Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              tertiæ, & hæc maior differentia tertiæ, & quartæ; atque ita deinceps, nec
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              aliter res eſſe poteſt. </s>
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            <p id="N17DFD" type="main">
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                <emph type="center"/>
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              Theorema
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              67.
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              </s>
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            <p id="N17E0B" type="main">
              <s id="N17E0D">
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              Hinc partes, quo fiunt minores, accedunt propiùs ad æqualitatem,
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              v.g. BD,
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              & DC accedunt propiùs ad æqualitatem quàm AB, BD, & DC, CE, pro­
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              piùs quàm CD, DB, & CE, EF, quàm EC, CD, atque ita deinceps, vt patet;
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              hinc poſt aliquot inſtantia motus, æqualia ferè redduntur inſtantia, vt
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              conſtat. </s>
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            <p id="N17E20" type="main">
              <s id="N17E22">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              68.
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              </s>
            </p>
            <p id="N17E2E" type="main">
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              Hinc qua proportione decreſcunt instantia, decreſcit etiam perfectio
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              impetus
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              ; </s>
              <s id="N17E3B">quia temporibus æqualibus eadem cauſa neceſſaria æqualem ef­
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              fectum producit per Ax. tertium igitur inæqualem inæqualibus, per Ax.
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              13. num.4. igitur minorem minore tempore; </s>
              <s id="N17E44">igitur minorem in eadem
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              proportione, in qua tempus eſt; igitur qua proportione, &c. </s>
            </p>
            <p id="N17E4A" type="main">
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                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              69.
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              </s>
            </p>
            <p id="N17E58" type="main">
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              Hinc vides quâm ſit neceſſaria illa diuerſa perfectio impetus, quam indi­
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              cauimus lib.
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              1. hinc impetus productus ſecundo, & tertio inſtanti adæ­
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              quat impetum productum primo, quem etiam adæquat productus quar­
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              to, quinto, ſexto, item productus ſeptimo, octauo, nono; decimo, atque ita
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              deinceps; </s>
              <s id="N17E6B">hinc eſt eadem differentia impetuum, quæ
                <expan abbr="inſtãtium">inſtantium</expan>
              ; </s>
              <s id="N17E73">hinc ſin­
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              gulis ſpatiis æqualibus primo ſpatio, quod percurritur primo inſtanti; </s>
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              reſpondent ſingula inſtantia, & ſingulis inſtantibus ſinguli, & ſingulares
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              impetus; </s>
              <s id="N17E80">hinc non eſt quod primo inſtanti dicantur produci plura pun­
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              cta impetus in eodem puncto corporis grauis; </s>
              <s id="N17E86">ſed vnicum tantùm pun­
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              ctum talis perfectionis ſcilicet phyſicum; cur enim potius duo puncta,
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              quam tria? </s>
              <s id="N17E8E">ſed quod vnum eſt determinatum eſt per Ax. 5. lib. 1. hinc
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              optima ratio cur potius tali inſtanti producatur impetus talis perfectio­
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              nis quàm alterius? </s>
              <s id="N17E95">quippe perfectio impetus ſequitur perfectionem in­
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              ſtantis quo producitur; </s>
              <s id="N17E9B">hinc dicendum videtur omnia puncta impetus
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              eſſe diuerſæ perfectionis, vel heterogenea; vt vulgò aiunt Philoſophi; </s>
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              cuius rationem demonſtratiuam afferemus lib. ſequenti cum de motu
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              violento; </s>
              <s id="N17EA8">hinc vides duplicem progreſſionem; </s>
              <s id="N17EAC">primam ſcilicet, qua ex
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              ſuppoſitis temporibus æqualibus acquiruntur ſpatia inæqualia, de qua
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              fusè ſuprà; </s>
              <s id="N17EB4">in hac enim velocitas eadem proportione cum impetu creſ­
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              cit, & cum ipſo tempore; </s>
              <s id="N17EBA">hoc eſt tempore triplo eſt tripla, quadruplo
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              quadrupla; </s>
              <s id="N17EC0">item impetus in duplo tempore eſt duplus, in triplo triplus; </s>
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              modò progreſſio fiat in temporibus primo inſtanti æqualibus; </s>
              <s id="N17EC9">ſecunda
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              progreſſio eſt qua ex ſuppoſitis ſpatiis æqualibus tempora fluunt inæ­
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              qualia, hoc eſt minora & minora; </s>
              <s id="N17ED1">quibus etiam reſpondet impetus im­
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              perfectior in eadem proportione temporum; prima fit per differentias
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              æquales, & proportiones inæquales, ſecunda verò per differentias inæ­
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              quales, & proportiones inæquales. </s>
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