Vitruvius Pollio, I dieci libri dell?architettura, 1567

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    <archimedes>
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                <p type="main">
                  <s id="s.007433">
                    <pb pagenum="400" xlink:href="045/01/414.jpg"/>
                    <emph type="italics"/>
                  nea piegata, che è detta parabole. </s>
                  <s id="s.007434">& in fine il terzo taglio trauerſo fa la linea detta ellipſe. </s>
                  <s id="s.007435">Sia
                    <lb/>
                  adunque il cono a b c d e. Il taglio del quale ſia f g h. egualmente distante al lato del
                    <lb/>
                  cono, dico che'l fondamento, & la pianta del detto cono ſarà il circolo b c d e. nel centro
                    <lb/>
                  a. & la apritura del taglio ſarà la linea g f h. detta parabole. </s>
                  <s id="s.007436">il che come ſi faccia, il Dure
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                  ro c'inſegna, & dice. </s>
                  <s id="s.007437">Sia diuiſo il taglio f g h. in dodici parti eguali, dal punto f. al punto
                    <lb/>
                  h. & ſiano apposti i numeri ne i punti delle diuiſioni
                    <emph.end type="italics"/>
                  1. 2. 3. 4.
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                  fin
                    <emph.end type="italics"/>
                  11.
                    <emph type="italics"/>
                  & paſſino per li
                    <lb/>
                  punti delle diuiſioni linee dritte egualmente diſtanti alla baſe del cono, & da gli isteſſi punti cadi
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                  no linee dritte ad anguli dritti ſopra la baſa del cono, & ſarà formato il cono con le ſue diuiſioni,
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                  le quali tutte ſi riporteranno nel fondamento, o pianta, che dire uogliamo in questo modo. </s>
                  <s id="s.007438">Fac­
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                  ciaſi un circolo il diametro, del quale ſia la linea b c d e. del cono. </s>
                  <s id="s.007439">& ſia il circolo b c d
                    <lb/>
                  e. il centro del quale ſia a. ſia il circolo b c d e. posto ſotto il cono, ſi che l'aſſe gli cada
                    <lb/>
                  nel centro a. fin al punto e. di ſotto. </s>
                  <s id="s.007440">& ſimilmente cadino ſopra quel circolo tutte le linee
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                  egualmente diſtanti all'aſſe i punti delle diuiſioni fatte nel taglio del cono, & ſiano ſegnate nel fon
                    <lb/>
                  damento le dette linee con le lettere, & con i numeri corriſpondenti alle lettere, & a i numeri ſe­
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                  gnati nel cono g h f.
                    <emph.end type="italics"/>
                  1 2 3 4.
                    <emph type="italics"/>
                  fin
                    <emph.end type="italics"/>
                  11.
                    <emph type="italics"/>
                  Fatto queſto per incontro, biſogna tagliare le det
                    <lb/>
                  te linee con proportione, accioche egli ſi poſſa formare la linea parabole. </s>
                  <s id="s.007441">il che farai a queſto mo
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                  do. </s>
                  <s id="s.007442">Piglia dal cono la lunghezza della linea del taglio ſegnato
                    <emph.end type="italics"/>
                  11.
                    <emph type="italics"/>
                  dico della linea egualmente di
                    <lb/>
                  ſtante alla baſa del cono, & poſto un piede del compaſſo nel centro a. del fondamento, farai tan
                    <lb/>
                  to di circolo, che tagli la linea ſegnata
                    <emph.end type="italics"/>
                  11.
                    <emph type="italics"/>
                  nel fondamento. </s>
                  <s id="s.007443">Il ſimile farai riportando dal cono
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                  nel fondamento tutte le altre linee ſegnate con gli altri numeri, fin al punto
                    <emph.end type="italics"/>
                  1.
                    <emph type="italics"/>
                  & a queſto mo­
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                  do hauerai formato la pianta della parabole. </s>
                  <s id="s.007444">L'apritura della quale ſi caua dalla pianta in que­
                    <lb/>
                  ſto modo. </s>
                  <s id="s.007445">Piglia dalla pianta la lunghezza della linea g h. & riportala in un piano; & ca­
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                  da ad anguli giuſti ſopra quella una linea tanto lunga, quanto è il taglio f g. nel cono. </s>
                  <s id="s.007446">& la ci
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                  ma ſua ſia f. </s>
                  <s id="s.007447">Partiſcaſi poi la detta linea in tante parti in quante è diuiſa la linea del taglio f g.
                    <lb/>
                  nel cono, & ſiano ſegnate quelle diuiſioni con i numeri corriſpondenti, & per quelli paſſino linee
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                  egualmente distanti alla linea g h. come uedi. </s>
                  <s id="s.007448">ſopra queſte linee egualmente diſtanti ſi hanno a
                    <lb/>
                  riportare i tagli proportionati dal fondamento. </s>
                  <s id="s.007449">Et però ſopra la linea ſegnata
                    <emph.end type="italics"/>
                  11.
                    <emph type="italics"/>
                  ſi riporta
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                  dal fondamento la lunghezza ſegnata nella linea
                    <emph.end type="italics"/>
                  11.
                    <emph type="italics"/>
                  dalla circonferenza corriſpondente, & il
                    <lb/>
                  ſimile ſi ſa delle altre linee. </s>
                  <s id="s.007450">& finito, che hauerai di ſegnare quelle linee proportionate della pa­
                    <lb/>
                  rabola, legherai con una linea tutti quelli punti, & a queſto modo ſarà formata la parabole,
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                  come dimoſtra la figura. </s>
                  <s id="s.007451">con quella intelligentia da i tagli, & da i fondamenti delle altre linee po
                    <lb/>
                  trai ſolo guardando nella figura conoſcere quanto ſi deue fare, per tirare proportionatamente, &
                    <lb/>
                  la hiperbole, & la elliſſe.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s id="s.007452">
                    <emph type="italics"/>
                  Hora perche ſi ſappia a che fine ſiano ſtate propoſte queſte figure, io dico, che il Sole girando
                    <lb/>
                  di giorno in giorno manda i raggi ſuoi nel Gnomone, la cima del quale imaginaremo, che ſia la ci
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                  ma del cono, & il circolo, che fa il Sole ſia la baſa del cono, & i raggi che ſi parteno dal corpo
                    <lb/>
                  del Sole ſia quella linea, che girandoſi a torno deſcriua il cono. </s>
                  <s id="s.007453">ſe uorremo ben conſiderare que­
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                  sto effetto, che fa il Sole con i ragginel Gnomone, uederemo, che egli fa una ſuperficie conica,
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                  perche è una ſuperficie fatta di due ſuperficie opposte per la cima del cono, l'una è dal circolo,
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                  che fa il Sole fin alla punta del Gnomone, l'altra è dalla punta del Gnomone in giu nella parte op­
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                  poſta, la quale anderebbe in infinito, ſe non gli ſi opponeſſe un piano. </s>
                  <s id="s.007454">Et perche queſto piano ſe
                    <lb/>
                  gli oppone diuerſamente, & taglia quei raggi della ſuperficie conica inferiore, però biſogna conſi
                    <lb/>
                  derare la proprietà di que tagli; perche fanno diuerſe linee. </s>
                  <s id="s.007455">Piano intendo il piano ſopra il
                    <lb/>
                  qual ſi fa l'horologio, il qual piano, hora è egualmente diſtante dall'Orizonte: come ſe uoglia­
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                  mo fare un horologio in terra piana, hora è drizzato ſopra l'Orizonte, ouero ad anguli dritti, co
                    <lb/>
                  me ſono i muri de gli edificij. </s>
                  <s id="s.007456">Ouero è piegato come i tetti delle caſe. </s>
                  <s id="s.007457">& perche questi piani ſe­
                    <lb/>
                  guitano la diuerſità de gli Orizonti, però tagliano diuerſamente la ſuperſicie conica. </s>
                  <s id="s.007458">Dal che
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                  ne naſce, che l'ombra della cima del Gnomone in detti piani, hora deſcriue una linea dritta, hora
                    <emph.end type="italics"/>
                  </s>
                </p>
              </subchap2>
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          </chap>
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    </archimedes>
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