Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N1A407">
            <pb pagenum="168" xlink:href="026/01/200.jpg"/>
            <p id="N1B27D" type="main">
              <s id="N1B27F">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              58.
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              </s>
            </p>
            <p id="N1B28B" type="main">
              <s id="N1B28D">
                <emph type="italics"/>
              Impetus naturalis non decreſcit etiam in arcu deſcenſus
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              ; probatur quia
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              creſcit, vt dictum eſt ſuprà, igitur non decreſcit. </s>
            </p>
            <p id="N1B298" type="main">
              <s id="N1B29A">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              59.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1B2A6" type="main">
              <s id="N1B2A8">
                <emph type="italics"/>
              Deſtruitur impetus violentus pro rata. </s>
              <s id="N1B2AD">id eſt, qua proportione eſt frustrà;
                <emph.end type="italics"/>
                <lb/>
              v.g. </s>
              <s id="N1B2B4">ſit impetus per AD inclinatam ſurſum, & alius per AB perpendi­
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              cularem deorſum; </s>
              <s id="N1B2BA">haud dubiè motus erit per AC; </s>
              <s id="N1B2BE">igitur concurrunt
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              ad motum AC motus AB & AD, vel potiùs impetus; </s>
              <s id="N1B2C4">igitur debet de­
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              ſtrui impetus in ea proportione, in qua AC eſt minor AG, id eſt com­
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              poſita ex AD, DC, quod impetus AB non poſſit deſtrui; </s>
              <s id="N1B2CC">totum id
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              quod deſtruetur detrahetur impetui AD; </s>
              <s id="N1B2D2">igitur aſſumatur DF ſcilicet
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              differentia AC, & AG; impetus deſtructus ita ſe habet ad impetum
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              AD, vt DF ad AD, & ad reſiduum impetum ex AD, vt DF ad FA,
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              quæ omnia conſtant ex Th.7. ſit ergo AC fig. </s>
              <s id="N1B2DC">49. perpendicularis ſur­
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              ſum, AD inclinata, AB horizontalis; ſit impetus violentus reſpondens
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              AD, & naturalis DG, ducatur AGK, ex AD detrahatur DF, id eſt
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              differentia AG & compoſitæ ex AD. DG, ſupereſt AF, cui aſſumitur
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              æqualis GK, ex qua detrahitur KH, id eſt differentia GL, & compoſitæ
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              ex GK, KL, ſupereſt GH, cui LO accipitur æqualis, cui detrahitur
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              OM, id eſt differentia LP & compoſitæ ex LO, OP, ſupereſt ML, cui
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              æqualis accipitur PR, atque ita deinceps. </s>
              <s id="N1B2EE">Porrò demonſtratur deſtrui
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              impetum violentum iuxta hanc proportionem; </s>
              <s id="N1B2F4">quia deſtruitur, qua
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              proportione eſt fruſtrà, pro rata per Ax.2.& Th.7.ſed totus impetus qui
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              concurrit ad ſecundam lineam AG, eſt compoſitus ex AD, GD; </s>
              <s id="N1B2FC">quia ſi
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              naturalis ſolus eſſet, percurreret ſpatium æquale DG; </s>
              <s id="N1B302">ſi verò ſolus eſſet
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              violentus percurreret ſpatium æquale AD; </s>
              <s id="N1B308">igitur vterque ſimul ſumptus
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              eſt vt
                <expan abbr="cõpoſita">compoſita</expan>
              , ex AG. DG. igitur ſi ea proportione eſt fruſtrà, qua motus
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              deficit, cùm AG ſit motus; </s>
              <s id="N1B314">certè motus eſt ad impetum, vt AG ad
                <expan abbr="compo-ſitã">compo­
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                ſitam</expan>
              ex AD. DG; </s>
              <s id="N1B31E">igitur deficit motus tota DF quæ eſt differentia AG &
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                <expan abbr="cõpoſitæ">compoſitæ</expan>
              ex AD. DG; </s>
              <s id="N1B327">igitur impetus eſt fruſtrà in ratione DF; </s>
              <s id="N1B32B">igitur de­
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              bet deſtrui in ratione DF; </s>
              <s id="N1B331">ſed impetus DG ſeu naturalis nihil deſtrui­
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              tur per Th.57. & 58. igitur ex violento AD deſtruitur DF; </s>
              <s id="N1B337">igitur ſu­
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              pereſt tantum AF vel æqualis GK; </s>
              <s id="N1B33D">ſimiliter impetui GK & KL re­
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              ſpondet motus GL, ſed GL eſt minor compoſita ex GK & KL ſeg­
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              mento KH; </s>
              <s id="N1B345">igitur eſt fruſtrà impetus in ratione KH; </s>
              <s id="N1B349">igitur deſtruitur
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              in eadem ratione KH, non ex naturali KL; </s>
              <s id="N1B34F">igitur ex violento GK;
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              igitur ſupereſt tantum GH, vel æqualis LO, in qua ſimiliter procedi­
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              tur. </s>
              <s id="N1B357">& ſupereſt LM vel æqualis PR, atque ita deinceps. </s>
            </p>
            <p id="N1B35A" type="main">
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                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
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              1.
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              </s>
            </p>
            <p id="N1B369" type="main">
              <s id="N1B36B">Hinc deſtruitur impetus initio motus in maiori quantitate, quia </s>
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