap1>
              <p type="main">
                <s id="s.002333">
                  <pb pagenum="105" xlink:href="045/01/113.jpg"/>
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                no quattro termini. </s>
                <s id="s.002334">c.d.e.f. de i quali ſaranno uentiquattro ordini. </s>
                <s id="s.002335">Il numero posto fuori della
                  <lb/>
                tauola dimoſtra due ordini, che fanno un ſolo interuallo, come il numero quinario, che è poſto
                  <emph.end type="italics"/>
                  <lb/>
                  <figure id="id.045.01.113.1.jpg" xlink:href="045/01/113/1.jpg" number="17"/>
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                  <emph type="italics"/>
                dentro la tauola, dinota che quel-
                  <emph.end type="italics"/>
                  <lb/>
                  <figure id="id.045.01.113.2.jpg" xlink:href="045/01/113/2.jpg" number="18"/>
                  <lb/>
                  <emph type="italics"/>
                l'ordine, a cui è prepoſto il deci­
                  <lb/>
                mo ſettimo, non compone ſpacio
                  <lb/>
                diuerſo da quello, che compone
                  <lb/>
                il quinto, perche ſi compone la
                  <lb/>
                iſteſſa proportione che è tra d. &
                  <lb/>
                e. & trac. & f. dinotata per lo
                  <lb/>
                decimo ſettimo modo. </s>
                <s id="s.002336">& di quel­
                  <lb/>
                la, che è tra c. & f. & trad. </s>
                <s id="s.002337">&
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                e. laqual pretende il quinto. </s>
                <s id="s.002338">
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                Adunque per li numeri eſtrinſe­
                  <lb/>
                chi ſi dinota, che queſti ordini,
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                quanto alla compoſitione delle
                  <lb/>
                proportioni ſono geminati, cioè
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                il terzodecimo. </s>
                <s id="s.002339">il quartodecimo,
                  <lb/>
                il quintodecimo, & coſi ſeguitan
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                do fin al uenteſimo quarto, il qua
                  <lb/>
                le anche ui s'include. </s>
                <s id="s.002340">la propor­
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                tione adunque, che tra a. & b.
                  <lb/>
                & la ſua conuerſa tra b. & a. ſi
                  <lb/>
                puo intendere, che ſia compoſta
                  <lb/>
                di dodici proportioni, tra quat­
                  <lb/>
                tro termini c. d. e. f. & coſi cia­
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                ſcuna delle predette. </s>
                <s id="s.002341">Eſſendo adunque trenta quelle che ſipoſſono componere, tutte le combina­
                  <lb/>
                tioni ſaranno trenta fiate dodici, che ſommano trecento & ſeſſanta. </s>
                <s id="s.002342">Ma di tutte queſte, posto,
                  <lb/>
                che la proportione, che è tra a. & b. ſia compoſta delle proportioni, che ſono: tra c. & d. & e.
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                & f. ſi dimoſtra, che ſole trenta ſei ſono utili. </s>
                <s id="s.002343">Ma le altre non tenere: & ci potrà baſtare di
                  <lb/>
                eſponerne quindici nella tauola, eſſendone quindici di quelle conuer-
                  <emph.end type="italics"/>
                  <lb/>
                  <figure id="id.045.01.113.3.jpg" xlink:href="045/01/113/3.jpg" number="19"/>
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                  <emph type="italics"/>
                ſe, & noi per la quarta propoſitione hauemo dimoſtrato, che ogni
                  <lb/>
                proportione conuerſa, ſi fa dalle conuerſe di quelle proportioni, del­
                  <lb/>
                lequali è compoſta la principale. </s>
                <s id="s.002344">come ſe la proportione, che è tra a.
                  <lb/>
                & b. è compoſta dalle proportioni che ſono tra c. & d. & tra e. & f.
                  <lb/>
                anche la conuerſa, cioè la proportione, che è tra b, & a. è compoſta
                  <lb/>
                dalle proportioni, che ſono tra. </s>
                <s id="s.002345">c. & d. et tra f. et e. et però eſpoſte
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                che ſaranno quindici di quelle, le altre quindici ſaranno manifeſte. </s>
                <s id="s.002346">
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                Eſponeremo adunque le quindici poſte nella tauola. </s>
                <s id="s.002347">dellequali di neceſ­
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                ſità noue ſaranno compoſte di due proportioni tra'l reſtante di quattro
                  <lb/>
                termini. </s>
                <s id="s.002348">ma le altre ſei non hanno queſta neceſſità. </s>
                <s id="s.002349">et quella, che ſi
                  <lb/>
                compone è manifeſta per la tauola, come anche è manifeſta quella, che
                  <lb/>
                non ſi compone.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="s.002350">
                  <emph type="italics"/>
                Ogni proportione adunque, laquale entra in compoſitione, a due
                  <lb/>
                modi ſi compone ſolamente: cioè dalla proportione del terzo al quar­
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                to, et del quinto al ſeſto, et ſimilmente dalla proportione del terzo al
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                ſeſto, et del quinto al quarto. </s>
                <s id="s.002351">per il che eſſendone noue compoſte ſi fa­
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                ranno diciotto compoſitioni, et altre tante delle loro conuerſe. </s>
                <s id="s.002352">Tren­
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                ta ſei adunque ſaranno i modi utili. </s>
                <s id="s.002353">Ma quelle, che non ſi compongo-
                  <emph.end type="italics"/>
                </s>
              </p>
            </subchap1>
          </chap>
        </body>
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    </archimedes>
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