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

Table of figures

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              clinato, et in perpendiculo, permutatim respondent longitudini et elevationi
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              eiusdem plani. </s>
              <s>” </s>
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              <s>“ Sit ad horizontem AB (fig. </s>
              <s>162) planum inclinatum CA, in quo su­
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              <s>Figura 162.
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              matur quodcumquo punctum C, et, dimissa perpendi­
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              culari ad horizontem CB, sit plani CA altitudo seu ele­
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              vatio. </s>
              <s>Dico momentum gravitatis mobilis D, super plano
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              CA, ad totale suum momentum in perpendiculo CB,
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              esse ut altitudo CB ad eiusdem plani longitudinem CA ”
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              (MSS. Gal., P. V, T. II, fol. </s>
              <s>179). Per la dimostrazione
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              di ciò rimanda Galileo al suo trattato Della scienza mec­
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              canica, che doveva dunque nel 1602 esser noto, benchè
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              andasse attorno anonimo e manoscritto. </s>
              <s>“ Id autem ex Mechanicis probatum
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              est ” (ibid.). </s>
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              <s>PROPOSITIO II. — “ Momenta gravitatis eiusdem mobilis, super diver­
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              sas planorum inclinationes, habent inter se permutatim eamdem rationem,
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              <s>Figura 163.
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              quam eorumdem planorum longitudines, dum eidem
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              elevationi respondeant. </s>
              <s>” </s>
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              <s>“ Sint diversae planorum inclinationes AB, AC
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              (fig. </s>
              <s>163) quae eidem elevationi AD respondeant. </s>
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              Dico momentum gravitatis eiusdem mobilis super
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              AB, ad momentum gravitatis super AC, eamdem
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              habere rationem quam longitudo AC habet ad lon­
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              gitudinem AB. </s>
              <s>Ex antecedenti enim momenta gra­
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              vitatis super AB, ad totale momentum in perpen­
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              diculo AD, est ut AD ad AB. </s>
              <s>Totale vero momen­
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              tum per AD, ad momentum per AC, est ut CA
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              ad AD. Ergo, ex aequali, in analogia perturbata, momentum per AB, ad
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              momentum per AC, erit ut longitudo AC ad longitudinem AB. </s>
              <s>Quod erat
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              demonstrandum ” (ibid.). </s>
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              <s>PROPOSITIO III. — “ Sit ad horizontalem AH (fig. </s>
              <s>164) perpendicula­
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              <s>Figura 164.
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              ris BC, et inclinata BD, in qua sumatur
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              BE, et ex E, ad BD, perpendicularis aga­
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              tur EF, ipsi BC occurrens in F. </s>
              <s>Demon­
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              strandum sit tempus per BE aequari
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              tempori per BF. ” </s>
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              <s>“ Ducatur ex E perpendicularis ad
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              AB, quae sit EG, et quia impetus per
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              BE, ad impetum per EG, est ut EG ad
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              BE, ut supra demonstratur, ut autem
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              EG ad BE, ita BE ad BF, ob similitudi­
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              nem triangulorum GEB, BEF; ergo, ut
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              BF spacium, ad spacium BE, ita impetus
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              per BF ad impetum per BE. </s>
              <s>Ergo eodem tempore fiet motus per BF et
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              per BE ” (ibid., fol. </s>
              <s>147 ad terg.). </s>
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