Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N15AC3">
            <p id="N16AAF" type="main">
              <s id="N16AB1">
                <pb pagenum="91" xlink:href="026/01/123.jpg"/>
                <emph type="italics"/>
              tertij ad ſecundum quàm quarti ad tertium, atque ita deinceps
                <emph.end type="italics"/>
              ; </s>
              <s id="N16AC5">ſit enim
                <lb/>
              primo inſtanti velocitas vt 1.ſecundo erit, vt 2.tertio, vt 3.quarto, vt 4.
                <lb/>
              ſed maior eſt proportio 2.ad 1.quàm 3.ad 2. & hæc maior quàm 4. ad 3.
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              atque ita deinceps; </s>
              <s id="N16ACF">ſimiliter maior eſt proportio ſpatij quod percurritur
                <lb/>
              ſecundo inſtanti ad ſpatium, quod percurritur primo, quàm ſpatij, quod
                <lb/>
              percurritur ſecundo inſtanti ad ſpatium, quod percurritur primo quàm
                <lb/>
              ſpatij quod percurritur tertio ad ſpatium, quod percurritur ſecundo, at­
                <lb/>
              que ita deinceps; eſt enim eadem ratio ſpatiorum quæ ſingulis inſtanti­
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              bus reſpondent, quæ velocitatum, vt demonſtratum eſt ſuprà. </s>
            </p>
            <p id="N16ADD" type="main">
              <s id="N16ADF">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              45.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16AEB" type="main">
              <s id="N16AED">
                <emph type="italics"/>
              Minor eſt proportio totius ſpatij, quod acquiritur duobus instantibus ad to
                <lb/>
              tum ſpatium, quod acquiritur vno, quàm ſit illius, quod acquiritur quatuor in­
                <lb/>
              ſtantibus ad aliud, quod acquiritur duobus
                <emph.end type="italics"/>
              ; patet ex dictis; </s>
              <s id="N16AFA">ſi enim primo
                <lb/>
              inſtanti acquiritur vnum ſpatium, ſecundo acquiruntur 2.igitur duobus
                <lb/>
              ſimul acquirantur 3. igitur proportio eſt vt 3.ad 1.Sed ſi duobus acqui­
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              runtur 3. ſpatia; </s>
              <s id="N16B04">certè 4.inſtantibus acquiruntur 10. igitur proportio eſt
                <lb/>
              vt 10.ad 3. ſed proportio 10/3 eſt maior 3/1, erit adhuc maior proportio ſpa­
                <lb/>
              tij quod acquiretur 6. inſtantibus ad illud quod acquiritur tribus; eſt
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              enim (21/6) vt patet. </s>
            </p>
            <p id="N16B0E" type="main">
              <s id="N16B10">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              46.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16B1C" type="main">
              <s id="N16B1E">
                <emph type="italics"/>
              Si componatur æquabilis motus ex ſubdupla velocitate maxima, & mini­
                <lb/>
              ma, æquali tempore, idem ſpatium percurretur hoc motu naturaliter accelera­
                <lb/>
              to
                <emph.end type="italics"/>
              ; </s>
              <s id="N16B2B">ſit enim maxima velocitas vt 6. minima vt 1. motu naturaliter acce­
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              lerato percurrentur ſpatia 21. cuius ſummæ termini ſunt 6.igitur 6. in­
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              ſtantibus conſtat hic motus; </s>
              <s id="N16B33">accipiatur ſubduplum maximæ, & minimæ
                <lb/>
              velocitatis, ſcilicet 3 1/2. sítque velocitas motus æquabilis inſtantium 6.
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              haud dubiè ſi ducantur 3 1/2 in 6 erunt 21.ratio ex eo petitur quod ſcili­
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              cet, vt habeatur ſumma progreſſionis arithmeticæ, debet addi primus
                <lb/>
              terminus maximo, & aſſumi ſubduplum totius; </s>
              <s id="N16B3F">illudque ducere in nu­
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              merum terminorum per regulam arithmeticam; </s>
              <s id="N16B45">atqui eadem eſt ratio
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              velocitatum, quæ ſpatiorum; vt dictum eſt ſuprà; ſcilice, in ſingulis
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              inſtantibus. </s>
            </p>
            <p id="N16B4D" type="main">
              <s id="N16B4F">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              47.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16B5B" type="main">
              <s id="N16B5D">
                <emph type="italics"/>
              Si aſſumantur partes temporis majores; quæ ſcilicet pluribus inſtantibus
                <lb/>
              constent, ſerueturque eadem accelerationis progreſſio arithmetica, ſpatium
                <lb/>
              quod ex ſumma huius progreſſionis reſultabit, erit minus vero,
                <emph.end type="italics"/>
              ſint enim 6.in­
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              ſtantia, & cuilibet iuxta progreſſionem prædictam ſuum ſpatium reſpon­
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              deat, haud dubiè ſpatium ſecundi erit duplum ſpatij primi, & tertium
                <lb/>
              triplum, &c. </s>
              <s id="N16B70">vt conſtat ex dictis; </s>
              <s id="N16B73">igitur erunt ſpatia 21. iam verò aſſu­
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              mantur 3. partes temporis, quarum quælibet ex 2. conſtet inſtantibus; </s>
              <s id="N16B79">
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              primæ parti tria ex prædictis ſpatiis reſpondeant; </s>
              <s id="N16B7E">certè ſi ſeruetur pro­
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              greſſio arithmetica, ſecundæ reſpondebunt 6. & tertiæ 9. igitur totum
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              ſpatium erit 18. minus vero quod erat 21. ſi verò aſſumantur tantùm 2.
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              partes, quarum quælibet tribus inſtantibus conſtet; </s>
              <s id="N16B88">primæ parti reſpon-</s>
            </p>
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