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

Page concordance

< >
Scan Original
101 86
102 87
103 88
104 89
105 90
106 91
107 92
108 93
109 94
110 95
111 96
112 97
113 98
114 99
115 100
116 101
117 102
118 103
119 104
120 105
121 106
122 107
123 108
124 109
125 110
126 111
127 112
128 113
129 114
130 115
< >
page |< < (202) of 325 > >|
    <echo version="1.0RC">
      <text xml:lang="it" type="free">
        <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>
          </p>
        </div>
      </text>
    </echo>
Impressum