Vitruvius, I Dieci Libri dell' Architettvra di M. Vitrvvio, 1556

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      <text xml:lang="it" type="free">
        <div xml:id="echoid-div174" type="section" level="1" n="27">
          <p style="it">
            <s xml:id="echoid-s6570" xml:space="preserve">
              <pb o="61" file="0067" n="69" rhead="TERZO."/>
            tutti ſono ſtati preſi. </s>
            <s xml:id="echoid-s6571" xml:space="preserve">lequal coſe manifeſte ſono nclla ſottoſcritta tauola, doue ſono cinque compartimenti, nel primo de i quali ė la compara-
              <lb/>
            tione del a. </s>
            <s xml:id="echoid-s6572" xml:space="preserve">à gli altri termini, & </s>
            <s xml:id="echoid-s6573" xml:space="preserve">de gli altri termini all’a. </s>
            <s xml:id="echoid-s6574" xml:space="preserve">Nel ſecondo é la comparatione del b. </s>
            <s xml:id="echoid-s6575" xml:space="preserve">à gli altri, & </s>
            <s xml:id="echoid-s6576" xml:space="preserve">de gli altri al b. </s>
            <s xml:id="echoid-s6577" xml:space="preserve">nel terzo è
              <lb/>
            la comparatione del c. </s>
            <s xml:id="echoid-s6578" xml:space="preserve">nel quarto del d. </s>
            <s xml:id="echoid-s6579" xml:space="preserve">nel quinto del e. </s>
            <s xml:id="echoid-s6580" xml:space="preserve">à gli altri, et de gli altri à quelli, perche ſono di ciaſcun di due termini due ſpatij. </s>
            <s xml:id="echoid-s6581" xml:space="preserve">come
              <lb/>
            dal a. </s>
            <s xml:id="echoid-s6582" xml:space="preserve">al b. </s>
            <s xml:id="echoid-s6583" xml:space="preserve">uno, & </s>
            <s xml:id="echoid-s6584" xml:space="preserve">l’altro dal b. </s>
            <s xml:id="echoid-s6585" xml:space="preserve">all’a. </s>
            <s xml:id="echoid-s6586" xml:space="preserve">& </s>
            <s xml:id="echoid-s6587" xml:space="preserve">coſi de gli altri, perche adunque eran ſei termini, rimosſi due, che faceuano lo ſpatio compoſto,
              <lb/>
            i reſtanti ſer anno quattro, de quali ne ſeranno uentiquattro ordini, che fanno ſolamente dodici ſpatij, & </s>
            <s xml:id="echoid-s6588" xml:space="preserve">perche queſto chiaramente s’intendi,
              <lb/>
              <note style="it" position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">
                <lb/>
              dritta \\ a.a.a.a.a. \\ b.c.d.e.f. # conuerſa \\ b.c.d.e.f. \\ a.a.a.a.a.
                <lb/>
              ## Primo ordine dieci.
                <lb/>
              dritta \\ b.b.b.b. \\ c.d.e.f. # conuerſa \\ c.d.e.f. \\ b.b.b.b.
                <lb/>
              ## Secondo ordine otto.
                <lb/>
              dritta \\ c.c.c. \\ d. e.f. # conuerſa \\ d.e.f. \\ c.c.c.
                <lb/>
              ## Terzo ordine ſei.
                <lb/>
              dritta \\ d. d. \\ c. f. # conuerſa \\ e. f. \\ d. d.
                <lb/>
              ## Quarto ordine quattro.
                <lb/>
              dritta \\ e. \\ f. # conuerſa \\ f. \\ e.
                <lb/>
              ## Quinto ordine due.
                <lb/>
              </note>
              <note style="it" position="right" xlink:label="note-0067-02" xlink:href="note-0067-02a" xml:space="preserve">
                <lb/>
              13 # c. d. \\ e. f. \\ Primo # d. c. \\ e. f. \\ Settimo # 19
                <lb/>
              14 # c. d. \\ f. e. \\ Secondo # d. c. \\ f. e. \\ Ottauo # 20
                <lb/>
              15 # c. e. \\ d. f. \\ Terzo # e. c. \\ d. f. \\ Nono # 21
                <lb/>
              16 # c. e. \\ f. d. \\ Quarto # e. c. \\ f. d. \\ Decimo # 22
                <lb/>
              17 # c. f. \\ d. e. \\ Quinto # f. c. \\ d. e. \\ Vndecimo # 23
                <lb/>
              18 # e. f. \\ e. d. \\ Seſto # f. e. \\ c. d. \\ duodecimo # 24
                <lb/>
              </note>
            ſian rimosſi queſti termini a. </s>
            <s xml:id="echoid-s6589" xml:space="preserve">& </s>
            <s xml:id="echoid-s6590" xml:space="preserve">b. </s>
            <s xml:id="echoid-s6591" xml:space="preserve">che fanno la proportione di a.</s>
            <s xml:id="echoid-s6592" xml:space="preserve">a
              <lb/>
            b. </s>
            <s xml:id="echoid-s6593" xml:space="preserve">& </s>
            <s xml:id="echoid-s6594" xml:space="preserve">la conuerſa del b al a. </s>
            <s xml:id="echoid-s6595" xml:space="preserve">reſteranno quattro termini c.</s>
            <s xml:id="echoid-s6596" xml:space="preserve">d.</s>
            <s xml:id="echoid-s6597" xml:space="preserve">e.</s>
            <s xml:id="echoid-s6598" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6599" xml:space="preserve">de
              <lb/>
            i quali ſeranno uentiquattro ordini. </s>
            <s xml:id="echoid-s6600" xml:space="preserve">il numero posto fuori della
              <lb/>
            tauola dimoſtra due ordini, che fanno un ſolo interuallo, come il
              <lb/>
            numero quinario, che è poſto dentro la tauola dinota, che quel-
              <lb/>
              <note position="left" xlink:label="note-0067-03" xlink:href="note-0067-03a" xml:space="preserve">10</note>
            l’ ordine à cui è preposto il decimo ſettimo non compone ſpatio di
              <lb/>
            uerſo da quello, che compone il quinto, perche ſi compone la
              <lb/>
            iſteſſa proportione di quella che è tra’l d, & </s>
            <s xml:id="echoid-s6601" xml:space="preserve">l’e. </s>
            <s xml:id="echoid-s6602" xml:space="preserve">& </s>
            <s xml:id="echoid-s6603" xml:space="preserve">il c & </s>
            <s xml:id="echoid-s6604" xml:space="preserve">lo f. </s>
            <s xml:id="echoid-s6605" xml:space="preserve">di-
              <lb/>
            notata per lo decimo ſettimo modo, & </s>
            <s xml:id="echoid-s6606" xml:space="preserve">di quella che è tra’l c & </s>
            <s xml:id="echoid-s6607" xml:space="preserve">
              <lb/>
            lo f. </s>
            <s xml:id="echoid-s6608" xml:space="preserve">& </s>
            <s xml:id="echoid-s6609" xml:space="preserve">tra’l d & </s>
            <s xml:id="echoid-s6610" xml:space="preserve">l’e. </s>
            <s xml:id="echoid-s6611" xml:space="preserve">laqual pretende il quinto. </s>
            <s xml:id="echoid-s6612" xml:space="preserve">Adunque per li
              <lb/>
            numeri eſtrinſeci ſi dinota, che queſti ordini quanto alla compoſi
              <lb/>
            tione delle proportioni ſono geminati, cio è il terzo decimo, il
              <lb/>
            quartodecimo, il quintodecimo, & </s>
            <s xml:id="echoid-s6613" xml:space="preserve">coſi ſeguitando fin al uente-
              <lb/>
            ſimo quarto, ilquale ancho ui s’include. </s>
            <s xml:id="echoid-s6614" xml:space="preserve">La proportione adunque
              <lb/>
            che è tra a. </s>
            <s xml:id="echoid-s6615" xml:space="preserve">& </s>
            <s xml:id="echoid-s6616" xml:space="preserve">b, & </s>
            <s xml:id="echoid-s6617" xml:space="preserve">la ſua conuerſa trab. </s>
            <s xml:id="echoid-s6618" xml:space="preserve">& </s>
            <s xml:id="echoid-s6619" xml:space="preserve">a. </s>
            <s xml:id="echoid-s6620" xml:space="preserve">ſi può intendere
              <lb/>
              <note position="left" xlink:label="note-0067-04" xlink:href="note-0067-04a" xml:space="preserve">20</note>
            che ſia composta di dodici proportioni tra quattro termini c.</s>
            <s xml:id="echoid-s6621" xml:space="preserve">d.</s>
            <s xml:id="echoid-s6622" xml:space="preserve">e.
              <lb/>
            </s>
            <s xml:id="echoid-s6623" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6624" xml:space="preserve">& </s>
            <s xml:id="echoid-s6625" xml:space="preserve">coſi ciaſcuna delle predette. </s>
            <s xml:id="echoid-s6626" xml:space="preserve">A dunque eſſendone trenta, che
              <lb/>
            ſi poſſono componer tutte le combinationi ſeranno trenta uolte
              <lb/>
            dodici, che fanno trecento ſeſſanta. </s>
            <s xml:id="echoid-s6627" xml:space="preserve">Ma di tutte queſte poſto che
              <lb/>
            la proportione che è tra l’a & </s>
            <s xml:id="echoid-s6628" xml:space="preserve">il b, composta ſia delle proportio
              <lb/>
            ni che ſono tra’l c el d. </s>
            <s xml:id="echoid-s6629" xml:space="preserve">& </s>
            <s xml:id="echoid-s6630" xml:space="preserve">l’e el’f, ſi dimoſtrino che ſolo trenta ſei
              <lb/>
            ſono utili, ma le altre non tenere. </s>
            <s xml:id="echoid-s6631" xml:space="preserve">& </s>
            <s xml:id="echoid-s6632" xml:space="preserve">ci potra baſtare di eſpo-
              <lb/>
            nerne quindeci nella tauola, eſſendcne quindeci di quelle conuer-
              <lb/>
            ſe, & </s>
            <s xml:id="echoid-s6633" xml:space="preserve">noi per la quarta propoſitione dimoſtrato hauemo, che
              <lb/>
            ogni conuerſa proportione, ſi fa dalle conuer ſe di quelle proportioni, delle quali è composta la principale. </s>
            <s xml:id="echoid-s6634" xml:space="preserve">come ſe la proportione, che è tra l’a
              <lb/>
              <note position="left" xlink:label="note-0067-05" xlink:href="note-0067-05a" xml:space="preserve">30</note>
            e’l b. </s>
            <s xml:id="echoid-s6635" xml:space="preserve">è compoſta dalle proportioni che ſono tra’l c. </s>
            <s xml:id="echoid-s6636" xml:space="preserve">e’l d. </s>
            <s xml:id="echoid-s6637" xml:space="preserve">& </s>
            <s xml:id="echoid-s6638" xml:space="preserve">tra l’e & </s>
            <s xml:id="echoid-s6639" xml:space="preserve">lo f.</s>
            <s xml:id="echoid-s6640" xml:space="preserve">ancho la conuerſa, cioè la proportione, che è tra’lb, & </s>
            <s xml:id="echoid-s6641" xml:space="preserve">l’a, ſerà compo
              <lb/>
            ſta dalle proportioni del d al c. </s>
            <s xml:id="echoid-s6642" xml:space="preserve">& </s>
            <s xml:id="echoid-s6643" xml:space="preserve">del f.</s>
            <s xml:id="echoid-s6644" xml:space="preserve">all’e. </s>
            <s xml:id="echoid-s6645" xml:space="preserve">& </s>
            <s xml:id="echoid-s6646" xml:space="preserve">però eſposte quindeci di quelle, le altre quindeci ci ſaranno paleſi.</s>
            <s xml:id="echoid-s6647" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6648" xml:space="preserve">Eſponeremo adunque le quindeci poste nella tauola, dellequali noue ſeranno di necesſità composte dì
              <lb/>
              <note style="it" position="right" xlink:label="note-0067-06" xlink:href="note-0067-06a" xml:space="preserve">
                <lb/>
              Prima. # a. b. \\ compoſta
                <lb/>
              Seconda. # a. c. \\ compoſta
                <lb/>
              Terza. # a. d.
                <lb/>
              Quarta. # a. e. \\ compoſta
                <lb/>
              Quinta. # a. f.
                <lb/>
              Sesta. # b. c.
                <lb/>
              Settima. # b. d. \\ compoſta
                <lb/>
              Ottaua. # b. e
                <lb/>
              Nona. # b. f. \\ compoſta
                <lb/>
              Decima. # c. d. \\ compoſta
                <lb/>
              Vndecima. # c. e.
                <lb/>
              Duodecima. # c. f. \\ compoſta
                <lb/>
              Terzadecima. # d. e. \\ compoſta
                <lb/>
              Quartadecima. \\ Quintadecima. # d. f. \\ e. f. \\ compoſta
                <lb/>
              </note>
            due proportioni tra il reſtante di quattro termini, ma le altre ſei non di necesſità ſi compongono,
              <lb/>
            & </s>
            <s xml:id="echoid-s6649" xml:space="preserve">quella, che ſi compone per la tauola è manifeſtà, come è chiara ancho quella, che non ſi compo
              <lb/>
            ne. </s>
            <s xml:id="echoid-s6650" xml:space="preserve">Ogni proportione adunque che ſi compone à due modi ſolamente ſi compone, cioè dalla propor-
              <lb/>
            tione del terzo al quarto, & </s>
            <s xml:id="echoid-s6651" xml:space="preserve">del quinto al ſeſto, & </s>
            <s xml:id="echoid-s6652" xml:space="preserve">ſimilmente dalla proportione del terzo al ſe-
              <lb/>
            sto, & </s>
            <s xml:id="echoid-s6653" xml:space="preserve">del quinto al quarto. </s>
            <s xml:id="echoid-s6654" xml:space="preserve">Per ilche eſſendone noue composte, ſi fanno dieciotto compoſitioni,
              <lb/>
            & </s>
            <s xml:id="echoid-s6655" xml:space="preserve">altretante delle loro conuerſe. </s>
            <s xml:id="echoid-s6656" xml:space="preserve">Trentaſei adunque ſeranno i modi utili. </s>
            <s xml:id="echoid-s6657" xml:space="preserve">Ma quelle, che non ſi
              <lb/>
            compongono ſono ſei, & </s>
            <s xml:id="echoid-s6658" xml:space="preserve">le loro conuerſe ſei, però dodici ſono inutili. </s>
            <s xml:id="echoid-s6659" xml:space="preserve">Tutti i modi adunque ſi utili
              <lb/>
              <note position="left" xlink:label="note-0067-07" xlink:href="note-0067-07a" xml:space="preserve">40</note>
            come inutili ſono quaranta otto.</s>
            <s xml:id="echoid-s6660" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6661" xml:space="preserve">Soppoſto adunque il primo modo, cioè che la proportione che è tra l’a e’lb. </s>
            <s xml:id="echoid-s6662" xml:space="preserve">composta ſia delle propor-
              <lb/>
            tioni, che ſono tra’l c. </s>
            <s xml:id="echoid-s6663" xml:space="preserve">e’l d. </s>
            <s xml:id="echoid-s6664" xml:space="preserve">& </s>
            <s xml:id="echoid-s6665" xml:space="preserve">tra lo e. </s>
            <s xml:id="echoid-s6666" xml:space="preserve">et lo f. </s>
            <s xml:id="echoid-s6667" xml:space="preserve">Io dimoſtrero il ſecondo. </s>
            <s xml:id="echoid-s6668" xml:space="preserve">che è compoſto della iſteſſa che
              <lb/>
            è tra c. </s>
            <s xml:id="echoid-s6669" xml:space="preserve">& </s>
            <s xml:id="echoid-s6670" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6671" xml:space="preserve">& </s>
            <s xml:id="echoid-s6672" xml:space="preserve">tra e & </s>
            <s xml:id="echoid-s6673" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6674" xml:space="preserve">perche io ponero tra c. </s>
            <s xml:id="echoid-s6675" xml:space="preserve">& </s>
            <s xml:id="echoid-s6676" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6677" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6678" xml:space="preserve">& </s>
            <s xml:id="echoid-s6679" xml:space="preserve">e. </s>
            <s xml:id="echoid-s6680" xml:space="preserve">& </s>
            <s xml:id="echoid-s6681" xml:space="preserve">la proportione tra c. </s>
            <s xml:id="echoid-s6682" xml:space="preserve">& </s>
            <s xml:id="echoid-s6683" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6684" xml:space="preserve">ſerà
              <lb/>
            compoſta delle proportioni, che ſono tra c. </s>
            <s xml:id="echoid-s6685" xml:space="preserve">& </s>
            <s xml:id="echoid-s6686" xml:space="preserve">d, & </s>
            <s xml:id="echoid-s6687" xml:space="preserve">tra d & </s>
            <s xml:id="echoid-s6688" xml:space="preserve">e. </s>
            <s xml:id="echoid-s6689" xml:space="preserve">& </s>
            <s xml:id="echoid-s6690" xml:space="preserve">tra e & </s>
            <s xml:id="echoid-s6691" xml:space="preserve">f, per il che ne ſeguirà, che
              <lb/>
            le proportioni che ſono tra c & </s>
            <s xml:id="echoid-s6692" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6693" xml:space="preserve">& </s>
            <s xml:id="echoid-s6694" xml:space="preserve">tra e & </s>
            <s xml:id="echoid-s6695" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6696" xml:space="preserve">ſeranno compoſte delle proportioni, che ſono tra
              <lb/>
            c. </s>
            <s xml:id="echoid-s6697" xml:space="preserve">& </s>
            <s xml:id="echoid-s6698" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6699" xml:space="preserve">tra d & </s>
            <s xml:id="echoid-s6700" xml:space="preserve">e. </s>
            <s xml:id="echoid-s6701" xml:space="preserve">& </s>
            <s xml:id="echoid-s6702" xml:space="preserve">tra e & </s>
            <s xml:id="echoid-s6703" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6704" xml:space="preserve">& </s>
            <s xml:id="echoid-s6705" xml:space="preserve">tra e & </s>
            <s xml:id="echoid-s6706" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6707" xml:space="preserve">Ma le proportioni che ſono tra c & </s>
            <s xml:id="echoid-s6708" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6709" xml:space="preserve">tra d. </s>
            <s xml:id="echoid-s6710" xml:space="preserve">& </s>
            <s xml:id="echoid-s6711" xml:space="preserve">e. </s>
            <s xml:id="echoid-s6712" xml:space="preserve">& </s>
            <s xml:id="echoid-s6713" xml:space="preserve">
              <lb/>
            tra e & </s>
            <s xml:id="echoid-s6714" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6715" xml:space="preserve">compongono quella proportione che ė tra c & </s>
            <s xml:id="echoid-s6716" xml:space="preserve">d, per la terza propoſitione poſti d & </s>
            <s xml:id="echoid-s6717" xml:space="preserve">e.
              <lb/>
            </s>
            <s xml:id="echoid-s6718" xml:space="preserve">tra c & </s>
            <s xml:id="echoid-s6719" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6720" xml:space="preserve">adunque e a d, & </s>
            <s xml:id="echoid-s6721" xml:space="preserve">c ad f, ſono ſi come c a d. </s>
            <s xml:id="echoid-s6722" xml:space="preserve">& </s>
            <s xml:id="echoid-s6723" xml:space="preserve">e ad f. </s>
            <s xml:id="echoid-s6724" xml:space="preserve">ma la proportione, che è tra a & </s>
            <s xml:id="echoid-s6725" xml:space="preserve">b,
              <lb/>
            è compostà delle proportioni, che ſono tra c. </s>
            <s xml:id="echoid-s6726" xml:space="preserve">& </s>
            <s xml:id="echoid-s6727" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6728" xml:space="preserve">& </s>
            <s xml:id="echoid-s6729" xml:space="preserve">tra e & </s>
            <s xml:id="echoid-s6730" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6731" xml:space="preserve">A dunque ancho la proportione tra
              <lb/>
              <note position="left" xlink:label="note-0067-08" xlink:href="note-0067-08a" xml:space="preserve">50</note>
            a & </s>
            <s xml:id="echoid-s6732" xml:space="preserve">b. </s>
            <s xml:id="echoid-s6733" xml:space="preserve">ſerà compoſta delle proportioni che ſono tra c. </s>
            <s xml:id="echoid-s6734" xml:space="preserve">& </s>
            <s xml:id="echoid-s6735" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6736" xml:space="preserve">et tra e et d. </s>
            <s xml:id="echoid-s6737" xml:space="preserve">che ſono le poſte nella con-
              <lb/>
            cluſione. </s>
            <s xml:id="echoid-s6738" xml:space="preserve">Il terzo modo, è che ancho la proportione tra a et c, ſerà compoſta della proportione di b.
              <lb/>
            </s>
            <s xml:id="echoid-s6739" xml:space="preserve">a d, et di c. </s>
            <s xml:id="echoid-s6740" xml:space="preserve">ad f. </s>
            <s xml:id="echoid-s6741" xml:space="preserve">Il ehe è manifeſto, perche poſto b. </s>
            <s xml:id="echoid-s6742" xml:space="preserve">tra a. </s>
            <s xml:id="echoid-s6743" xml:space="preserve">& </s>
            <s xml:id="echoid-s6744" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6745" xml:space="preserve">la proportione che è tra a & </s>
            <s xml:id="echoid-s6746" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6747" xml:space="preserve">ſerà
              <lb/>
            compoſta da quella, che è tra l’a & </s>
            <s xml:id="echoid-s6748" xml:space="preserve">b, & </s>
            <s xml:id="echoid-s6749" xml:space="preserve">tra b & </s>
            <s xml:id="echoid-s6750" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6751" xml:space="preserve">ma la proportione che è tra a & </s>
            <s xml:id="echoid-s6752" xml:space="preserve">b. </s>
            <s xml:id="echoid-s6753" xml:space="preserve">ſi compo-
              <lb/>
            ne, da c & </s>
            <s xml:id="echoid-s6754" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6755" xml:space="preserve">& </s>
            <s xml:id="echoid-s6756" xml:space="preserve">da e & </s>
            <s xml:id="echoid-s6757" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6758" xml:space="preserve">ſecondo il ſuppoſito adunque a a c è fatta di b & </s>
            <s xml:id="echoid-s6759" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6760" xml:space="preserve">di c & </s>
            <s xml:id="echoid-s6761" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6762" xml:space="preserve">& </s>
            <s xml:id="echoid-s6763" xml:space="preserve">di e et f. </s>
            <s xml:id="echoid-s6764" xml:space="preserve">
              <lb/>
            ma b a.</s>
            <s xml:id="echoid-s6765" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6766" xml:space="preserve">& </s>
            <s xml:id="echoid-s6767" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6768" xml:space="preserve">a.</s>
            <s xml:id="echoid-s6769" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6770" xml:space="preserve">compongono la b.</s>
            <s xml:id="echoid-s6771" xml:space="preserve">a.</s>
            <s xml:id="echoid-s6772" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6773" xml:space="preserve">trappoſto il c tra b. </s>
            <s xml:id="echoid-s6774" xml:space="preserve">& </s>
            <s xml:id="echoid-s6775" xml:space="preserve">e.</s>
            <s xml:id="echoid-s6776" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6777" xml:space="preserve">Adunque la proportione che è tra a. </s>
            <s xml:id="echoid-s6778" xml:space="preserve">& </s>
            <s xml:id="echoid-s6779" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6780" xml:space="preserve">e compoſta di b. </s>
            <s xml:id="echoid-s6781" xml:space="preserve">& </s>
            <s xml:id="echoid-s6782" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6783" xml:space="preserve">& </s>
            <s xml:id="echoid-s6784" xml:space="preserve">di e. </s>
            <s xml:id="echoid-s6785" xml:space="preserve">& </s>
            <s xml:id="echoid-s6786" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6787" xml:space="preserve">Il quarto modo ſi come il
              <lb/>
            ſecondo modo dal primo, coſi il quarto prociede dal terzo poſti tra b. </s>
            <s xml:id="echoid-s6788" xml:space="preserve">& </s>
            <s xml:id="echoid-s6789" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6790" xml:space="preserve">communemente d. </s>
            <s xml:id="echoid-s6791" xml:space="preserve">& </s>
            <s xml:id="echoid-s6792" xml:space="preserve">e.
              <lb/>
            </s>
            <s xml:id="echoid-s6793" xml:space="preserve">& </s>
            <s xml:id="echoid-s6794" xml:space="preserve">coſi tutti i modi pari, con i lor difpari ſi collegano, per ſchifare il repeter quella iſteſſa uia. </s>
            <s xml:id="echoid-s6795" xml:space="preserve">Il
              <lb/>
            quinto modo. </s>
            <s xml:id="echoid-s6796" xml:space="preserve">Componeſi ancho a. </s>
            <s xml:id="echoid-s6797" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s6798" xml:space="preserve">di b.</s>
            <s xml:id="echoid-s6799" xml:space="preserve">ad f. </s>
            <s xml:id="echoid-s6800" xml:space="preserve">& </s>
            <s xml:id="echoid-s6801" xml:space="preserve">di c. </s>
            <s xml:id="echoid-s6802" xml:space="preserve">a d.</s>
            <s xml:id="echoid-s6803" xml:space="preserve">perche poſto b. </s>
            <s xml:id="echoid-s6804" xml:space="preserve">tra a. </s>
            <s xml:id="echoid-s6805" xml:space="preserve">& </s>
            <s xml:id="echoid-s6806" xml:space="preserve">e. </s>
            <s xml:id="echoid-s6807" xml:space="preserve">ſi fa l’argo-
              <lb/>
              <note position="left" xlink:label="note-0067-09" xlink:href="note-0067-09a" xml:space="preserve">60</note>
            mento del terzo, perche lo a. </s>
            <s xml:id="echoid-s6808" xml:space="preserve">all’e. </s>
            <s xml:id="echoid-s6809" xml:space="preserve">è compoſto dello a.</s>
            <s xml:id="echoid-s6810" xml:space="preserve">al b. </s>
            <s xml:id="echoid-s6811" xml:space="preserve">& </s>
            <s xml:id="echoid-s6812" xml:space="preserve">del b all’e. </s>
            <s xml:id="echoid-s6813" xml:space="preserve">ma lo a al b. </s>
            <s xml:id="echoid-s6814" xml:space="preserve">è compoſto
              <lb/>
            dello e all’f. </s>
            <s xml:id="echoid-s6815" xml:space="preserve">& </s>
            <s xml:id="echoid-s6816" xml:space="preserve">del c al d. </s>
            <s xml:id="echoid-s6817" xml:space="preserve">perche coſi s’è preſuppoſto. </s>
            <s xml:id="echoid-s6818" xml:space="preserve">Adunque lo a al e, ſi compone del b all’c. </s>
            <s xml:id="echoid-s6819" xml:space="preserve">dell’e
              <lb/>
            all’f. </s>
            <s xml:id="echoid-s6820" xml:space="preserve">& </s>
            <s xml:id="echoid-s6821" xml:space="preserve">del c al d. </s>
            <s xml:id="echoid-s6822" xml:space="preserve">ma il b all’e. </s>
            <s xml:id="echoid-s6823" xml:space="preserve">& </s>
            <s xml:id="echoid-s6824" xml:space="preserve">l’e. </s>
            <s xml:id="echoid-s6825" xml:space="preserve">all’f. </s>
            <s xml:id="echoid-s6826" xml:space="preserve">compongono il b. </s>
            <s xml:id="echoid-s6827" xml:space="preserve">all’f. </s>
            <s xml:id="echoid-s6828" xml:space="preserve">trappoſto l’e tra’l b & </s>
            <s xml:id="echoid-s6829" xml:space="preserve">lo f. </s>
            <s xml:id="echoid-s6830" xml:space="preserve">la proportione adunque tra a & </s>
            <s xml:id="echoid-s6831" xml:space="preserve">e è compoſta del-
              <lb/>
            le proportioni tra b. </s>
            <s xml:id="echoid-s6832" xml:space="preserve">& </s>
            <s xml:id="echoid-s6833" xml:space="preserve">f. </s>
            <s xml:id="echoid-s6834" xml:space="preserve">é tra c. </s>
            <s xml:id="echoid-s6835" xml:space="preserve">& </s>
            <s xml:id="echoid-s6836" xml:space="preserve">d.</s>
            <s xml:id="echoid-s6837" xml:space="preserve">Il ſeſto modo ſi caua dal quinto per l’argomento del ſecondo trappoſto f. </s>
            <s xml:id="echoid-s6838" xml:space="preserve">& </s>
            <s xml:id="echoid-s6839" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6840" xml:space="preserve">tra b & </s>
            <s xml:id="echoid-s6841" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6842" xml:space="preserve">Il ſettimo. </s>
            <s xml:id="echoid-s6843" xml:space="preserve">egli ſi
              <lb/>
            fa ſimilmente la proportione del b. </s>
            <s xml:id="echoid-s6844" xml:space="preserve">al d. </s>
            <s xml:id="echoid-s6845" xml:space="preserve">delle proportioni dell’a al c. </s>
            <s xml:id="echoid-s6846" xml:space="preserve">& </s>
            <s xml:id="echoid-s6847" xml:space="preserve">del f. </s>
            <s xml:id="echoid-s6848" xml:space="preserve">all’e. </s>
            <s xml:id="echoid-s6849" xml:space="preserve">perche eſſendo compoſto l’a al b. </s>
            <s xml:id="echoid-s6850" xml:space="preserve">del c al d. </s>
            <s xml:id="echoid-s6851" xml:space="preserve">& </s>
            <s xml:id="echoid-s6852" xml:space="preserve">dell’e al f.</s>
            <s xml:id="echoid-s6853" xml:space="preserve">ne ſe-
              <lb/>
            guirà per la quarta propoſitione, che la proportione tra’l b. </s>
            <s xml:id="echoid-s6854" xml:space="preserve">& </s>
            <s xml:id="echoid-s6855" xml:space="preserve">l’a. </s>
            <s xml:id="echoid-s6856" xml:space="preserve">ſerà compoſta di d & </s>
            <s xml:id="echoid-s6857" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6858" xml:space="preserve">& </s>
            <s xml:id="echoid-s6859" xml:space="preserve">di f & </s>
            <s xml:id="echoid-s6860" xml:space="preserve">e. </s>
            <s xml:id="echoid-s6861" xml:space="preserve">poſto adunque a trab & </s>
            <s xml:id="echoid-s6862" xml:space="preserve">d.</s>
            <s xml:id="echoid-s6863" xml:space="preserve">la propor-
              <lb/>
            tion, che è tra b & </s>
            <s xml:id="echoid-s6864" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6865" xml:space="preserve">ſer à fatta di b & </s>
            <s xml:id="echoid-s6866" xml:space="preserve">a, & </s>
            <s xml:id="echoid-s6867" xml:space="preserve">di a, & </s>
            <s xml:id="echoid-s6868" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6869" xml:space="preserve">Ma b & </s>
            <s xml:id="echoid-s6870" xml:space="preserve">a. </s>
            <s xml:id="echoid-s6871" xml:space="preserve">è compoſto di d & </s>
            <s xml:id="echoid-s6872" xml:space="preserve">c, & </s>
            <s xml:id="echoid-s6873" xml:space="preserve">di f. </s>
            <s xml:id="echoid-s6874" xml:space="preserve">& </s>
            <s xml:id="echoid-s6875" xml:space="preserve">e. </s>
            <s xml:id="echoid-s6876" xml:space="preserve">Adunque la proportione di b.</s>
            <s xml:id="echoid-s6877" xml:space="preserve">a.</s>
            <s xml:id="echoid-s6878" xml:space="preserve">d.</s>
            <s xml:id="echoid-s6879" xml:space="preserve">ſer à
              <lb/>
            compoſtà di tre proportioni, cioé di a.</s>
            <s xml:id="echoid-s6880" xml:space="preserve">a.</s>
            <s xml:id="echoid-s6881" xml:space="preserve">d.</s>
            <s xml:id="echoid-s6882" xml:space="preserve">di d.</s>
            <s xml:id="echoid-s6883" xml:space="preserve">a.</s>
            <s xml:id="echoid-s6884" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6885" xml:space="preserve">& </s>
            <s xml:id="echoid-s6886" xml:space="preserve">di f. </s>
            <s xml:id="echoid-s6887" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s6888" xml:space="preserve">Ma la a.</s>
            <s xml:id="echoid-s6889" xml:space="preserve">al.</s>
            <s xml:id="echoid-s6890" xml:space="preserve">d, & </s>
            <s xml:id="echoid-s6891" xml:space="preserve">la d al c.</s>
            <s xml:id="echoid-s6892" xml:space="preserve">compõgono, quella che é tra a & </s>
            <s xml:id="echoid-s6893" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6894" xml:space="preserve">trapposto d. </s>
            <s xml:id="echoid-s6895" xml:space="preserve">tra d.
              <lb/>
            </s>
            <s xml:id="echoid-s6896" xml:space="preserve">& </s>
            <s xml:id="echoid-s6897" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6898" xml:space="preserve">Adunque la proportione di b a d. </s>
            <s xml:id="echoid-s6899" xml:space="preserve">ſer à compoſta delle proportioni di a.</s>
            <s xml:id="echoid-s6900" xml:space="preserve">a.</s>
            <s xml:id="echoid-s6901" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6902" xml:space="preserve">& </s>
            <s xml:id="echoid-s6903" xml:space="preserve">di f. </s>
            <s xml:id="echoid-s6904" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s6905" xml:space="preserve">il che era il propoſto. </s>
            <s xml:id="echoid-s6906" xml:space="preserve">L’ottauo modo. </s>
            <s xml:id="echoid-s6907" xml:space="preserve">ſi come preſup-
              <lb/>
            poſto il primo ſi caua il ſecondo modo, coſi per lo iſteſſo argomento ſi caua l’ottauo da i ſuppoſti, & </s>
            <s xml:id="echoid-s6908" xml:space="preserve">prouati ne i prècedenti, trappoſto e. </s>
            <s xml:id="echoid-s6909" xml:space="preserve">& </s>
            <s xml:id="echoid-s6910" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0067-10" xlink:href="note-0067-10a" xml:space="preserve">70</note>
            f. </s>
            <s xml:id="echoid-s6911" xml:space="preserve">tra a & </s>
            <s xml:id="echoid-s6912" xml:space="preserve">e. </s>
            <s xml:id="echoid-s6913" xml:space="preserve">Il nono modo. </s>
            <s xml:id="echoid-s6914" xml:space="preserve">ſimilmente la proportione di b ad f, ſer à fatta delle proportioni dell’a all’e. </s>
            <s xml:id="echoid-s6915" xml:space="preserve">& </s>
            <s xml:id="echoid-s6916" xml:space="preserve">del d al c. </s>
            <s xml:id="echoid-s6917" xml:space="preserve">perche b. </s>
            <s xml:id="echoid-s6918" xml:space="preserve">ad a. </s>
            <s xml:id="echoid-s6919" xml:space="preserve">è composto
              <lb/>
            del d al c. </s>
            <s xml:id="echoid-s6920" xml:space="preserve">& </s>
            <s xml:id="echoid-s6921" xml:space="preserve">del f.</s>
            <s xml:id="echoid-s6922" xml:space="preserve">all’e trappoſto l’a tra’lb & </s>
            <s xml:id="echoid-s6923" xml:space="preserve">lo f.</s>
            <s xml:id="echoid-s6924" xml:space="preserve">ſerà la proportion tra’l b et la f.</s>
            <s xml:id="echoid-s6925" xml:space="preserve">cõpostà della b. </s>
            <s xml:id="echoid-s6926" xml:space="preserve">all’a. </s>
            <s xml:id="echoid-s6927" xml:space="preserve">& </s>
            <s xml:id="echoid-s6928" xml:space="preserve">dell’a al f. </s>
            <s xml:id="echoid-s6929" xml:space="preserve">& </s>
            <s xml:id="echoid-s6930" xml:space="preserve">però la b al f.</s>
            <s xml:id="echoid-s6931" xml:space="preserve">ſerà cõpo-
              <lb/>
            ſtà dell’a. </s>
            <s xml:id="echoid-s6932" xml:space="preserve">al f. </s>
            <s xml:id="echoid-s6933" xml:space="preserve">& </s>
            <s xml:id="echoid-s6934" xml:space="preserve">del f.</s>
            <s xml:id="echoid-s6935" xml:space="preserve">al’e, & </s>
            <s xml:id="echoid-s6936" xml:space="preserve">del d. </s>
            <s xml:id="echoid-s6937" xml:space="preserve">al c. </s>
            <s xml:id="echoid-s6938" xml:space="preserve">ma la a. </s>
            <s xml:id="echoid-s6939" xml:space="preserve">al f & </s>
            <s xml:id="echoid-s6940" xml:space="preserve">lo f. </s>
            <s xml:id="echoid-s6941" xml:space="preserve">all’e. </s>
            <s xml:id="echoid-s6942" xml:space="preserve">cõpongono l’a all’e. </s>
            <s xml:id="echoid-s6943" xml:space="preserve">A dunque la b al f.</s>
            <s xml:id="echoid-s6944" xml:space="preserve">è cõpoſta della a all’e, & </s>
            <s xml:id="echoid-s6945" xml:space="preserve">della d. </s>
            <s xml:id="echoid-s6946" xml:space="preserve">al c. </s>
            <s xml:id="echoid-s6947" xml:space="preserve">Il deci
              <lb/>
            mo con l’argomento del ſecondo procede dalle coſe prouate nel precedente, trappoſto e & </s>
            <s xml:id="echoid-s6948" xml:space="preserve">d.</s>
            <s xml:id="echoid-s6949" xml:space="preserve">tra a & </s>
            <s xml:id="echoid-s6950" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6951" xml:space="preserve">L’undecimo. </s>
            <s xml:id="echoid-s6952" xml:space="preserve">egli ſi cõpone ancho la c, al
              <lb/>
            d. </s>
            <s xml:id="echoid-s6953" xml:space="preserve">dalla a al b. </s>
            <s xml:id="echoid-s6954" xml:space="preserve">& </s>
            <s xml:id="echoid-s6955" xml:space="preserve">dalla f. </s>
            <s xml:id="echoid-s6956" xml:space="preserve">al c. </s>
            <s xml:id="echoid-s6957" xml:space="preserve">perche per la terza la a al c. </s>
            <s xml:id="echoid-s6958" xml:space="preserve">ſi compone della b. </s>
            <s xml:id="echoid-s6959" xml:space="preserve">al d. </s>
            <s xml:id="echoid-s6960" xml:space="preserve">& </s>
            <s xml:id="echoid-s6961" xml:space="preserve">della e alla f. </s>
            <s xml:id="echoid-s6962" xml:space="preserve">egli ſi cõponerà la c alla a. </s>
            <s xml:id="echoid-s6963" xml:space="preserve">dal d. </s>
            <s xml:id="echoid-s6964" xml:space="preserve">al b. </s>
            <s xml:id="echoid-s6965" xml:space="preserve">& </s>
            <s xml:id="echoid-s6966" xml:space="preserve">dal f.
              <lb/>
            </s>
            <s xml:id="echoid-s6967" xml:space="preserve">alla c. </s>
            <s xml:id="echoid-s6968" xml:space="preserve">posto adunque a tra c & </s>
            <s xml:id="echoid-s6969" xml:space="preserve">d. </s>
            <s xml:id="echoid-s6970" xml:space="preserve">ſarà la c. </s>
            <s xml:id="echoid-s6971" xml:space="preserve">al d. </s>
            <s xml:id="echoid-s6972" xml:space="preserve">compoſta dalla a. </s>
            <s xml:id="echoid-s6973" xml:space="preserve">al d. </s>
            <s xml:id="echoid-s6974" xml:space="preserve">della d. </s>
            <s xml:id="echoid-s6975" xml:space="preserve">al b. </s>
            <s xml:id="echoid-s6976" xml:space="preserve">& </s>
            <s xml:id="echoid-s6977" xml:space="preserve">dalla f.</s>
            <s xml:id="echoid-s6978" xml:space="preserve">al c.</s>
            <s xml:id="echoid-s6979" xml:space="preserve">ma la a al d. </s>
            <s xml:id="echoid-s6980" xml:space="preserve">& </s>
            <s xml:id="echoid-s6981" xml:space="preserve">la d. </s>
            <s xml:id="echoid-s6982" xml:space="preserve">al b.</s>
            <s xml:id="echoid-s6983" xml:space="preserve">compongono la a al b.</s>
            <s xml:id="echoid-s6984" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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