Vitruvius Pollio, I dieci libri dell?architettura, 1567

List of thumbnails

< >
111
111 		112
112
113
113 		114
114
115
115 		116
116
117
117 		118
118
119
119 		120
120
< >
page |< < of 520 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <p type="main">
                <s id="s.002309">
                  <pb pagenum="104" xlink:href="045/01/112.jpg"/>
                  <emph type="italics"/>
                denominata la tripla. </s>
                <s id="s.002310">ſia dunque due a. quattro b. dodici c. il denominatore tra due & quat
                  <lb/>
                tro d. tra quattro & dodici e. & il denominatore tra a & c ſia f. perche adunque da
                  <lb/>
                f. nel c. ſi fa a. & da e in c ſi fa b. per la prima propoſitione lo f. allo e. è come lo
                  <lb/>
                a. al b. & però eſſendo il d. il denominatore tra a & b. egli ſarà il denominatore tra
                  <lb/>
                f. & e. adunque per la iſteſſa prima propoſitione dal d in e ſi fa f. perche adunque la
                  <lb/>
                denominatione dello a. al c. è prodotta dalla denominatione del b. al c. ne ſegue per la ter
                  <lb/>
                za diffinitione, che la proportione, che è tra lo a, & il c. come tra due & dodici, che è la
                  <lb/>
                ſeſtupla, ſia compoſta dalla proportione, che è tra lo a, & b. cioè tra due, & quattro, che
                  <lb/>
                è doppia, & tra b. & c. cioè quattro & dodici, che è tripla. </s>
                <s id="s.002311">adunque da una doppia, &
                  <lb/>
                da una tripla ne naſce una ſeſtupla. </s>
                <s id="s.002312">Seguita la terza propoſitione di Alchindo.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="s.002313">
                  <emph type="italics"/>
                Siano quanti mezi ſi noglia, dico che la proportione, che è tra gli estremi, è compoſta di
                  <lb/>
                tutte le proportioni, che hanno i mezi tra ſe. </s>
                <s id="s.002314">Sia tra a, & d. due intermedij b, & c. io di­
                  <lb/>
                co, che la proportione di a, à d. è composta delle proportioni, che ſono tra a, & b. tra
                  <lb/>
                b, & c. tra c & d. imperoche per la precedente la proportione, che è tra a, & c. è
                  <lb/>
                compoſta dalla proportione, che è tra a & b. & tra b & c. ma la proportione che è tra
                  <lb/>
                b, & d. è composta dalla proportione che è tra b. & c. & c, & d. per la iſteſſa pro­
                  <lb/>
                poſitione. </s>
                <s id="s.002315">adonque la proportione, che è tra a, & d. è compoſta di tutte proportioni,
                  <lb/>
                che ſono tra i mezi. </s>
                <s id="s.002316">& coſi ſi hauerà a prouare, quando fuſſero piu mezi. </s>
                <s id="s.002317">& di ſopra
                  <lb/>
                ne hauemo con gli eſſempi detto a baſtanza: ma hora ſi replica per ſeguitar l'ordine di Al­
                  <lb/>
                chindo, & per eſſercitio della memoria, in coſa di tantaimportanza.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="s.002318">
                  <emph type="italics"/>
                La quarta è, che ſe alcuna proportione, è compoſta di due proportioni, la ſua conuerſa
                  <lb/>
                è compoſta delle conuerſe. </s>
                <s id="s.002319">ſia la proportione di a, à b. compoſta della proportione di c, à
                  <lb/>
                d. & di e, à f. io dico che la proportione di b. ad a. ſarà compoſta della proportio­
                  <lb/>
                ne di d, à c. & di f. ad e. perche ſiano continuate le proportioni di c, à d. & die,
                  <lb/>
                ad f. tra g. h. K. di modo che g. ſia ad h. come c, à d. & h, à K. come e. ad
                  <lb/>
                f. dico, che la proportione tra a, & b. ſarà compoſta della proportione di g. ad h. & di
                  <lb/>
                h. à K. & però per la ſeconda propoſitione, la proportione di a, à b.ſarà come la propor­
                  <lb/>
                tione di g, à K. adunque all'incontro la proportione di b ad a. ſarà come K. à g. mala pro
                  <lb/>
                portione di K à g. per la iſteſſa propoſitione è fatta dalla proportione di K. ad h. & di h. à
                  <lb/>
                g. ma K ad h. è come f. ad e. & h. à g. & come d. à c. adunque b ad a. ſarà compo­
                  <lb/>
                ſto dalla proportione, che è tra d & e. & tra f. & e. il che è lo intento noſtro. </s>
                <s id="s.002320">Finite le
                  <lb/>
                diffinitioni, & le propoſitioni, che pone Alchindo, ſiuiene alle regole, lequali ſono queſte.
                  <emph.end type="italics"/>
                </s>
              </p>
              <p type="main">
                <s id="s.002321">
                  <emph type="italics"/>
                Quando di ſei quantità la proportione, che è tra la prima, & la ſeconda, è compoſta
                  <lb/>
                della proportione, che ha la terza alla quarta, & la quinta alla ſeſta, ſi fanno tre­
                  <lb/>
                cento, & ſeſſanta ſpecie di compoſuioni, di trentaſei, delle quali ſolamente ci potemo
                  <lb/>
                ſeruire. </s>
                <s id="s.002322">il reſtante è inutile. </s>
                <s id="s.002323">& queſto è manifeſto. </s>
                <s id="s.002324">ſe noi ponemo, che la proportio­
                  <lb/>
                ne, che è tra a, & b. ſia compoſta delle proportioni, che ſono tra e, & d. tra e, & f.
                  <lb/>
                perche eſſendo ſei i termini, ſi puo intendere la proportione di due, qual ſi uoglia eſſer composta
                  <lb/>
                di due proportioni, che ſiano tra i quattro termini reſtanti. </s>
                <s id="s.002325">Il che ſarà dichiarito poterſi fare
                  <lb/>
                per uia della moltiplicatione. </s>
                <s id="s.002326">Da queſti ſei termini uengono trenta ſpacij diſtinti. </s>
                <s id="s.002327">dieci da a. ot­
                  <lb/>
                to da b. ſei da c. quattro da d. due da e. & niuno da f. perche tutti ſono ſtati prima compreſi. </s>
                <s id="s.002328">
                  <lb/>
                le quali coſe ſono manifeſte dalla ſottopoſta tauola. </s>
                <s id="s.002329">doue ſono cinque compartimenti, nel primo
                  <lb/>
                de i quali è la comparatione di a. agli altri termini, & de gli altri termini ad a. nel ſecondo è
                  <lb/>
                la comparatione di b, agli altri, & de gli altri à b. nel terzo è la comparatione del e. nel quar
                  <lb/>
                to di b. nel quinto die. </s>
                <s id="s.002330">agli altri, & de gli altri a quelli. </s>
                <s id="s.002331">perche adunque erano ſei termini ri­
                  <lb/>
                moſſidue, che faceuano lo ſpacio compoſto, i reſtanti ſeranno quattro. </s>
                <s id="s.002332">de i quali ne ſaranno uin­
                  <lb/>
                tiquattro ordini, che fanno ſolamente dodici ſpacij. </s>
                <s id="s.002333">& perche questo s'intenda bene ſiano ri­
                  <lb/>
                moſſi queſti termini a b. che fanno la proportione dia, à b. & la conuerſa di b. ad a. reſtaran-
                  <emph.end type="italics"/>
                </s>
              </p>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum