Fabri, Honoré, Tractatus physicus de motu locali, 1646

Table of figures

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              tunc enim deſcendunt inæqualiter, ſiue diuerſæ materiæ & diuerſæ fi­
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              guræ; </s>
              <s id="N18F48">tunc enim deſcendunt modò æqualiter, modò inæqualiter; </s>
              <s id="N18F4C">æquali­
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              ter certè, cum figura compenſat materiam; </s>
              <s id="N18F52">cum verò non compenſat,
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              inæqualiter pro rata; </s>
              <s id="N18F58">denique ſi comparentur duo corpora cum diuerſis
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              mediis; primo inuenienda eſt proportio motuum vtriuſque in eodem
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              tùm ſingulorum in diuerſis mediis, vt ſuprà dictum eſt. </s>
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            <p id="N18F60" type="main">
              <s id="N18F62">
                <emph type="center"/>
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              Theorema
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              124.
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              </s>
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            <p id="N18F6E" type="main">
              <s id="N18F70">
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              In modico vacuo omnia æquè velociter deſcenderent
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              : </s>
              <s id="N18F79">Probatur, quia tota
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              diuerſitas vel inæqualitas mediorum petitur à diuerſa proportione acti­
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              uitatis cum reſiſtentia medij per Ax. 5. ſed in vacuo nulla eſt reſiſten­
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              tia; </s>
              <s id="N18F83">igitur nulla proportio; igitur nulla ratio motus inæqualis. </s>
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            <p id="N18F87" type="main">
              <s id="N18F89">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              125.
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              </s>
            </p>
            <p id="N18F95" type="main">
              <s id="N18F97">
                <emph type="italics"/>
              In motu natur aliter accelerato deorſum creſcit reſistentia medij ſingulis in­
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              ſtantibus
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              : </s>
              <s id="N18FA2">probatur, quia ſingulis inſtantibus plures partes medij ſunt
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              ſuperandæ; </s>
              <s id="N18FA8">creſcunt enim ſpatia, vt conſtat ex dictis; igitur creſcit reſi­
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              ſtentia ſingulis inſtantibus. </s>
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            <p id="N18FAE" type="main">
              <s id="N18FB0">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              126.
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              </s>
            </p>
            <p id="N18FBC" type="main">
              <s id="N18FBE">
                <emph type="italics"/>
              Creſcit reſistentia iuxta rationem ſpatiorum,
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              probatur; </s>
              <s id="N18FC7">quia creſcit iux­
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              ta rationem plurium partium medij, quæ temporibus æqualibus percur­
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              runtur; ſed eæ creſcunt iuxta rationem ſpatiorum, vt conſtat. </s>
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            <p id="N18FCF" type="main">
              <s id="N18FD1">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              127.
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              </s>
            </p>
            <p id="N18FDD" type="main">
              <s id="N18FDF">
                <emph type="italics"/>
              Hinc creſcit reſiſtentia iuxta rationem velocitatum ſingulis instantibus
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              ; </s>
              <s id="N18FE8">
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              quæ ratio ſequitur progreſſionem arithmeticam ſimplicem numerorum
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              1.2.3.4.5.6. ex ſuppoſitione quòd tempus conſtet ex partibus finitis actu; </s>
              <s id="N18FEF">
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              nam eodem modo creſcit velocitas, quo creſcunt numeri prædicti; </s>
              <s id="N18FF4">ſed
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              eodem modo creſcunt ſpatia, ſi dumtaxat accipiantur in ſingulis inſtan­
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              tibus; </s>
              <s id="N18FFC">reſiſtentia creſcit iuxta rationem ſpatiorum; igitur iuxta ratio­
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              nem velocitatum. </s>
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            <p id="N19002" type="main">
              <s id="N19004">
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              Scholium.
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                <emph.end type="center"/>
              </s>
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            <p id="N19010" type="main">
              <s id="N19012">Obſeruabis, ſi tempus conſtet ex infinitis actu partibus, ita vt ſingu­
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              læ partes motus ſingulis partibus temporis & infinitæ infinitis reſpon­
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              deant; </s>
              <s id="N1901A">non poteſt eſſe alia progreſſio, in qua fiat acceleratio motus na­
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              turalis, quàm illa Galilei iuxta hos numeros 1. 3. 5. 7. vt conſtat ex dictis
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              per illud Principium; </s>
              <s id="N19022">
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              æqualibus temporibus æqualia acquiruntur velocita­
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              tis momenta
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              ; </s>
              <s id="N1902D">ſi verò tempus conſtat ex finitis inſtantibus æqualibus, nul­
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              la datur progreſſio motus naturaliter accelerati; </s>
              <s id="N19033">quia motus accelerari
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              non poteſt; </s>
              <s id="N19039">ne ſcilicet eodem inſtanti mobile ſit in pluribus locis adæ­
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              quatis; denique ſi tempus conſtat ex finitis inſtantibus actu, & infinitis
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              potentiâ, non poteſt eſſe alia progreſſio huius accelerationis, quam hæc
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              noſtra iuxta numeros toties repetitos 1.2.3.4.5. attamen quia illa finita
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              inſtantia ſunt ferè innumera in qualibet parte ſenſibili temporis, in
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              praxi ſine ſenſibili errore in partibus temporis ſenſibilibus poſſumus </s>
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