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

Table of figures

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                <pb xlink:href="020/01/2103.jpg" pagenum="346"/>
              e a un'altra corda qualunque. </s>
              <s>Ora se GP, GQ sono uguali, e similmente
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              inclinate alle DF, DO, i moti per queste è evidente dover essere i mede­
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              simi dei moti per quelle, cosicchè insomma si riduce l'accennato Corollario
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              a dire che in qualunque corda si conduca dall'estremità D o dalla sommità
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              C del diametro a un punto della circonferenza, si spedisce il moto nel me­
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              desimo tempo come se cadesse il mobile per tutta la lunghezza verticale del
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              diametro stesso. </s>
              <s>Le quali cose così ben predisposte conducono Galileo a di­
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              mostrar la seguente proposizione fondamentale. </s>
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              <s>PROPOSITIO VI. — “ Sit planum horizontis secundum lineam ABC (fig. </s>
              <s>167)
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              ad quam sint duo plana inclinata secundum lineas DB, DA. </s>
              <s>Dico idem mo­
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                <figure id="id.020.01.2103.1.jpg" xlink:href="020/01/2103/1.jpg" number="358"/>
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              <s>Figura 167.
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              bile tardius moveri per DA, quam per
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              DB, secundum rationem longitudinis
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              DA ad longitudinem DB. ” </s>
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              <s>“ Erigatur enim ex B perpendicu­
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              laris ad horizontem, quae sit BE: ex D
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              vero, ipsi BD perpendicularis, DE oc­
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              curcens BE in E, et circa BDE trian­
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              gulum circulus describatur, qui tanget
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              AC in puncto B, ex quo, ipsi AD pa­
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              rallela, ducatur BF, et connectatur FD. </s>
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              Patet tarditatem per FB esse consimilem tarditati per DA. </s>
              <s>Quia vero tempore
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              eodem movetur mobile per DB et FB, patet velocitates per BD, ad velocita­
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              tes per BF, esse ut DB ad FB, ita ut semper iisdem temporibus duo mo­
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              bilia, ex punctis D, F venientia, linearum DB, FB partes, integris lineis DB,
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              FB proportione respondentes, peregerint. </s>
              <s>” </s>
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              <s>“ Cum vero angulus BFD, in portione, angulo DBA ad tangentem sit
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              aequalis, angulus vero DBF alterno BDA; aequiangula erunt triangula BFD,
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              ABD, et, ut BD ad BF, ita AD ad DB. </s>
              <s>Ergo ut AD ad DB, ita velocitas
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              per DB ad velocitatem per DA, et ex opposito tarditas per DA, ad tardita­
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              tem per BD. ” </s>
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              <s>“ Si hoc ponatur, reliqua demonstrari possunt. </s>
              <s>Ponatur igitur augeri
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              et imminui motus velocitatem secundum proportionem, qua augentur et
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              minuuntur gravitatis momenta, et cum constet eiusdem mobilis momenta
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              gravitatis super plano DB, ad momenta super plano DA, esse ut longitudo
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              DA ad longitudinem DB; idcirco velocitatem per DB, ad velocitatem per DA,
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              esse ut AD ad DB ” (ibid., fol. </s>
              <s>34). </s>
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              <s>Il linguaggio stesso accenna, come si disse, essere stata delle prime a
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              dimostrarsi questa proposizione, nella quale
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              tardità,
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              o
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              diuturnità,
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              come ad
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              altri piacque dir meglio, si chiama quello, che poi Galileo, nel perfezionato
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              esercizio della sua scienza, chiamerà sempre col nome di
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              tempo.
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              A questo
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              ultimamente trascritto. </s>
              <s>come a teorema antecedentemente dimostrato, accenna
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              il discorso pubblicatosi dall'Albèri (Tomo XI, pag. </s>
              <s>61, 62), da cui si con­
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              ferma che, posto essere i tempi come le lunghezze delle oblique ugualmente
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              elevate,
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              reliqua demonstrari possunt.
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