Caverni, Raffaello, Storia del metodo sperimentale in Italia, 1891-1900

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="020/01/2810.jpg" pagenum="435"/>
              circonferenza. </s>
              <s>Quanto al metodo degli indivisibili si lusingava il buon Cava­
                <lb/>
              lieri di essere egli stato il primo a insegnarlo, ma il Nardi riconosce di così
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              fatte dottrine, che apparvero nuove, più antichi e autorevoli maestri. </s>
              <s>La cosa,
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              come s'intende, è di tale e tanta importanza, da non doversene passare con
                <lb/>
              sentenza sì asciutta. </s>
            </p>
            <p type="main">
              <s>La seconda Ricercata geometrica, qual si legge nel manoscritto donato
                <lb/>
              alla Biblioteca di Roma, conclude le risposte alle obiezioni contro Archimede
                <lb/>
              col pronunziare che queste son nulle, o per lo più leggere. </s>
              <s>Si direbbe no­
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              nostante, soggiunge l'Autore, essersi il Siracusano messo a inchieste ardue
                <lb/>
              e lubriche, se non si pensasse agl'impulsi ch'egli ebbe, nello speculare e
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              nell'inventare, dalle precedenti tradizioni, e al molto aiuto che gli venne
                <lb/>
              dall'usare il metodo degli indivisibili, e dal praticar l'esperienze. </s>
              <s>A queste,
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              risolvendo le questioni accennate da noi nel secondo capitolo della prima
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              parte di questa Storia, attribuisce l'invenzione del centro di gravità nella
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              rettangola conoidale, supposto noto nella IIa del secondo libro
                <emph type="italics"/>
              De insiden­
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              tibus humido:
                <emph.end type="italics"/>
              e a quello, cioè al metodo degl'indivisibili, il segreto di tante
                <lb/>
              geometriche verità, da parer quasi rivelazioni di un Nume. </s>
            </p>
            <p type="main">
              <s>Da Archimede confessa dunque il Nardi di avere appresa la dottrina del­
                <lb/>
              l'infinito, riducendo per essa le quantità lineari a tal piccolezza da trasfor­
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              mare il curvo nel retto. </s>
              <s>Ma delle particolari applicazioni del metodo gli sparse
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              nella mente i primi semi una pellegrina dimostrazione di Pappo, chi ripensi
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              alla quale sentesi compreso da uno stupore, com'a vedere sotto il sol me­
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              ridiano scintillare una stella in mezzo al cielo profondo. </s>
              <s>È data quella dimo­
                <lb/>
              strazione dal Matematico alessandrino nel teorema XXI del quarto libro delle
                <lb/>
                <emph type="italics"/>
              Collezioni,
                <emph.end type="italics"/>
              per concluderne che lo spazio, compreso tra la spirale e la linea
                <lb/>
                <figure id="id.020.01.2810.1.jpg" xlink:href="020/01/2810/1.jpg" number="797"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 292.
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              condotta al centro dal princi­
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              pio della circolazione, è la ter­
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              za parte della superficie del
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              cerchio. </s>
            </p>
            <p type="main">
              <s>Sia lo spazio da misurare
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              BEFAB, nella figura 292. Di­
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              visa tutta la circonferenza in
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              parti uguali, sian due di que­
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              ste AC, CD, dalle quali e dalle
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              loro concentriche FG, EH sian
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              chiusi quattro settori. </s>
              <s>Espon­
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              gasi anche insieme un rettangolo KL, di cui i lati KP, KN sian divisi in tante
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              parti uguali, in quante fu divisa la stessa circonferenza, ed essendo due di
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              queste parti KR, RQ sopra l'un lato, KM, MS sopra l'altro; si conducano
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              RT, QV parallele a KN, e MZ, SO parallele a KP. </s>
            </p>
            <p type="main">
              <s>Per la genesi della spirale archimedea, per supposizione e per costru­
                <lb/>
              zione, sarà, chiamata C la circonferenza, BC:CF=C:CA=KP:KR=
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              KL:KZ=RT:RZ. </s>
              <s>Dividendo la prima e l'ultima ragione e de'loro ter­
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              mini facendo il quadrato, BC2:BF2=RT2:TZ2. </s>
              <s>Con simile ragione dimo-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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