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

Table of figures

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              tutta intera la AB. </s>
              <s>Se s'immagini ora nel punto C essere applicato un piano
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              EF, perpendicolare ad AC, tanto fa al grave a pendere dal braccio della
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              Leva, quanto a riposare sul piano, per scendere lungo il quale esercita ugual
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              momento che lungo l'arco del cerchio. </s>
              <s>Dunque anche il momento parziale di
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              C, posato sul piano EF, sarà al momento totale come AD ad AC, ossia AB,
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              e come EG sta ad EF, per la similitudine dei triangoli. </s>
              <s>“ Però concluderemo,
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              scrive Galileo, questa universal proposizione col dire: sopra il piano la forza
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              al peso avere la medesima proporzione che la perpendicolare, dal termine
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              del piano tirata all'orizzonte, alla lunghezza di esso piano ” (ivi, pag. </s>
              <s>118). </s>
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              <s>Correva attorno questa galileiana dimostrazione manoscritta, prima del­
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              l'anno 1615, sotto il nome del Vieta, cosa creduta da molti, come dal Ba­
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              liani (Alb. </s>
              <s>XVI, 105) anche in Italia, ma benchè più seducente era nondi­
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              meno più lubrica di quella del Tartaglia. </s>
              <s>Attribuisce Alessandro Marchetti
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              a questa lubricità, delìa quale vedremo nella seguente parte del nostro di­
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              scorso gli esempii, l'aver Galileo tenuto altro modo nell'aggiunta postuma
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              al terzo dialogo Delle due nuove scienze. </s>
              <s>Ivi, come lo stesso Tartaglia, sug­
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              geritogli forse dall'Herigonio, di cui siam certi aver esso Galileo fra'suoi
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              libri il Corso matematico (Alb. </s>
              <s>X, 211, 28); dimostra esser due gravi con­
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              giunti insieme in equilibrio, quando le ascese e le discese virtuali nel per­
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              pendicolo stanno reciprocamente fra loro come i pesi. </s>
              <s>“ Mentrechè dunque
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              il grave D (nella passata figura CIX) movendosi da A in C, resiste solo nel
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              salire lo spazio perpendicolare CB, ma che l'altro G scende a perpendicolo,
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              necessariamente quanto tutto lo spazio AC, e che tal proporzione di salita
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              e scesa si mantiene sempre l'istessa, poco o molto che sia il moto dei detti
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              mobili, per esser collegati insieme; possiamo assertivamente affermare che,
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              quando debba seguire l'equilibrio, cioè la quiete tra essi mobili, i momenti,
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              le velocità o le lor propensioni al moto, cioè gli spazii che da loro si pas­
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              serebbero nel medesimo tempo, devon rispondere reciprocamente alle loro
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              gravità ” (Alb. </s>
              <s>XIII, 176). Posto il qual principio, professato dal Tartaglia,
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              la conclusione era necessariamente la medesima, cosicchè il teorema del Ma­
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              tematico di Brescia aveva un secolo dopo dal Fiorentino la sua più solenne
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              conferma. </s>
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              <s>Era venuto però in quel tempo il Nardi a mettere scrupolo intorno alle
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              discese, e alle velocità virtuali, invocando il logicale assioma che
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              a posse ad
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              esse non valet illatio,
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              nè parendo ragionevole il trattar di una cosa da farsi,
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              come se fosse già fatta. </s>
              <s>Persuaso anche il Torricelli che dalle propensioni
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              al moto non si potesse ragionevolmente argomentare al moto, ebbe a cer­
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              care altro principio così formulato: “ Duo gravia simul coniuncta ex se
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              moveri non posse, nisi centrum commune gravitatis ipsorum descendat ”
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              (Op. </s>
              <s>geom., P. </s>
              <s>I cit., pag. </s>
              <s>99); principio che si trovò opportuno a dimo­
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              strare il teorema del Tartaglia, e fecondo di altre bellissime conseguenze. </s>
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              <s>Se sopra i due piani CM, CN (fig. </s>
              <s>111) diversamente inclinati, e insi­
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              stenti sulla medesima orizzontale MN, sien posati due corpi tali, che i loro
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              pesi stiano come le linee CM, CN, bilanciati insieme poseranno in equilibrio, </s>
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