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-s17470" xml:space="preserve">
              <pb o="205" file="0215" n="224" rhead="NONO."/>
            piu, & </s>
            <s xml:id="echoid-s17471" xml:space="preserve">il ſodo otto piu. </s>
            <s xml:id="echoid-s17472" xml:space="preserve">Fu adunque dimandato da Geometri, in che modo ſtãdo quel ſodo nella iſteſſa figura ſi poteſſe raddoppiarlo, & </s>
            <s xml:id="echoid-s17473" xml:space="preserve">questa di
              <lb/>
            manda fu detta il raddoppiamento del cubo, imperoche propoſtoli un cubo cercauano in che modo poteſſero ſarne un doppio à quello. </s>
            <s xml:id="echoid-s17474" xml:space="preserve">Affaticã-
              <lb/>
            do adũque molti per molto tempo primo fu Hipocrate, che pensò, che ſe egli ſi trouaua come propoſteci due linee dritte, delle quali la mag-
              <lb/>
            giore ſuſſe doppia alla minore, ſi pigliaſſero due altre di mezzo proportionate in continua proportione, che il cubo ageuolmente ſi raddoppia-
              <lb/>
            rebbe, per ilche la ſua dubitatione ſi riuolſe in una maggiore. </s>
            <s xml:id="echoid-s17475" xml:space="preserve">Non molto dapoi egli ſi dice, che eßendo à gli habitatori di Delo, che era-
              <lb/>
            no appeſtati, dall’oraculo impoſto, che raddoppiaſſero un certo altare, ſi uenne nella isteſſa dubitatione, & </s>
            <s xml:id="echoid-s17476" xml:space="preserve">eſſendo richie ſti quaſi con ripren-
              <lb/>
            ſione quei Geometri, che erano nella Academia appreſſo Platone. </s>
            <s xml:id="echoid-s17477" xml:space="preserve">Fu dimandato loro, che trouaſſero quello, che ſi andaua cercando. </s>
            <s xml:id="echoid-s17478" xml:space="preserve">Quelli
              <lb/>
            hauẽdoſi dato alla fatica, e cercando di trouare due linee di mezzo à due propoſte, dicono, che Archita Tarentino le trouò per uia de i Semici-
              <lb/>
            lindri, Eudoxo per uia di linee oblique, Auuenne, che ciaſcuno trouò bene la dimostratione approuata di tai coſe, ma niuno puote accommodar
              <lb/>
            le all’uſo, & </s>
            <s xml:id="echoid-s17479" xml:space="preserve">eſſercitarle con le mani. </s>
            <s xml:id="echoid-s17480" xml:space="preserve">Eccetto Menechmo, ilquale però ſece poco, & </s>
            <s xml:id="echoid-s17481" xml:space="preserve">con gran difficultà. </s>
            <s xml:id="echoid-s17482" xml:space="preserve">Ma noi imaginato hauemo una faci-
              <lb/>
              <note position="left" xlink:label="note-0215-01" xlink:href="note-0215-01a" xml:space="preserve">10</note>
            le inuentione per uia di ſtrumenti, con la quale non ſolamente ſi potranno trouare due linee di mezzo à due proposte, ma quante cì ſera impo-
              <lb/>
            ſto, che noi trouamo, & </s>
            <s xml:id="echoid-s17483" xml:space="preserve">con quello ritrouamento potremo in ſomma ridurre al cubo il propoſto ſodo contenuto da linee egualmente diſtanti,
              <lb/>
            ò uero uſcir d’una figura, & </s>
            <s xml:id="echoid-s17484" xml:space="preserve">ſormarne un’altra, & </s>
            <s xml:id="echoid-s17485" xml:space="preserve">renderla pare, ò maggiore, ſeruando la ſimiglianza, perche non ha dubbio, che non ſi poſſa
              <lb/>
            con tale ſtrumanto raddoppiare gli altari, i Tempi, & </s>
            <s xml:id="echoid-s17486" xml:space="preserve">ridurre al cubo le miſure delle coſe liquide, & </s>
            <s xml:id="echoid-s17487" xml:space="preserve">ſecche, come ſono i Moggi, & </s>
            <s xml:id="echoid-s17488" xml:space="preserve">i Miri,
              <lb/>
            per dir’ à modo nostro, con i lati delle qual miſure la capacità de, i uaſi, è, conoſciuta, & </s>
            <s xml:id="echoid-s17489" xml:space="preserve">in ſomma la cognitione di quest a dimanda, e utile, & </s>
            <s xml:id="echoid-s17490" xml:space="preserve">
              <lb/>
            commoda à quelli, che uogliono radoppiare, ò far maggiori tutti quelli ſtrumenti, che ſono per trar dardi, pietre, ò palle di ſerro, percioche,
              <lb/>
            è, neceſſario, che ogni coſa creſca in larghezza, & </s>
            <s xml:id="echoid-s17491" xml:space="preserve">grandezza con proportione, ò ſian fori, ò nerui, che u’entrano, ò quello, che occorre ſe
              <lb/>
            pur uolemo, che il tutto creſca con proportione, ilche non ſi puo ſare ſenza la inuentione del mezzo. </s>
            <s xml:id="echoid-s17492" xml:space="preserve">La dimoſtratione adunque, & </s>
            <s xml:id="echoid-s17493" xml:space="preserve">l’appa-
              <lb/>
            rato del ſopradetto ſtrumento ti ho qui ſotto deſcritto, & </s>
            <s xml:id="echoid-s17494" xml:space="preserve">prima la dimoſtrationc.</s>
            <s xml:id="echoid-s17495" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s17496" xml:space="preserve">Proposte ſiano due linee dritte, è diſſeguali, l’una ſia a b. </s>
            <s xml:id="echoid-s17497" xml:space="preserve">l’altra c. </s>
            <s xml:id="echoid-s17498" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17499" xml:space="preserve">cerchiamo tra queſte hauerne due di mezzo, che ſiano in continua proportio-
              <lb/>
              <note position="left" xlink:label="note-0215-02" xlink:href="note-0215-02a" xml:space="preserve">20</note>
            ne, cioe, che ſi come ſi ha la prima alla ſeconda, coſi ſi habbia la ſeconda alla terza, & </s>
            <s xml:id="echoid-s17500" xml:space="preserve">la terza alla quarta, concedici, che l’una, & </s>
            <s xml:id="echoid-s17501" xml:space="preserve">l’al
              <lb/>
            tra delle propoſte linee a b. </s>
            <s xml:id="echoid-s17502" xml:space="preserve">& </s>
            <s xml:id="echoid-s17503" xml:space="preserve">c d. </s>
            <s xml:id="echoid-s17504" xml:space="preserve">cadino à piombo ſopra una dritta linea, & </s>
            <s xml:id="echoid-s17505" xml:space="preserve">quella ſia b. </s>
            <s xml:id="echoid-s17506" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17507" xml:space="preserve">& </s>
            <s xml:id="echoid-s17508" xml:space="preserve">delle due proposte ſia la maggiore a b. </s>
            <s xml:id="echoid-s17509" xml:space="preserve">& </s>
            <s xml:id="echoid-s17510" xml:space="preserve">le mi
              <lb/>
            nore c. </s>
            <s xml:id="echoid-s17511" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17512" xml:space="preserve">& </s>
            <s xml:id="echoid-s17513" xml:space="preserve">dall’a. </s>
            <s xml:id="echoid-s17514" xml:space="preserve">al c. </s>
            <s xml:id="echoid-s17515" xml:space="preserve">uenga una linea, che tirata piu oltre cada ſopra la linea b. </s>
            <s xml:id="echoid-s17516" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17517" xml:space="preserve">nel punto e. </s>
            <s xml:id="echoid-s17518" xml:space="preserve">Vegni ancho dal punto a ſopra la linea b. </s>
            <s xml:id="echoid-s17519" xml:space="preserve">d.
              <lb/>
            </s>
            <s xml:id="echoid-s17520" xml:space="preserve">una linea, & </s>
            <s xml:id="echoid-s17521" xml:space="preserve">ſia quella a. </s>
            <s xml:id="echoid-s17522" xml:space="preserve">f. </s>
            <s xml:id="echoid-s17523" xml:space="preserve">& </s>
            <s xml:id="echoid-s17524" xml:space="preserve">dal punto f. </s>
            <s xml:id="echoid-s17525" xml:space="preserve">ſia tirata una linea paralella alla linea a. </s>
            <s xml:id="echoid-s17526" xml:space="preserve">b. </s>
            <s xml:id="echoid-s17527" xml:space="preserve">& </s>
            <s xml:id="echoid-s17528" xml:space="preserve">ſia quella f. </s>
            <s xml:id="echoid-s17529" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17530" xml:space="preserve">che tagli la linea a. </s>
            <s xml:id="echoid-s17531" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17532" xml:space="preserve">nel punto. </s>
            <s xml:id="echoid-s17533" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17534" xml:space="preserve">per ſi-
              <lb/>
            mile conceſione dal punto. </s>
            <s xml:id="echoid-s17535" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17536" xml:space="preserve">ſia tir ata una linea egualmente diſtante alla linea a. </s>
            <s xml:id="echoid-s17537" xml:space="preserve">f. </s>
            <s xml:id="echoid-s17538" xml:space="preserve">& </s>
            <s xml:id="echoid-s17539" xml:space="preserve">ſia quella g. </s>
            <s xml:id="echoid-s17540" xml:space="preserve">h. </s>
            <s xml:id="echoid-s17541" xml:space="preserve">che taglie la linea b d. </s>
            <s xml:id="echoid-s17542" xml:space="preserve">nel punto h. </s>
            <s xml:id="echoid-s17543" xml:space="preserve">ſopra
              <lb/>
            ilqual punto ſi drizza una linea egualmente diſtante, ò paralella alla linea a. </s>
            <s xml:id="echoid-s17544" xml:space="preserve">b. </s>
            <s xml:id="echoid-s17545" xml:space="preserve">& </s>
            <s xml:id="echoid-s17546" xml:space="preserve">ſia quella h. </s>
            <s xml:id="echoid-s17547" xml:space="preserve">i. </s>
            <s xml:id="echoid-s17548" xml:space="preserve">che tagli la linea a. </s>
            <s xml:id="echoid-s17549" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17550" xml:space="preserve">nel punto i. </s>
            <s xml:id="echoid-s17551" xml:space="preserve">dalqual pun-
              <lb/>
            to diſcenda una linea egualmente diſtante alla linea a. </s>
            <s xml:id="echoid-s17552" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s17553" xml:space="preserve">& </s>
            <s xml:id="echoid-s17554" xml:space="preserve">termini nel punto d. </s>
            <s xml:id="echoid-s17555" xml:space="preserve">fatto queſto, per maggior dichiar atione chiamaremo la linea
              <lb/>
            a b. </s>
            <s xml:id="echoid-s17556" xml:space="preserve">la f. </s>
            <s xml:id="echoid-s17557" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17558" xml:space="preserve">la h. </s>
            <s xml:id="echoid-s17559" xml:space="preserve">i. </s>
            <s xml:id="echoid-s17560" xml:space="preserve">& </s>
            <s xml:id="echoid-s17561" xml:space="preserve">la c. </s>
            <s xml:id="echoid-s17562" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17563" xml:space="preserve">le priune paralelle, & </s>
            <s xml:id="echoid-s17564" xml:space="preserve">la a f. </s>
            <s xml:id="echoid-s17565" xml:space="preserve">la g. </s>
            <s xml:id="echoid-s17566" xml:space="preserve">h. </s>
            <s xml:id="echoid-s17567" xml:space="preserve">la d. </s>
            <s xml:id="echoid-s17568" xml:space="preserve">i. </s>
            <s xml:id="echoid-s17569" xml:space="preserve">le ſeconde paralelle. </s>
            <s xml:id="echoid-s17570" xml:space="preserve">Similmente ciſono due gran triangoli l’uno é, lo a b. </s>
            <s xml:id="echoid-s17571" xml:space="preserve">e. </s>
            <s xml:id="echoid-s17572" xml:space="preserve">
              <lb/>
            che ha lo angulo, b. </s>
            <s xml:id="echoid-s17573" xml:space="preserve">giuſto, l’altro e lo a. </s>
            <s xml:id="echoid-s17574" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s17575" xml:space="preserve">e. </s>
            <s xml:id="echoid-s17576" xml:space="preserve">quello chiameremo primo triangolo, queſto ſecondo triangolo, nel primo triangolo ci ſono
              <lb/>
            quelli triangoli fatti dalle prime paralelle, & </s>
            <s xml:id="echoid-s17577" xml:space="preserve">ſono g ſe, ihe. </s>
            <s xml:id="echoid-s17578" xml:space="preserve">cde. </s>
            <s xml:id="echoid-s17579" xml:space="preserve">queſti perche ſono di anguli eguali, come ſi ha per la 29. </s>
            <s xml:id="echoid-s17580" xml:space="preserve">del primo di
              <lb/>
              <note position="left" xlink:label="note-0215-03" xlink:href="note-0215-03a" xml:space="preserve">30</note>
            Euclide hanno i lati proportionali, come ſi conclude per la quarta del ſeſto; </s>
            <s xml:id="echoid-s17581" xml:space="preserve">Similmente perche i ſecondi triangoli ſatti dalle ſeconde para-
              <lb/>
            lelle ſono di lati eguali, ſenza dubbio haueranno i loro lati proportionati. </s>
            <s xml:id="echoid-s17582" xml:space="preserve">A dunque ſi come nelle prime paralelle hanno proportione tra ſe,
              <lb/>
            a e. </s>
            <s xml:id="echoid-s17583" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s17584" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17585" xml:space="preserve">coſi banno b e. </s>
            <s xml:id="echoid-s17586" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s17587" xml:space="preserve">ſ & </s>
            <s xml:id="echoid-s17588" xml:space="preserve">ſi come a e. </s>
            <s xml:id="echoid-s17589" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s17590" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17591" xml:space="preserve">nelle ſeconde paralelle ſi hanno, coſi f. </s>
            <s xml:id="echoid-s17592" xml:space="preserve">e. </s>
            <s xml:id="echoid-s17593" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s17594" xml:space="preserve">h. </s>
            <s xml:id="echoid-s17595" xml:space="preserve">& </s>
            <s xml:id="echoid-s17596" xml:space="preserve">di nouo come nelle prime f. </s>
            <s xml:id="echoid-s17597" xml:space="preserve">e. </s>
            <s xml:id="echoid-s17598" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s17599" xml:space="preserve">h.
              <lb/>
            </s>
            <s xml:id="echoid-s17600" xml:space="preserve">coſi g. </s>
            <s xml:id="echoid-s17601" xml:space="preserve">e. </s>
            <s xml:id="echoid-s17602" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s17603" xml:space="preserve">i. </s>
            <s xml:id="echoid-s17604" xml:space="preserve">ma nelle ſecondo egualmente diſtanti, come g. </s>
            <s xml:id="echoid-s17605" xml:space="preserve">e. </s>
            <s xml:id="echoid-s17606" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s17607" xml:space="preserve">i. </s>
            <s xml:id="echoid-s17608" xml:space="preserve">co4i h. </s>
            <s xml:id="echoid-s17609" xml:space="preserve">e. </s>
            <s xml:id="echoid-s17610" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s17611" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17612" xml:space="preserve">Sono adũnque continue proportionali a b. </s>
            <s xml:id="echoid-s17613" xml:space="preserve">f g. </s>
            <s xml:id="echoid-s17614" xml:space="preserve">h i. </s>
            <s xml:id="echoid-s17615" xml:space="preserve">c d. </s>
            <s xml:id="echoid-s17616" xml:space="preserve">
              <lb/>
            perche ſi come ſi ha b. </s>
            <s xml:id="echoid-s17617" xml:space="preserve">e ad e. </s>
            <s xml:id="echoid-s17618" xml:space="preserve">ſ coſi ſi ha a. </s>
            <s xml:id="echoid-s17619" xml:space="preserve">b. </s>
            <s xml:id="echoid-s17620" xml:space="preserve">ad ſ. </s>
            <s xml:id="echoid-s17621" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17622" xml:space="preserve">& </s>
            <s xml:id="echoid-s17623" xml:space="preserve">come f. </s>
            <s xml:id="echoid-s17624" xml:space="preserve">e. </s>
            <s xml:id="echoid-s17625" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s17626" xml:space="preserve">h coſi f. </s>
            <s xml:id="echoid-s17627" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17628" xml:space="preserve">ad h. </s>
            <s xml:id="echoid-s17629" xml:space="preserve">i. </s>
            <s xml:id="echoid-s17630" xml:space="preserve">& </s>
            <s xml:id="echoid-s17631" xml:space="preserve">come h. </s>
            <s xml:id="echoid-s17632" xml:space="preserve">e. </s>
            <s xml:id="echoid-s17633" xml:space="preserve">ad e. </s>
            <s xml:id="echoid-s17634" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17635" xml:space="preserve">coſi h. </s>
            <s xml:id="echoid-s17636" xml:space="preserve">i. </s>
            <s xml:id="echoid-s17637" xml:space="preserve">a. </s>
            <s xml:id="echoid-s17638" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17639" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17640" xml:space="preserve">propoſte adunque due
              <lb/>
            drite linee a. </s>
            <s xml:id="echoid-s17641" xml:space="preserve">b. </s>
            <s xml:id="echoid-s17642" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17643" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17644" xml:space="preserve">trouate hauemo due di mezzo, che ſono ſ. </s>
            <s xml:id="echoid-s17645" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17646" xml:space="preserve">& </s>
            <s xml:id="echoid-s17647" xml:space="preserve">h i. </s>
            <s xml:id="echoid-s17648" xml:space="preserve">iche far doueuamo. </s>
            <s xml:id="echoid-s17649" xml:space="preserve">Questa è l’opinione di Eratoſthene circa la dimo
              <lb/>
            ſtratione, & </s>
            <s xml:id="echoid-s17650" xml:space="preserve">ſe ben egli uuole, che la linea a b. </s>
            <s xml:id="echoid-s17651" xml:space="preserve">& </s>
            <s xml:id="echoid-s17652" xml:space="preserve">la c d ſiano dritte ſopra la linea b d. </s>
            <s xml:id="echoid-s17653" xml:space="preserve">non è pero, che non ſegua la steſſa concluſione in qualun-
              <lb/>
            que modo l’ una, & </s>
            <s xml:id="echoid-s17654" xml:space="preserve">l’altra linea cada ſopra la linea b d. </s>
            <s xml:id="echoid-s17655" xml:space="preserve">pur che amendue facciano anguli ſimiglianti. </s>
            <s xml:id="echoid-s17656" xml:space="preserve">& </s>
            <s xml:id="echoid-s17657" xml:space="preserve">ſiano per ſimili congiugnimenti egual-
              <lb/>
            mente diſtanti, perche tutto è ſondato ſopra queſta ragione, che di que trianguli, che hanno gli anguli eguali, ſono i lati proportionali. </s>
            <s xml:id="echoid-s17658" xml:space="preserve">In ſom
              <lb/>
            ma ſe noi uorremo trouare piu di due linee proportionali tra le lince a. </s>
            <s xml:id="echoid-s17659" xml:space="preserve">b. </s>
            <s xml:id="echoid-s17660" xml:space="preserve">& </s>
            <s xml:id="echoid-s17661" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17662" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17663" xml:space="preserve">biſognerd ſecondo il ſopradetto modo formare piu linee para
              <lb/>
              <note position="left" xlink:label="note-0215-04" xlink:href="note-0215-04a" xml:space="preserve">40</note>
            lelle, ſi delle prime, come delle ſeconde.</s>
            <s xml:id="echoid-s17664" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s17665" xml:space="preserve">Lo ſtrumento colquale ſi poſſa fare, & </s>
            <s xml:id="echoid-s17666" xml:space="preserve">porre in oper a coſi bella inuentione ſecondo Era
              <lb/>
            toſthene e queſto. </s>
            <s xml:id="echoid-s17667" xml:space="preserve">Piglia una piana di legno, ò di rame piu lunga, che larga, di figu-
              <lb/>
              <figure xlink:label="fig-0215-01" xlink:href="fig-0215-01a" number="110">
                <variables xml:id="echoid-variables40" xml:space="preserve">a g i c b f h d e</variables>
              </figure>
            ra quadrangulare, che habbia tutti gli anguli giuſti, & </s>
            <s xml:id="echoid-s17668" xml:space="preserve">ſia per eſſempio la tauola ab
              <lb/>
            d c ſe noi uorremo cõ eſſa tirare due linee di mezzo proportionate ? </s>
            <s xml:id="echoid-s17669" xml:space="preserve">biſognara accõ
              <lb/>
            ciare tre lamette ſopra eſſa in questo modo, piglia tre lamette ſottilisſime di qualche
              <lb/>
            ſoda materia quadrangulari, & </s>
            <s xml:id="echoid-s17670" xml:space="preserve">di giuſti anguli, & </s>
            <s xml:id="echoid-s17671" xml:space="preserve">una di queſte ferma nel mezzo
              <lb/>
            della piana, ſi che non ſi poſſa mouere, & </s>
            <s xml:id="echoid-s17672" xml:space="preserve">ſia questa e f g h. </s>
            <s xml:id="echoid-s17673" xml:space="preserve">& </s>
            <s xml:id="echoid-s17674" xml:space="preserve">ne i punti e & </s>
            <s xml:id="echoid-s17675" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s17676" xml:space="preserve">hab
              <lb/>
            bia fitte due regole con i ſuoi pironi in modo, che ciaſcuna ſi poſſa in ogni parte riuol-
              <lb/>
            gere ſia una regola e m. </s>
            <s xml:id="echoid-s17677" xml:space="preserve">l’altra f n. </s>
            <s xml:id="echoid-s17678" xml:space="preserve">ma l’altra lametta ſia K d c che ſia poſta in tal mo
              <lb/>
              <note position="left" xlink:label="note-0215-05" xlink:href="note-0215-05a" xml:space="preserve">50</note>
            do nella piana, che ſi poſſa mouere uerſo la lametta ſermata e. </s>
            <s xml:id="echoid-s17679" xml:space="preserve">f. </s>
            <s xml:id="echoid-s17680" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17681" xml:space="preserve">h. </s>
            <s xml:id="echoid-s17682" xml:space="preserve">& </s>
            <s xml:id="echoid-s17683" xml:space="preserve">ancho rimouer da quella hauendo ſempre i lati ſuoi paralle lli al lato ſ. </s>
            <s xml:id="echoid-s17684" xml:space="preserve">h.
              <lb/>
            </s>
            <s xml:id="echoid-s17685" xml:space="preserve">tenendo ancho ſul punto K. </s>
            <s xml:id="echoid-s17686" xml:space="preserve">una regola, che ſi poſſa uolgere, & </s>
            <s xml:id="echoid-s17687" xml:space="preserve">ſia questa regola K. </s>
            <s xml:id="echoid-s17688" xml:space="preserve">o. </s>
            <s xml:id="echoid-s17689" xml:space="preserve">laquale inſieme con le due altre c. </s>
            <s xml:id="echoid-s17690" xml:space="preserve">m. </s>
            <s xml:id="echoid-s17691" xml:space="preserve">& </s>
            <s xml:id="echoid-s17692" xml:space="preserve">f. </s>
            <s xml:id="echoid-s17693" xml:space="preserve">n. </s>
            <s xml:id="echoid-s17694" xml:space="preserve">ſia acconcia
              <lb/>
            in modo, che tutte ſiano tra loro paralelle, & </s>
            <s xml:id="echoid-s17695" xml:space="preserve">i loro communi tagli, che fanno con la a g. </s>
            <s xml:id="echoid-s17696" xml:space="preserve">ſ h. </s>
            <s xml:id="echoid-s17697" xml:space="preserve">& </s>
            <s xml:id="echoid-s17698" xml:space="preserve">l. </s>
            <s xml:id="echoid-s17699" xml:space="preserve">ſiano nella iſteſſa dritta linea m n l o. </s>
            <s xml:id="echoid-s17700" xml:space="preserve">Simil
              <lb/>
            mente la a. </s>
            <s xml:id="echoid-s17701" xml:space="preserve">m. </s>
            <s xml:id="echoid-s17702" xml:space="preserve">ſia eguale alla d K perche la a.</s>
            <s xml:id="echoid-s17703" xml:space="preserve">m. </s>
            <s xml:id="echoid-s17704" xml:space="preserve">inſenſibileẽte auanza la d K. </s>
            <s xml:id="echoid-s17705" xml:space="preserve">Eſſendo queste coſi ordinate tra due linee dritte a b, & </s>
            <s xml:id="echoid-s17706" xml:space="preserve">c d. </s>
            <s xml:id="echoid-s17707" xml:space="preserve">ſi dan
              <lb/>
            no due dimezzo in continu a proportione, che ſono e n. </s>
            <s xml:id="echoid-s17708" xml:space="preserve">& </s>
            <s xml:id="echoid-s17709" xml:space="preserve">f o. </s>
            <s xml:id="echoid-s17710" xml:space="preserve">per le ſopradette ragioni. </s>
            <s xml:id="echoid-s17711" xml:space="preserve">Ma ſe per caſo le due linee propoſte come ſarebbe
              <lb/>
            la. </s>
            <s xml:id="echoid-s17712" xml:space="preserve">s. </s>
            <s xml:id="echoid-s17713" xml:space="preserve">& </s>
            <s xml:id="echoid-s17714" xml:space="preserve">la. </s>
            <s xml:id="echoid-s17715" xml:space="preserve">t. </s>
            <s xml:id="echoid-s17716" xml:space="preserve">allequali biſogno ſiaritrouarne due di mezzo in cõtinua proportione, non ſer anno eguali à quelle linee, che ſon nello ſtrumento
              <lb/>
            a b. </s>
            <s xml:id="echoid-s17717" xml:space="preserve">& </s>
            <s xml:id="echoid-s17718" xml:space="preserve">r d. </s>
            <s xml:id="echoid-s17719" xml:space="preserve">facciaſi col mouere ſecondo il biſogno la lametta K. </s>
            <s xml:id="echoid-s17720" xml:space="preserve">d. </s>
            <s xml:id="echoid-s17721" xml:space="preserve">c. </s>
            <s xml:id="echoid-s17722" xml:space="preserve">tirandola uerſo la lametta ferma, ò allargandola, & </s>
            <s xml:id="echoid-s17723" xml:space="preserve">facendola ſempre egual
              <lb/>
            mente diſtante, facciaſi dico, che ſi come ſi ha la s. </s>
            <s xml:id="echoid-s17724" xml:space="preserve">alla t. </s>
            <s xml:id="echoid-s17725" xml:space="preserve">coſi ſi habbia la a b. </s>
            <s xml:id="echoid-s17726" xml:space="preserve">all’r d. </s>
            <s xml:id="echoid-s17727" xml:space="preserve">perche alla a b. </s>
            <s xml:id="echoid-s17728" xml:space="preserve">& </s>
            <s xml:id="echoid-s17729" xml:space="preserve">r d. </s>
            <s xml:id="echoid-s17730" xml:space="preserve">che ſono nello ſtrumento ritrouate ſi
              <lb/>
            ſono due di mezzo proportionate. </s>
            <s xml:id="echoid-s17731" xml:space="preserve">Seguita che alla s. </s>
            <s xml:id="echoid-s17732" xml:space="preserve">& </s>
            <s xml:id="echoid-s17733" xml:space="preserve">alla t. </s>
            <s xml:id="echoid-s17734" xml:space="preserve">propoſte trouate ſeranno due di mezzo in continua proportione.</s>
            <s xml:id="echoid-s17735" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">60</note>
          <figure number="111">
            <variables xml:id="echoid-variables41" xml:space="preserve">m p a b x n g e u i h o f l k c r d q s t</variables>
          </figure>
          <p style="it">
            <s xml:id="echoid-s17736" xml:space="preserve">Quanto piu adunque artificioſo ſera lo inſtrumento, & </s>
            <s xml:id="echoid-s17737" xml:space="preserve">ben ſatto, tan
              <lb/>
            to piu facilmente ſi trouer anno le due proportionali, pero le teſte
              <lb/>
            delle lamette, che ſi moueno entrer anno ne i lor canali aſſettate, & </s>
            <s xml:id="echoid-s17738" xml:space="preserve">
              <lb/>
            ſi moueranno dolcemente, & </s>
            <s xml:id="echoid-s17739" xml:space="preserve">ſe alcuno uorra trouare piu di due li-
              <lb/>
            nee proportlonali, egli potra con l’aggiunta di piu regole, e lamette
              <lb/>
            commodamente farlo, & </s>
            <s xml:id="echoid-s17740" xml:space="preserve">queſta è ſtata la inuentione di Eratoſthe-
              <lb/>
            ne, biſogna però auuertire che le regole ſiano longe, perche quan-
              <lb/>
            do biſogna allargare le lamette, posſino aggiugnere à i tagli delle
              <lb/>
            linee, che ſi uorranno, è tocchino il lato ſuperiore dello ſtrumento come e m. </s>
            <s xml:id="echoid-s17741" xml:space="preserve">f x. </s>
            <s xml:id="echoid-s17742" xml:space="preserve">K u. </s>
            <s xml:id="echoid-s17743" xml:space="preserve">anzi per dir meglio ſiano tanto grandi quanto ſarebbe la
              <lb/>
            diagonale della lametta ferma e. </s>
            <s xml:id="echoid-s17744" xml:space="preserve">f. </s>
            <s xml:id="echoid-s17745" xml:space="preserve">g. </s>
            <s xml:id="echoid-s17746" xml:space="preserve">h. </s>
            <s xml:id="echoid-s17747" xml:space="preserve">ò uer poco piu. </s>
            <s xml:id="echoid-s17748" xml:space="preserve">Reſta di dire con piu chiarezza e ſacilita coſi debbia uſare questo ſtrumento, cioe co-
              <lb/>
              <note position="left" xlink:label="note-0215-07" xlink:href="note-0215-07a" xml:space="preserve">70</note>
            me con eßo ſi poſſan trouare tra due linee altre due, ò piu proportionate ſecondo la mente di Eratosthene, & </s>
            <s xml:id="echoid-s17749" xml:space="preserve">prima tra due due, & </s>
            <s xml:id="echoid-s17750" xml:space="preserve">poi tra
              <lb/>
            due piu propotionali.</s>
            <s xml:id="echoid-s17751" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s17752" xml:space="preserve">Sian due linee dritte a b. </s>
            <s xml:id="echoid-s17753" xml:space="preserve">c d. </s>
            <s xml:id="echoid-s17754" xml:space="preserve">caggiano amendue ſopra una linea dritta in modo, che ſiano egualmente diſtanti, e tanto ſi aggiugna alla linea. </s>
            <s xml:id="echoid-s17755" xml:space="preserve">c d.
              <lb/>
            </s>
            <s xml:id="echoid-s17756" xml:space="preserve">che ella ſia pari alla linea a b. </s>
            <s xml:id="echoid-s17757" xml:space="preserve">il cui capo ſia, e, & </s>
            <s xml:id="echoid-s17758" xml:space="preserve">dallo a. </s>
            <s xml:id="echoid-s17759" xml:space="preserve">ſia tirata una linea ſin’all’e. </s>
            <s xml:id="echoid-s17760" xml:space="preserve">ſiche ſi faccia una ſoperficie quadrangulare a b c e. </s>
            <s xml:id="echoid-s17761" xml:space="preserve">par-
              <lb/>
            tiſcaſi poï la lined b c. </s>
            <s xml:id="echoid-s17762" xml:space="preserve">in tre parti, una dellequali ſia la doue è la f. </s>
            <s xml:id="echoid-s17763" xml:space="preserve">& </s>
            <s xml:id="echoid-s17764" xml:space="preserve">alquanto piu inanzi dal punto f. </s>
            <s xml:id="echoid-s17765" xml:space="preserve">ſia ſegnato il punto g. </s>
            <s xml:id="echoid-s17766" xml:space="preserve">di modo, che dal
              <lb/>
            b. </s>
            <s xml:id="echoid-s17767" xml:space="preserve">al g. </s>
            <s xml:id="echoid-s17768" xml:space="preserve">ſia alqnanto piu d’un terzo della linea b c. </s>
            <s xml:id="echoid-s17769" xml:space="preserve">ſimilmente nella linea a. </s>
            <s xml:id="echoid-s17770" xml:space="preserve">ſia ſegnato un punto tanto diſtante dallo a. </s>
            <s xml:id="echoid-s17771" xml:space="preserve">quanto e il g. </s>
            <s xml:id="echoid-s17772" xml:space="preserve">dal b. </s>
            <s xml:id="echoid-s17773" xml:space="preserve">& </s>
            <s xml:id="echoid-s17774" xml:space="preserve">
              <lb/>
            ſia quello h. </s>
            <s xml:id="echoid-s17775" xml:space="preserve">& </s>
            <s xml:id="echoid-s17776" xml:space="preserve">ſi leghi poi il g. </s>
            <s xml:id="echoid-s17777" xml:space="preserve">con la a, & </s>
            <s xml:id="echoid-s17778" xml:space="preserve">con la h. </s>
            <s xml:id="echoid-s17779" xml:space="preserve">& </s>
            <s xml:id="echoid-s17780" xml:space="preserve">lo a con il d, & </s>
            <s xml:id="echoid-s17781" xml:space="preserve">la g h. </s>
            <s xml:id="echoid-s17782" xml:space="preserve">taglie la a d. </s>
            <s xml:id="echoid-s17783" xml:space="preserve">nel punto, i, ſimilmente ſi tagli tanto della linea a b.</s>
            <s xml:id="echoid-s17784" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
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