Vitruvius Pollio, I dieci libri dell?architettura, 1567

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                <p type="main">
                  <s id="s.006637">
                    <pb pagenum="359" xlink:href="045/01/373.jpg"/>
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                  le inuentioni daranno in luce, & questa, & altre belle coſe, io laſcierò il carieo a loro di publi­
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                  carle, hauendone molte gratie. </s>
                  <s id="s.006638">Hora uenirò alla dimoſtratione, & allo inſtrumento di Platone. </s>
                  <s id="s.006639">
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                  Lega adunque le due dritte, tra le quali uuoi trouare le due di mezo proportionali ad angolo drit­
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                  to nel punto b. ſia la maggiore b g. & la minore e b. </s>
                  <s id="s.006640">Allunga poi l'una, & l'altra fuor
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                  dello angolo b. la maggiore uerſo il d. & la minore uerſo il c. </s>
                  <s id="s.006641">Et fa due anguli dritti trouan
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                  do il punto c. & il punto d. nelle loro linee conuenienti, & ſia uno angulo g c d. & l'al­
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                  tro c d e. dico, che tra le due dritte e b. & b g. hauerai proportionate due altre linee,
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                  che ſono b d. & b c. perche hauemo preſuppoſto, che lo angolo e d c. è dritto, & la
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                  e a. eſſer parallela alla c g. però ne ſegue per la uenteſima nona del primo, che lo angolo g
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                  c d. ſia giusto, & eguale allo angolo c d e. il quale ſimilmente preſupponemo eſſer giusto. </s>
                  <s id="s.006642">
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                  ma la d b. per lo nostro componimento cade perpendicolare ſopra la c b e. ſimilmente la
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                  c b. è perpendicolare alla d b g. adunque per lo corolario della ottaua del ſesto, la b d. è
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                  quella linea proportionata, che cade nella e b. & la b c. & ſimilmente la linea b c. è la
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                  mezana proportionale tra la b d. & la b g. poſta adunque la ragione, & la proportione
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                  commune della linea b d. & della linea b c. ne ſeguita, che la g b. hauerà quello riſpet­
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                  to di comparatione alla linea b d. che hauerà la c b. alla e b. perche l'una, & l'altra ra­
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                  gione, come è ſtato manifesto, è come b d. à b c. per la undecima del quinto. </s>
                  <s id="s.006643">adunque ſi
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                  me g b. à b d. coſi b d. à b c. coſi la c d. alla b e. </s>
                  <s id="s.006644">Date adunque due linee, b g.
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                  & c b. ſono state ritrouate due di mezo proportionali b d. & b c. </s>
                  <s id="s.006645">Et questa è la ragio­
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                  ne di Platone. </s>
                  <s id="s.006646">Ma lo inſtrumento è questo. </s>
                  <s id="s.006647">Sia una ſquadra K m l. & in uno braccio di
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                  quella ſia accommodata una riga, che ſia n o. & che faccia con detto braccio gli angoli drit­
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                  ti, & ſi poſſa mouere hora uerſo il punto m. hora uerſo il punto e. fatto questo ſimpliciſſimo
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                  instrumento, & uolendo trouare le due proportionali di mezo alle due date, farai, che le due da
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                  te ſiano per eſſempio la e b. & la b g. come hauemo poſto nella dimoſtratione, congiunte
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                  nel punto b. ad angulo giusto & ſiano prolungate come di ſopra. </s>
                  <s id="s.006648">Allhora ſi piglia lo instru­
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                  mento, & coſi egli s'accommoda alle linee c b. & b g. che il lato K m. della ſquadra ca
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                  da ſopra il g. & lo angulo m. ſi uniſca alla linea b c. lo angulo o. ſia ſopra la linea b d.
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                  & la regola mobile uenga per lo punto e. di modo, che il punto m. ſia ſoprapoſto al punto
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                  c. & il punto o. cada ſopra d. & coſi ordinato che hauerai, & acconcio lo instrumento,
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                  hauerai trouato tra le linee e b. & b g. due proportionate di mezo, cioè la b d. & la b
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                  c. del che la dimoſtratione è la isteſſa con quella di ſopra. </s>
                  <s id="s.006649">Nicomede uſaua un'altra dimostra
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                  tione, & formau a un'altro instrumento ſecondo quella dimoſtratione, & con grande ſottigliez­
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                  za d'inuentione ſuperando Eratoſthene è stato di gran giouamento alli ſtudioſi della Geometria. </s>
                  <s id="s.006650">
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                  Per fare lo instrumento, piglia due righe, & ponle una ſopra l'altra ad angoli giusti di modo,
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                  che d'amendue ſia uno iſteſſo piano nè una ſia piu alta dell'altra, ma rappreſentino la lettera T. &
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                  ſia una di eſſe a b. dritta & l'altra c d. trauerſa. </s>
                  <s id="s.006651">facciaſi nella a b. un canale nel mezo, nel
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                  quale u'entri a coda di rondine, & ſotto ſquadra uno cuneo, che ſi poſſa ſpignere in ſu, & in giu
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                  per quel canale ſenza uſcir fuori: ſia poi nel mezo della riga c d. trauerſa per lnngo di eſſa una
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                  linea, & nella teſta di eſſa, doue è la lettera d. ſia posto un pirone, & ſia quello g h. ad an­
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                  goli dritti, il quale eſca alquanto fuori del piano della riga c d. ſia nel detto pirone un foro nel
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                  quale entri una regoletta, che ſia e f. la quale ſia congiunta nel cuneo, che era posto ſotto
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                  ſquadra nel canale della regola a b. & ſia il capo della detta regoletta K. </s>
                  <s id="s.006652">Se adunque moue­
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                  rai il cuneo per lo canale ouero uerſo il punto a. ouero uerſo il punto b. inſieme con la con­
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                  giunta regoletta, ſempre il punto e. ſimouerà per dritta linea, & la regoletta e f. penetran
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                  do per lo foro del pirone g h. entrerà, & uſcirà, & la dritta linea di mezo della regoletta e
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                  f. ſi mouerà col ſuo predetto mouimento per lo perno del ſuo pirone. </s>
                  <s id="s.006653">Egli ſi oſſerua finalmente,
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                  che lo ecceſſo e
                    <emph.end type="italics"/>
                  k.
                    <emph type="italics"/>
                  della regoletta e f. ſia ſempre lo iſteſſo, & della iſteſſa lunghezza. </s>
                  <s id="s.006654">per
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                  il che ſe noi poneremo nel punto
                    <emph.end type="italics"/>
                  k.
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                  alcuna coſa, che poſſa ſegnare un piano ſottoposto mouen-
                    <emph.end type="italics"/>
                  </s>
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