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

Table of figures

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              dici de gradibus latitudinis trianguli ABC (fig. </s>
              <s>147), et tamen haud credo
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              negaturum il um quin inter punctum A et lineam BC reperiuntur latitudi­
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                <figure id="id.020.01.2076.1.jpg" xlink:href="020/01/2076/1.jpg" number="338"/>
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              <s>Figura 147.
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              nes omnes ipsa BC minores ” (Epistol., P. II cit., pag. </s>
              <s>249). </s>
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              <s>Le censure del Fermat sulla legge galileiana de'moti
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              accelerati, e le risposte di Galileo stesso e del Cartesio ri­
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              masero per qualche tempo ne'privati commerci scientifici
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              di quegli Autori, cosicchè le prime delle dette censure,
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              pubblicamente note, vennero da quel Baliani, il quale ve­
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              demmo quanto si fosse compiaciuto di aver ritrovato della
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              detta legge galileiana una nuova dimostrazione. </s>
              <s>Notabile
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              che poi confessasse di essersi messo a dimostrar quel teo­
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              rema, non perchè lo credesse vero, ma per emulare o per prevenire, in
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              una esercitazione geometrica, Galileo rimasto ingannato, diceva, da fallaci
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              esperienze, alle quali, chi saviamente supplisca con la ragione, troverebbe
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              non crescer veramente gli spazi secondo la serie dei numeri impari, ma se­
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              condo quella piuttosto dei numeri naturali. </s>
              <s>Il discorso, che faceva il Mate­
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              matico genovese, per provare il suo assunto, si riduce al seguente. </s>
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              <s>Sia da A (fig. </s>
              <s>148) passato un mobile in E, indipendentemente dall'im­
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              peto acquistato per la forza d'inerzia, la quale incominci ad agire in E. È
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                <figure id="id.020.01.2076.2.jpg" xlink:href="020/01/2076/2.jpg" number="339"/>
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              <s>Figura 148.
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              chiaro che tanto maggiori sa­
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              ranno le parti, in che s'intende
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              esser diviso lo spazio AE, quanto
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              saranno più piccole. </s>
              <s>Suppongasi
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              che siano dieci, e che il mobile abbia in tre tempi uguali successivamente
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              passati gli spazi AB, BC, CD. Quante, in questi spazi, si troveranno ad AE
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              particelle uguali? </s>
              <s>Sarà facile a dar di ciò la risposta, sommando la serie
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              de'numeri naturali da uno infino a dieci; da 11 infino a 20, e da 21 infino
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              a 30. E perchè la prima somma dà 55, la seconda 155, e la terza 255, delle
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              particelle uguali ad AE se ne conteranno in AB 55, in BC 155, in CD 255.
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              Gl'incrementi dunque degli spazi AB, BC, CD staranno come 55; 155; 255,
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              ossia come 11; 31; 51, con qualche notabile differenza dalla serie de'numeri
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              impari. </s>
              <s>Ora, se non in dieci, ma in cento parti, dividasi lo spazio AE, si
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              troverà, come dianzi operando, contenersene in AB, di quelle centesime
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              5050; in BC 15050; in CD 25050, procedenti nella serie de'numeri 101,
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              301, 501, pochissimo differente da quella de'numeri impari ab unitate. </s>
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              <s>Da un tal discorso poi il Baliani stesso trae questa conclusione: “ Au­
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              getur igitur, ni fallor, motus iuxta progressionem arithmeticam, non nume­
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              rorum imparium ab unitate hucusque creditam, sed naturalem. </s>
              <s>At nihilo­
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              minus cum fere idem effectus subsequatur, ob insensibilem discrepantiam,
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              mirandum non est creditum fuisse spatia esse in duplicata ratione tempo­
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              rum, quando quidem, etiamsi verum praecise fortasse non sit, est attamen
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              adeo veritati proximum, ut veritatem in adhibitis experimentis sensus per­
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              cipere nequiverit: quamobrem excusandi sunt quicumque ita censuerunt. </s>
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              Ego autem modo veritatem delitescentem detexisse spero, causam nimirum, </s>
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