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

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        <div xml:id="echoid-div607" type="section" level="1" n="110">
          <p style="it">
            <s xml:id="echoid-s18048" xml:space="preserve">
              <pb o="207" file="0217" n="226" rhead="NONO."/>
            ragione, come é ſtato manifeſto e come la b d alla b c. </s>
            <s xml:id="echoid-s18049" xml:space="preserve">per la undeci-
              <lb/>
              <figure xlink:label="fig-0217-01" xlink:href="fig-0217-01a" number="114">
                <variables xml:id="echoid-variables44" xml:space="preserve">d c b e g l n o k m</variables>
              </figure>
            ma del quinto. </s>
            <s xml:id="echoid-s18050" xml:space="preserve">A dunque tra le due dritte propoſte, che erano e b, & </s>
            <s xml:id="echoid-s18051" xml:space="preserve">
              <lb/>
            b g. </s>
            <s xml:id="echoid-s18052" xml:space="preserve">trouate ne hauemo due ſotto la iſteſſa ragione cõtinuamẽte pro-
              <lb/>
            portionali, che ſono b d, et b c. </s>
            <s xml:id="echoid-s18053" xml:space="preserve">Et questa è la ragione di Platone. </s>
            <s xml:id="echoid-s18054" xml:space="preserve">Lo
              <lb/>
            inſtrumẽto ueramẽte é ſacile, imperoche egli ſi fa d’una ſquadra & </s>
            <s xml:id="echoid-s18055" xml:space="preserve">
              <lb/>
            d’una rega in que ſto modo. </s>
            <s xml:id="echoid-s18056" xml:space="preserve">Sia una ſquadra K m l, et in un braccio di
              <lb/>
            eſſa accõmodata ſia una rega, che ſia n o. </s>
            <s xml:id="echoid-s18057" xml:space="preserve">et che faccia con detto brac
              <lb/>
            cio gli anguli giuſti, e mouer ſi poſſa hora uer ſo il punto m. </s>
            <s xml:id="echoid-s18058" xml:space="preserve">hora uer
              <lb/>
            ſo il punto l. </s>
            <s xml:id="echoid-s18059" xml:space="preserve">fatto queſto è uolendo trouare due linee tra mezzo in
              <lb/>
            continua proportione à due propoſte, farai che le due date, ſiano per
              <lb/>
              <note position="left" xlink:label="note-0217-01" xlink:href="note-0217-01a" xml:space="preserve">10</note>
            eſſempio la e b, & </s>
            <s xml:id="echoid-s18060" xml:space="preserve">la b g. </s>
            <s xml:id="echoid-s18061" xml:space="preserve">(come di ſopra hauemo detto) congiunte
              <lb/>
            nel punto b. </s>
            <s xml:id="echoid-s18062" xml:space="preserve">in un’angulo giuſto, & </s>
            <s xml:id="echoid-s18063" xml:space="preserve">ſiano prolongate come di ſopra.
              <lb/>
            </s>
            <s xml:id="echoid-s18064" xml:space="preserve">Allhora ſi piglia lo inſtrumento, & </s>
            <s xml:id="echoid-s18065" xml:space="preserve">coſi egli s’ accommoda alle linee
              <lb/>
            dritte c b, & </s>
            <s xml:id="echoid-s18066" xml:space="preserve">b g. </s>
            <s xml:id="echoid-s18067" xml:space="preserve">che il lato K m. </s>
            <s xml:id="echoid-s18068" xml:space="preserve">della ſquadra cada ſopra il g. </s>
            <s xml:id="echoid-s18069" xml:space="preserve">& </s>
            <s xml:id="echoid-s18070" xml:space="preserve">
              <lb/>
            lo angulo m. </s>
            <s xml:id="echoid-s18071" xml:space="preserve">ſi uniſca alla linea b c. </s>
            <s xml:id="echoid-s18072" xml:space="preserve">lo angulo o ſia ſopra la linea b d. </s>
            <s xml:id="echoid-s18073" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s18074" xml:space="preserve">la regola mobile uegna per lo punto, e, di modo che il punto m ſia
              <lb/>
            ſoprapoſto al punto c. </s>
            <s xml:id="echoid-s18075" xml:space="preserve">& </s>
            <s xml:id="echoid-s18076" xml:space="preserve">il ſegno e. </s>
            <s xml:id="echoid-s18077" xml:space="preserve">cada ſopra d. </s>
            <s xml:id="echoid-s18078" xml:space="preserve">& </s>
            <s xml:id="echoid-s18079" xml:space="preserve">coſi ordinato, che hauerai, & </s>
            <s xml:id="echoid-s18080" xml:space="preserve">acconcio lo ſtrumento trouato hauerai tra le linee e b, & </s>
            <s xml:id="echoid-s18081" xml:space="preserve">
              <lb/>
            b g. </s>
            <s xml:id="echoid-s18082" xml:space="preserve">due proportionate linee di mezzo cioe la b d. </s>
            <s xml:id="echoid-s18083" xml:space="preserve">& </s>
            <s xml:id="echoid-s18084" xml:space="preserve">la b c. </s>
            <s xml:id="echoid-s18085" xml:space="preserve">del che la dimostratione è la iſteſſa con quella di ſopra.</s>
            <s xml:id="echoid-s18086" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s18087" xml:space="preserve">Nicomede uſaua un’altra dimoſtratione, & </s>
            <s xml:id="echoid-s18088" xml:space="preserve">ſormaua un’ altro ſtrumento ſecondo quella dimoſtratione, molto artiſicio ſamente, & </s>
            <s xml:id="echoid-s18089" xml:space="preserve">con gran ſottili
              <lb/>
              <note position="left" xlink:label="note-0217-02" xlink:href="note-0217-02a" xml:space="preserve">20</note>
            tà de inuentione ſuperando Eratosthene é ſtato di gran giouamento à gli ſtudioſi della Geometria. </s>
            <s xml:id="echoid-s18090" xml:space="preserve">Per ſare lo strumento è neceſſario pianar
              <lb/>
            due righe, & </s>
            <s xml:id="echoid-s18091" xml:space="preserve">porle una ſopr a l’altra con anguli giuſti di modo, che d’amendue ſia uno isteſſo piano, ne una ſia piu alta dell’altra, ſia una d’eſſe
              <lb/>
            a b. </s>
            <s xml:id="echoid-s18092" xml:space="preserve">l’altra c d. </s>
            <s xml:id="echoid-s18093" xml:space="preserve">facciaſi nell’a b. </s>
            <s xml:id="echoid-s18094" xml:space="preserve">un canale, che u’entri à coda di Rondine, è ſotto ſquadra un legno, che andar poſſa in ſu, & </s>
            <s xml:id="echoid-s18095" xml:space="preserve">in giu per quel ca-
              <lb/>
            nale ſenza uſcir fuori: </s>
            <s xml:id="echoid-s18096" xml:space="preserve">ſia nel mezzo della riga c d. </s>
            <s xml:id="echoid-s18097" xml:space="preserve">per longo di eſſa una linea, & </s>
            <s xml:id="echoid-s18098" xml:space="preserve">nella testa di eſſa, doue è la d ſia posto un pirone, & </s>
            <s xml:id="echoid-s18099" xml:space="preserve">ſia quello
              <lb/>
            g h, ilquale eſca alquanto fuori del piano della riga c d. </s>
            <s xml:id="echoid-s18100" xml:space="preserve">& </s>
            <s xml:id="echoid-s18101" xml:space="preserve">in quella uolger ſi poſſa, & </s>
            <s xml:id="echoid-s18102" xml:space="preserve">ſia pertuggiata, & </s>
            <s xml:id="echoid-s18103" xml:space="preserve">u’entri un pironcino, che la formi ſo-
              <lb/>
            pra la coda di Rondine, che dicemo andar in ſu, & </s>
            <s xml:id="echoid-s18104" xml:space="preserve">in giu per lo canale della riga a b. </s>
            <s xml:id="echoid-s18105" xml:space="preserve">& </s>
            <s xml:id="echoid-s18106" xml:space="preserve">nel pirone g h. </s>
            <s xml:id="echoid-s18107" xml:space="preserve">ſia un foro, nelqual entri la regoletta,
              <lb/>
            e f. </s>
            <s xml:id="echoid-s18108" xml:space="preserve">Se adũque piglier ai l’eſtremo capo K della regoletta e f. </s>
            <s xml:id="echoid-s18109" xml:space="preserve">& </s>
            <s xml:id="echoid-s18110" xml:space="preserve">mouer ai quella o uerſo le parti dello a. </s>
            <s xml:id="echoid-s18111" xml:space="preserve">ò uero uerſo le parti del b. </s>
            <s xml:id="echoid-s18112" xml:space="preserve">ſempre il pun
              <lb/>
            to e ſi mouera per la dritta linea a b. </s>
            <s xml:id="echoid-s18113" xml:space="preserve">& </s>
            <s xml:id="echoid-s18114" xml:space="preserve">la regoletta e ſ penetrando per lo foro del pirone g h. </s>
            <s xml:id="echoid-s18115" xml:space="preserve">entrera, & </s>
            <s xml:id="echoid-s18116" xml:space="preserve">uſcira, & </s>
            <s xml:id="echoid-s18117" xml:space="preserve">la dritta linea di mezzo
              <lb/>
            della regoletta e f ſi mouera col ſuo predetto mouimcto per lo perno del ſuo pirone, oſſeruaſi ſinalmẽte, che lo ecceſſo e K della regoletta ſia e f.
              <lb/>
            </s>
            <s xml:id="echoid-s18118" xml:space="preserve">ſempre lo iſteſſo, et della iſteſſa lun
              <lb/>
              <note position="left" xlink:label="note-0217-03" xlink:href="note-0217-03a" xml:space="preserve">30</note>
            ghezza. </s>
            <s xml:id="echoid-s18119" xml:space="preserve">per ilche ſe noi ponere-
              <lb/>
            mo nel punto K una punta di for-
              <lb/>
            ro, che tocchi un piano egli ſi for
              <lb/>
              <figure xlink:label="fig-0217-02" xlink:href="fig-0217-02a" number="115">
                <variables xml:id="echoid-variables45" xml:space="preserve">c b g b d n m l k e a</variables>
              </figure>
            mera una linea piegata come la l
              <lb/>
            m n. </s>
            <s xml:id="echoid-s18120" xml:space="preserve">laquale Nicome de chiama pri
              <lb/>
            ma Concoide, & </s>
            <s xml:id="echoid-s18121" xml:space="preserve">lo ſpacio, che è
              <lb/>
            tra e, & </s>
            <s xml:id="echoid-s18122" xml:space="preserve">K. </s>
            <s xml:id="echoid-s18123" xml:space="preserve">egli chiama la grãdez
              <lb/>
            za della regoletta, & </s>
            <s xml:id="echoid-s18124" xml:space="preserve">il punto d il
              <lb/>
            Polo. </s>
            <s xml:id="echoid-s18125" xml:space="preserve">In queſta linea piegata Ni-
              <lb/>
            comede ne troua tre principali
              <lb/>
              <note position="left" xlink:label="note-0217-04" xlink:href="note-0217-04a" xml:space="preserve">40</note>
            propietà; </s>
            <s xml:id="echoid-s18126" xml:space="preserve">L’una è che quanto piu
              <lb/>
            s’allarga la linea torta l m n. </s>
            <s xml:id="echoid-s18127" xml:space="preserve">tanto
              <lb/>
            meno è lontana dalla dritta a b. </s>
            <s xml:id="echoid-s18128" xml:space="preserve">co
              <lb/>
            me ſi uede, che il punto c, è piu
              <lb/>
            lontano dalla linea a b. </s>
            <s xml:id="echoid-s18129" xml:space="preserve">che il pun-
              <lb/>
            to. </s>
            <s xml:id="echoid-s18130" xml:space="preserve">n. </s>
            <s xml:id="echoid-s18131" xml:space="preserve">& </s>
            <s xml:id="echoid-s18132" xml:space="preserve">il punto n, piu lontano
              <lb/>
            che il punto m. </s>
            <s xml:id="echoid-s18133" xml:space="preserve">& </s>
            <s xml:id="echoid-s18134" xml:space="preserve">il punto m. </s>
            <s xml:id="echoid-s18135" xml:space="preserve">piu
              <lb/>
            lontano che il punto l. </s>
            <s xml:id="echoid-s18136" xml:space="preserve">ilche ſi ue-
              <lb/>
            de chiaramente facendo da i detti
              <lb/>
            punti c n m l cadere le perpendico
              <lb/>
              <note position="left" xlink:label="note-0217-05" xlink:href="note-0217-05a" xml:space="preserve">50</note>
            lari ſopra la linea a b. </s>
            <s xml:id="echoid-s18137" xml:space="preserve">La ſeconda
              <lb/>
            propietà è questa, che ſe tra la re
              <lb/>
            gola a b. </s>
            <s xml:id="echoid-s18138" xml:space="preserve">& </s>
            <s xml:id="echoid-s18139" xml:space="preserve">la linea piegata ſi ti-
              <lb/>
            rera una linea quella ſinalmente
              <lb/>
            taglier à la piegata, come ſi uede
              <lb/>
            tirando la linea p. </s>
            <s xml:id="echoid-s18140" xml:space="preserve">q. </s>
            <s xml:id="echoid-s18141" xml:space="preserve">la terza pro-
              <lb/>
            pietà, é che la dritta a b. </s>
            <s xml:id="echoid-s18142" xml:space="preserve">& </s>
            <s xml:id="echoid-s18143" xml:space="preserve">la pie-
              <lb/>
            gata primamente deſcritta mai nõ
              <lb/>
            concorreranno in uno, ſe ben fuſſe
              <lb/>
              <note position="left" xlink:label="note-0217-06" xlink:href="note-0217-06a" xml:space="preserve">60</note>
            ro tirate in infinito. </s>
            <s xml:id="echoid-s18144" xml:space="preserve">Et queſto ſi
              <lb/>
            uede euidentemente ſe alcuno con-
              <lb/>
            ſidera bene guardando la forma
              <lb/>
            dello ſtrumento predetto, perche
              <lb/>
              <figure xlink:label="fig-0217-03" xlink:href="fig-0217-03a" number="116">
                <variables xml:id="echoid-variables46" xml:space="preserve">d f g a e b l c</variables>
              </figure>
              <note position="left" xlink:label="note-0217-07" xlink:href="note-0217-07a" xml:space="preserve">70</note>
            </s>
          </p>
        </div>
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    </echo>
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