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

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          <chap>
            <pb xlink:href="020/01/2109.jpg" pagenum="352"/>
            <p type="main">
              <s>COROLLARIUM II. — “ Patet rursus totum tempus per ABC, ad tempus
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              per AB, esse sesquialterum ” (ibid., fol. </s>
              <s>181). </s>
            </p>
            <p type="main">
              <s>Le proposizioni III e IV, che contengono in sè dimostrato il principio
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              meccanico, son le medesime della I e II, scritte nel primo Libro, e si pre­
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              mettono qui come necessarie a concluderne la proposizione V, che è la V
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              di quello stesso primo Libro, corredata però di un elegante corollario. </s>
              <s>Fu
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              un tal corollario suggerito a Galileo dall'essersi, in cercare i mezzi termini
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              della detta V proposizione, incontrato nel seguente teorema: Sia CDA (fig. </s>
              <s>174)
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                <figure id="id.020.01.2109.1.jpg" xlink:href="020/01/2109/1.jpg" number="365"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 174.
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              un circolo, a cui giunga nel punto A la AF tan­
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              gente. </s>
              <s>Se si conducano dal punto di contatto le due
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              corde AC, AD, e presa AB=AD, si abbassino da
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              B, D alla AF due perpendicolari, s'avrà la propor­
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              zione DF:EB=AD:AC. </s>
            </p>
            <p type="main">
              <s>Facendo ora il trapasso dalla Geometria alla
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              Meccanica, considerando la AF orizzontalmente di­
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              retta, e AD, AC quali due piani inclinati, il dimo­
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              strato teorema geometrico, insieme con la detta pro­
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              posizione V, davan facile modo a Galileo di risolver
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              questo meccanico teorema: Sopra il piano AC trovare il punto, da cui par­
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              tendosi un mobile, giunga in A nel medesimo tempo, che vi giungerebbe
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              quel medesimo mobile, partendosi da D sull'altro piano; imperocchè la cer­
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              cata lunghezza AC s'è trovato esser quarta proporzionale dopo DF, EB, AD,
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              ed essere di più una corda che, partendosi dal medesimo infimo punto del
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              diametro a un punto della medesima circonferenza, si sa, per la dimostrata
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              proposizione V, dover essere alla corda AD tautocrona, per cui soggiungesi
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              da Galileo così a quella stessa V proposizione, per modo di corollario: </s>
            </p>
            <p type="main">
              <s>“ Collige, existentibus planis inaequaliter inclinatis AD, AC, atque data
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              longitudine AD, inveniri posse, in plano AC, portionem, quae eodem tem­
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              pore cum DA peragatur. </s>
              <s>Ducto enim perpendiculo DF, et, posita AB ae­
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              quali AD, ducto perpendiculo BE, fiat, ut DF ad EB, ita DA ad AC, erit­
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              que tempus per CA aequalc tempori per DA ” (ibid., fol. </s>
              <s>47). </s>
            </p>
            <p type="main">
              <s>Così nuovamente preparate le cose, nel corollario della prima proposi­
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              zione, nel teorema meccanico, e in questo ultimo del tautocronismo delle
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              corde nel cerchio; passava felicemente Galileo, senza nulla supporre, a di­
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              mostrar questa, che è in ordine la VI proposizione del Libro, e che può
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              considerarsi rispetto all'altre come la canocchia, dalla quale si dovrà trarre
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              e compilare il lungo filo. </s>
            </p>
            <p type="main">
              <s>PROPOSITIO VI. — “ Tempus casus per planum inclinatum, ad tempus
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              sasus per lineam suae altitudinis, est ut eiusdem plani longitudo ad longi­
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              tudinem suae altitudinis. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Sit planum inclinatum BA (fig. </s>
              <s>175) ad lineam horizontis AC, sitque
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              linea altitudinis perpendicularis BC: Dico tempus casus, quo mobile move­
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              tur per BA, ad tempus, in quo cadit per BC, esse ut BA ad BC. ” </s>
            </p>
            <p type="main">
              <s>“ Erigatur perpendicularis ad horizontem ex A, quae sit AD, cui oc-</s>
            </p>
          </chap>
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