Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

Table of figures

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              Cap. 10. de
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              æquitempo­
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              ranea natu­
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              rali veloci­
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              tate
                <expan abbr="grauiũ">grauium</expan>
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              PROP. CCVII.
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              Corpora homogenea commenſurabilem proportionem haben­
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              tia æquè velocitèr deſcendent ablatis omnibus impe­
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              dimentis.
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              <s id="s.002305">SInt quęlibet duo corpora homogenea A, & B, quę
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              habeant quamcumque commenſurabilem pro­
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              portionem. </s>
              <s id="s.002306">Dico, quod ex ſui na­
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              tura ablatis omnibus
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                tis</expan>
              , hæc duo corpora æquali velo­
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              citate deſcendent, nempè eodem
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              tempore T percurrent duo ſpatia
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              D, & E inter ſe æqualia. </s>
              <s id="s.002307">Reperia­
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              tur corpus C homogeneum ipſis
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              A, & B, quod communis menſura
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              ſit eorum; hoc verò tempore T deſcendat ſpatium F; &
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              quia duorum corporum ſimiliarium A multiplex eſt
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              ipſius C, ergo æquè velocia erunt, nempè ſpatia D, &
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              F eodem tempore T exacta æqualia ſunt inter ſe. </s>
              <s id="s.002308">ea­
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              dem ratione duo ſpatia E, & F tranſacta eodem tem­
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              pore T ab homogeneis corporibus B, & C
                <expan abbr="multiplicẽ">multiplicem</expan>
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              proportionem habentibus æqualia erunt inter ſę;
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              vnde ſequitur quod duo ſpatia D, & E. excurſa
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              tempore T ab homogeneis corporibus A, & B æqua­
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              lia ſint inter ſe, cùm æquentur vni tertio F. </s>
              <s id="s.002309">Quare pa­
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              tet propoſitum.
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