Baliani, Giovanni Battista
,
De motu naturali gravium solidorum
,
1638
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<
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">PROPOSITIO XXIII.
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<
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">Duo gravia descendentia super planis diversa ratione
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declinantibus, perveniunt ad idem planum orizon-
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tale ea ratione, ut sit eadem proportio inter diutur-
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nitates, quae inter dicta plana si ab eodem puncto ad
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idem planum orizontale producta sint.
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</
subchap1
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<
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<
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id
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">Datis planis AB, AC declinantibus, ductis ab eodem
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puncto A ad planum orizontale BC.
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<
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id
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">Dico quod diuturnitates gravium descendentium per AB, AC
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sint ut AB ad AC.
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<
s
id
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s.000286
">Fiat ut AC ad AB ita AB ad AD, ita ut grave perveniat
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in D eodem tempore quo pervenit in B
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.
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Per 13.
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hujus.
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<
s
id
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">Quoniam est ut AD ad AC, ita quadratum temporis AD
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ad quadratum temporis AC
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, & tempora AD, AB
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sunt aequalia
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, & proinde eorum quadrata; ergo ut AD
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ad AC ita quadratum temporis AB, ad quadratum tem-
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poris AC
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, sed ut AD ad AC, ita quadratum AB ad qua-
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dratum AC
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, ergo ut quadratum temporis AB ad quadra-
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tum temporis AC, ita quadratum AB ad quadratum AC,
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ergo ut tempus AB ad tempus AC, ita AB ad AC
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.
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<
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id
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">Quod fuit probandum.
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Per Cor.
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7. hujus.
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Per 17.
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hujus.
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<
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Per 2.
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pronun.
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<
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Per 19.
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sexti.
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<
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Per 22.
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sexti.
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</
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</
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