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

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        <div xml:id="echoid-div591" type="section" level="1" n="106">
          <pb o="202" file="0212" n="221" rhead="LIBRO"/>
        </div>
        <div xml:id="echoid-div595" type="section" level="1" n="107">
          <head xml:id="echoid-head107" xml:space="preserve">CAP L IL MODO RITTROVATO DA PLA
            <lb/>
          TONE PER MISVRARE
            <lb/>
          VN CAMPO.</head>
          <p>
            <s xml:id="echoid-s17270" xml:space="preserve">SE IL luogo, òueroil campo di lati eguali ſerà quadrato, & </s>
            <s xml:id="echoid-s17271" xml:space="preserve">biſogno ſia di nouo con lati eguali rad
              <lb/>
            doppiarlo, perche queſto per numeri, ò per moltiplicatione non ſi ritroua, pero ſi puo fare con
              <lb/>
              <note position="left" xlink:label="note-0212-01" xlink:href="note-0212-01a" xml:space="preserve">10</note>
            emendate deſcrittioni di linee, & </s>
            <s xml:id="echoid-s17272" xml:space="preserve">queſto ſi dimoſtra coſi. </s>
            <s xml:id="echoid-s17273" xml:space="preserve">Certo è che un quadro di dieci piedi per
              <lb/>
            ogni lato, e piedi cento per quadro, ſe adunque e biſogno di raddoppiarlo, & </s>
            <s xml:id="echoid-s17274" xml:space="preserve">far un ſpatio di du-
              <lb/>
            cento piedi, & </s>
            <s xml:id="echoid-s17275" xml:space="preserve">che ſia di lati eguali, egli ſi deue cercare quanto grande ſi deue fare un lato di quello
              <lb/>
            quadrato, accioche da quello dncento piedi riſpondino à gli raddoppiamenti dello ſpacio. </s>
            <s xml:id="echoid-s17276" xml:space="preserve">Que-
              <lb/>
            ſto per uia di numeri niuno puo ritrouare, perche ſe egli ſi fa un lato di quattordici piedi moltiplicandolo uerrà
              <lb/>
            alla ſomma di piedi 196 ſe di 15 fara 225, & </s>
            <s xml:id="echoid-s17277" xml:space="preserve">però perche queſto per nnmeri non ſi fa chiaro, Egli ſi deue nel quadro,
              <lb/>
            che è dieci piedi per ogni lato tirare una linea da uno angulo all’altro in modo, che il quadrato ſia partito in due tri-
              <lb/>
            angoli eguali, e ciaſcuno de i detti triangoli ſia di piedi 50 di piano. </s>
            <s xml:id="echoid-s17278" xml:space="preserve">Adunque ſecondo la lunghezza della deſcritta
              <lb/>
            linea facciaſi un piano quadrato di lati egaali, & </s>
            <s xml:id="echoid-s17279" xml:space="preserve">coſi quanto grandi ſeranno i due triangoli nel quadrato minore di
              <lb/>
            50 piedi con la linea diagonale diſſegnati, tanto con quello iſteſſo numero di piedi nel quadro maggiore ſeranno de-
              <lb/>
              <note position="left" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">20</note>
            ſcritti quattro triangoli, con queſta ragione come appare per la ſottopoſta figura per uia di linee ſu da Platone fat-
              <lb/>
            to il raddoppiamento del campo quadro.</s>
            <s xml:id="echoid-s17280" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s17281" xml:space="preserve">Qui non ci è altro che dichiarire par hora, eſſendo Vitr. </s>
            <s xml:id="echoid-s17282" xml:space="preserve">da ſe maniſesto, imperoche il quadro ſi rad-
              <lb/>
              <figure xlink:label="fig-0212-01" xlink:href="fig-0212-01a" number="104">
                <variables xml:id="echoid-variables35" xml:space="preserve">a c 10 50 d 50 50 50 10 50 d b</variables>
              </figure>
            doppia tirando la diagonale, che coſi è detta quella linea, che da angulo ad angulo tirata in due par-
              <lb/>
            ti eguali il quadrato diuide, & </s>
            <s xml:id="echoid-s17283" xml:space="preserve">facendo di quella un lato del quadrato deue eſſer doppio al primo.
              <lb/>
            </s>
            <s xml:id="echoid-s17284" xml:space="preserve">Ecco il quadrato a b c d. </s>
            <s xml:id="echoid-s17285" xml:space="preserve">da eſſer raddoppiato, e di dieci piedi per lato. </s>
            <s xml:id="echoid-s17286" xml:space="preserve">La ſua diagonale e, a b,
              <lb/>
            che lo parte in due triangoli a d b. </s>
            <s xml:id="echoid-s17287" xml:space="preserve">& </s>
            <s xml:id="echoid-s17288" xml:space="preserve">a c b. </s>
            <s xml:id="echoid-s17289" xml:space="preserve">di 50 piedi di piano, queſta diagonale ſi fa un lato
              <lb/>
            del quadrato a b d e, che è doppio al quadrato a b c d. </s>
            <s xml:id="echoid-s17290" xml:space="preserve">puo ben èſſer che la diagonale ſi troue per uia
              <lb/>
            di numeri, ma ci potranno eſſer ancho de i rotti, ilche non e al propoſito nostro.</s>
            <s xml:id="echoid-s17291" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s17292" xml:space="preserve">Trouaſi la diagonale à queſto modo. </s>
            <s xml:id="echoid-s17293" xml:space="preserve">Moltiphca due lati del quadrato in ſe ciaſcuno ſeparata-
              <lb/>
              <note position="left" xlink:label="note-0212-03" xlink:href="note-0212-03a" xml:space="preserve">30</note>
            mente, e raccoglie inſieme la ſomma di quella moltiplicatione. </s>
            <s xml:id="echoid-s17294" xml:space="preserve">& </s>
            <s xml:id="echoid-s17295" xml:space="preserve">di quella cauane la radice
              <lb/>
            quadrata tanto ſer à la diagonale. </s>
            <s xml:id="echoid-s17296" xml:space="preserve">Ecco ſia il quadrato a b c d di pie di cinque per lato: </s>
            <s xml:id="echoid-s17297" xml:space="preserve">molti-
              <lb/>
            plica a b in ſe cioe cinque uia cinque fa 25. </s>
            <s xml:id="echoid-s17298" xml:space="preserve">& </s>
            <s xml:id="echoid-s17299" xml:space="preserve">coſi farai del lato b c fara ſara ſimilmente 25, che po-
              <lb/>
            ſte inſieme col primo 25 produce 50. </s>
            <s xml:id="echoid-s17300" xml:space="preserve">la cui radice quadrate è 7 {1/4}, & </s>
            <s xml:id="echoid-s17301" xml:space="preserve">di tanti piedi ſera la
              <lb/>
            diagonale. </s>
            <s xml:id="echoid-s17302" xml:space="preserve">Similmente nelle altre figure quadre. </s>
            <s xml:id="echoid-s17303" xml:space="preserve">& </s>
            <s xml:id="echoid-s17304" xml:space="preserve">di anguli dritti ſi proua, come nella figu-
              <lb/>
            ra. </s>
            <s xml:id="echoid-s17305" xml:space="preserve">eſgh.</s>
            <s xml:id="echoid-s17306" xml:space="preserve"/>
          </p>
          <figure number="105">
            <variables xml:id="echoid-variables36" xml:space="preserve">a 5 d b c 5 7{1/14} 25</variables>
          </figure>
        </div>
        <div xml:id="echoid-div599" type="section" level="1" n="108">
          <note position="left" xml:space="preserve">40</note>
          <head xml:id="echoid-head108" xml:space="preserve">CAP II. DELLA SQVADRA IN-
            <lb/>
          VENTIONE DI PITHAGO
            <lb/>
          RA PER FORMAR L’ANGV- LO GIVSTO.</head>
          <figure number="106">
            <variables xml:id="echoid-variables37" xml:space="preserve">e 6 f 8 10 84 g h</variables>
          </figure>
          <p>
            <s xml:id="echoid-s17307" xml:space="preserve">PITHAGORA ſimilmente dimoſtrò la ſquadra trouata ſen-
              <lb/>
            za opera di artefice alcuno, & </s>
            <s xml:id="echoid-s17308" xml:space="preserve">fece chiaro con quanta gran fati-
              <lb/>
            ca i fabri facendola à pena ridur la poſſono al giuſto. </s>
            <s xml:id="echoid-s17309" xml:space="preserve">Que-
              <lb/>
            ſta coſa con ragioni, & </s>
            <s xml:id="echoid-s17310" xml:space="preserve">uie emendata da ſuoi precetti ſi dichia-
              <lb/>
              <note position="left" xlink:label="note-0212-05" xlink:href="note-0212-05a" xml:space="preserve">50</note>
            ra. </s>
            <s xml:id="echoid-s17311" xml:space="preserve">Perche ſe egli ſi prendera tre regole, dellequali una ſia piedi
              <lb/>
            tre, l’altra quattro, la terza cinque, & </s>
            <s xml:id="echoid-s17312" xml:space="preserve">queſte regole tra ſe com
              <lb/>
            poſte ſiano, che con i capi ſi tocchino inſieme facendo una figura triangolare condurranno la ſquadra giuſta; </s>
            <s xml:id="echoid-s17313" xml:space="preserve">& </s>
            <s xml:id="echoid-s17314" xml:space="preserve">ſe
              <lb/>
            ſerano le longhezze di ciaſcuna regola di pari lati ſi fara un quadrato, dico, che dellato ditre piedi, ſi fara un qua
              <lb/>
            drato di noue piedi quadri, del lato di quattro piedi ſi fara un quadrato di ſedici piedi quadri, & </s>
            <s xml:id="echoid-s17315" xml:space="preserve">del lato di cinque pie
              <lb/>
            di ſi fara un quadrato di uinticinque piedi quadri, & </s>
            <s xml:id="echoid-s17316" xml:space="preserve">coſi quanto di ſpacio ſerà occupato da due quadri l’uno di tre
              <lb/>
            l’altro di quattro piedi per lato, tanto numero di piedi quadri uenira dal quadro tirato ſecondo il lato di cinque pie
              <lb/>
            di. </s>
            <s xml:id="echoid-s17317" xml:space="preserve">Hauendo queſto Pithagora ritrouato, non dubitando di non eſſer ſtato in quella inuentione dalle Muſe am-
              <lb/>
            monito riferendole grandisſime gratie ſi dice, che le ſacrificaſſe le uittime, & </s>
            <s xml:id="echoid-s17318" xml:space="preserve">quella ragione come in molte coſe, & </s>
            <s xml:id="echoid-s17319" xml:space="preserve">
              <lb/>
            in molte miſure è utile, coſi ne gli edificij per fare le ſcale, accioche ſiano i gradi di proportionata miſura, e molto
              <lb/>
              <note position="left" xlink:label="note-0212-06" xlink:href="note-0212-06a" xml:space="preserve">60</note>
            ſpedita, perche ſe l’altezza del Palcho da i capi della trauatura al liuello, & </s>
            <s xml:id="echoid-s17320" xml:space="preserve">piano da baſſo ſerà in tre parti diuiſa, la
              <lb/>
            ſceſa delle ſcale ſerà cinque parti di quelle con giuſta larghezza de i fuſti, e, tronchi; </s>
            <s xml:id="echoid-s17321" xml:space="preserve">perche quanto grandi ſe-
              <lb/>
            ranno le tre parti dalla ſomma trauatura al liuello di ſotto, quattro di quelle ſi hanno à tirare in fuori, &</s>
            <s xml:id="echoid-s17322" xml:space="preserve">ſcoſtar-
              <lb/>
            ſi dal dritto, perche coſi moderate ſeranno le impoſte de, i, gradi, & </s>
            <s xml:id="echoid-s17323" xml:space="preserve">delle ſcale, & </s>
            <s xml:id="echoid-s17324" xml:space="preserve">ancho di tal coſa la forma ſerà
              <lb/>
            diſſegnata.</s>
            <s xml:id="echoid-s17325" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s17326" xml:space="preserve">Pone Vitr. </s>
            <s xml:id="echoid-s17327" xml:space="preserve">la inuentione della ſquadra, & </s>
            <s xml:id="echoid-s17328" xml:space="preserve">putilità, che ſi ha da quella. </s>
            <s xml:id="echoid-s17329" xml:space="preserve">la inuentione fu di Pithagora, ilquale ueramente fu Diuino in mol-
              <lb/>
            te coſe, ma in queſta inuentione trappaßò digran lunga molti degni artifici, & </s>
            <s xml:id="echoid-s17330" xml:space="preserve">però merita grandisſima commendatione. </s>
            <s xml:id="echoid-s17331" xml:space="preserve">La ſquadra ſi
              <lb/>
            fa di tre righe poſte in triangolo, che una ſia tre, Paltra quattro, laterza cinque parti; </s>
            <s xml:id="echoid-s17332" xml:space="preserve">Da queſta inuentione ſi comprende, che facen-
              <lb/>
            doſi tre quadri perfetti ſecondo la longhezza di ciaſcuna righa. </s>
            <s xml:id="echoid-s17333" xml:space="preserve">Il quadro fatto dalla righa di cinque parti, ſerà tanto grande, & </s>
            <s xml:id="echoid-s17334" xml:space="preserve">capira
              <lb/>
            tanto, quanto i due quadri fatti dalle due altre righe, come per la figura ſi uede. </s>
            <s xml:id="echoid-s17335" xml:space="preserve">L’uſo della ſquadra in tutte le ſorti di fabriche, & </s>
            <s xml:id="echoid-s17336" xml:space="preserve">di edi-
              <lb/>
              <note position="left" xlink:label="note-0212-07" xlink:href="note-0212-07a" xml:space="preserve">70</note>
            ficij, è molto utile, & </s>
            <s xml:id="echoid-s17337" xml:space="preserve">neceſſario, & </s>
            <s xml:id="echoid-s17338" xml:space="preserve">troppo ſarebbe coſa lunga il uolerne ragionare partitamente: </s>
            <s xml:id="echoid-s17339" xml:space="preserve">ma in ſomma, questo è, che lo angulo giu
              <lb/>
            sto e miſura di tutte le coſe, la doue i Quadranti, i Raggi, i Triangoli, & </s>
            <s xml:id="echoid-s17340" xml:space="preserve">ogni altro ſtrumento col quale ſi miſura l’altezza, la larghezza,
              <lb/>
            & </s>
            <s xml:id="echoid-s17341" xml:space="preserve">la proſondità, tutti hanno la uirtù loro nello angulo giuſto, che alla ſquadra, che Norma ſi chiama, e poſto, però Vitruuio fuggendo </s>
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