Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              <s id="N1A916">
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              Theorema
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              17.
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            <p id="N1A922" type="main">
              <s id="N1A924">
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              Si motus mixtus conſtet ex æquabili, & accelerato naturaliter ſit per li­
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              neam curuam
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              ; </s>
              <s id="N1A92F">ſit enim impetus per AF motu æquabili, & per AC motu
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              accelerato naturaliter, ita vt eo tempore quo percurritur ſeorſim ſpa­
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              tium AB percurratur AD triplum; </s>
              <s id="N1A937">certè ex vtroque primo tempore re­
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              ſultat linea motus mixti AE, ſecundo tempore EG, ſed AEG non eſt
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              recta; alioquin duo triangula ABE, ACG eſſent proportionalia, quod
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              eſt abſurdum. </s>
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            <p id="N1A941" type="main">
              <s id="N1A943">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              18.
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              </s>
            </p>
            <p id="N1A94F" type="main">
              <s id="N1A951">
                <emph type="italics"/>
              Hæc linea eſt Parabola
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              ; </s>
              <s id="N1A95A">quod ipſe Galileus toties inſinuauit, & quiuis
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              etiam rudior Geometra intelliget; in quo diutiùs non hæreo, præſertim
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              cùm nullus ſit motus, qui conſtet ex æquabili, & naturaliter accelerato,
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              vt demonſtrabimus infrà. </s>
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            <p id="N1A964" type="main">
              <s id="N1A966">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              19.
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              </s>
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            <p id="N1A972" type="main">
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              Si motus mixtus conſtet ex æquabili & naturaliter retardato, fit per lineam
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              curuam
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              ; ſi enim eo
                <expan abbr="tẽpore">tempore</expan>
              quo per NE ſurſum proiicitur corpus graue
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              & conſequenter motu naturaliter retardato impellatur per NI motu
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              æquabili, diuidatur NI in 4. partes æquales v.g. ductis parallelis RD,
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              NE, PC, &c. </s>
              <s id="N1A98B">aſſumatur NS vel RM, cui affigatur quilibet numerus impar; </s>
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              putà 7. itaque RM ſint 7. ducatur HM parallelæ IN, aſſumatur QL 5.
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              ducatur GL parallela, accipiatur VK 3. ducatur FK: </s>
              <s id="N1A996">denique aſſumatur
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              FAI ducaturque AE parallela IN, & deſcribatur per puncta AKLMN,
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              linea curua; </s>
              <s id="N1A99E">hæc eſt Parabola, vt conſtat ex Geometria; </s>
              <s id="N1A9A2">nam ſi BK eſt 1.
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              CL erit 4. DM 9. EV 16. ſed æquales ſunt AF.AG.AH.AI. prioribus vt
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              patet; </s>
              <s id="N1A9AA">igitur ſagittæ ſunt vt quadrata
                <expan abbr="applicatarũ">applicatarum</expan>
              ; </s>
              <s id="N1A9B2">igitur hæc eſt Parabola;
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              igitur curua, atqui motus mixtus prædictus fieret per hanc lineam, nam
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              eo tempore quo mobile eſſet in S, erit in M, concurrit enim vterque im­
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              petus pro rata, & eo tempore, quo eſſet in K erit in L, atque ita
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              deinceps. </s>
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            <p id="N1A9BE" type="main">
              <s id="N1A9C0">
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              Scholium.
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            <p id="N1A9CC" type="main">
              <s id="N1A9CE">Obſeruabis eſſe prorſus inuerſam prioris, quæ ſit ex motu æquabili, &
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              naturaliter accelerato; </s>
              <s id="N1A9D4">ſi enim per AE ſit æquabilis & æqualis priori
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              per NI, & per AI ſit acceleratus, ſi quo tempore peruenit in B motu æ­
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              quabili perueniat in F motu accelerato; haud dubiè perueniet in K, mox
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              in L, &c. </s>
              <s id="N1A9DE">quia eadem proportione, ſed inuerſa quâ retardatur,
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              acceleratur; </s>
              <s id="N1A9E4">igitur ſi vltimo tempore retardati acquirit tantùm
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              YE; </s>
              <s id="N1A9EA">primo tempore æquali ſcilicet accelerati acquiret AF, atque ita
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              deinceps ſi per NE ſit retardatus, & per NI æquabilis linea motus mixti
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              erit NLA; </s>
              <s id="N1A9F2">ſi verò ſit per AI acceleratus, & per AE æquabilis æqualis
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              priori per NI, lineamosus mixti erit ALN eadem ſcilicet cum priori
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              mutatis tantùm terminis à quo, & ad quem; vtrùm verò in rerum natu­
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              ra ſit huiuſmodi motus videbimus infrà. </s>
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