Gallaccini, Teofilo, Perigonia, o vero degli angoli, ca. 1590-1598

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="folios 26v-27r"/>
              </s>
            </p>
            <p type="main">
              <s>La terza e la quarta si possano dichiarar con la definitione II del 3° d’Euclide e con la dodicesima aggionta dal Commandino.</s>
            </p>
            <p type="main">
              <s>La quinta è manifesta; perciochè ciascuna volta che più portioni di circonfernza sono accozzate insieme non possono haver un centro commune non essendo collocate in guisa che sieno concentriche; ma essendo eccentriche. </s>
              <s>Però necessariamente avviene che ciascuna habbia ‘l suo centro particolare.</s>
            </p>
            <p type="main">
              <s>La sesta si può dichiarare per la simiglianza delle parti e degli angoli o linee contenute; ansi per la uguaglianza degli angoli che si truovano nella circonferenza, come si vede nella XI def. del 3° d’Euclide e nella XII aggionta dal Commandino. </s>
            </p>
            <p type="main">
              <s>Proponiamo due essempij d’angoli e ciascuno de’ quali sia adattato al cerchio, cioè l’angolo ABC. applicato al cerchio DFE. e l’angolo GFH. adattato al cerchio GHI. e formiamo la dimostratione in questo modo. </s>
            </p>
            <p type="main">
              <s>Sieno nella prima figura due linee rette AB. e BC. che facciano l’angolo ABC. e dal punto B. del contatto dell’angolo, si tiri una perpendicolare, cioè la BF. costituiscasi in essa il punto M.(pel 3° Post. di Euclide) e fatto l’intervallo MF. si formi ‘l cerchio DFE che tocchi i termini delle linee rette AB. e BC., così sopra il centro M. posto il centro T alto 3 portioni della linea MF. si faccia il cerchio GHI. e sopra il punto T pongasi ‘l centro R. di uguale altezza, e si descriva il cerchio KML. ed ascendendo quasi per due portioni si ponga il centro V e si disegni ‘l cerchio NO e nel taglio fatto dal cerchio KLM. nella perpendicolare, dico nel segno S. si determini un altro centro e si descriva il cerchio piccolo PQX. di maniera che si saranno formati cinque cerchi i quali col convesso della circonferenza loro si congiogneranno con le linee
                <lb/>
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                <lb/>
              AB. e BC. formando con esse l’angolo ABC. I quali cerchi sono fra loro proportionali perciochè tutti sono di proportione sesquialtera; poiché per la diminutione loro si palesa la commune proportione in fra essi. </s>
              <s>Sono ancho simili come è manifesto per la terza positione e come si può confermare con la undicesima def. del 3° d’Euclide, perciochè le portioni di loro prendono angoli uguali, o sopra esse si fanno angoli uguali; che l’angolo ABM. è uguale all’angolo ABC. essendo uguali le basi AM. MC. *(Per la contrapositione della ventiquattresima e venticinquesima del primo d’Euclide) [nota in margine] </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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