Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              co inſtans primum motus; cui æqualia deinde ſuccedunt tem­
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              pora. </s>
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            <p id="N167F7" type="main">
              <s id="N167F9">
                <emph type="center"/>
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              Theorema
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              37.
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              </s>
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            <p id="N16805" type="main">
              <s id="N16807">
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              Hinc creſcit impetus iuxta progreſſionem arithmeticam; </s>
              <s id="N1680D">cum ſingula in­
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              ſtantia æqualem impetum addant
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              ; </s>
              <s id="N16816">ſi primo inſtanti ſit vnus gradus, erunt
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              duo; productus ſcilicet alteri additus qui conſeruatur, tertio erunt;. </s>
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              quarto 4. quinto 5. &c. </s>
              <s id="N16820">igitur creſcit ſecundum progreſſionem arith­
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              meticam. </s>
            </p>
            <p id="N16825" type="main">
              <s id="N16827">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              38.
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              </s>
            </p>
            <p id="N16833" type="main">
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              Eodem modo creſcit velocitas, quia ſingulis inſtantibus æqualia acquirun­
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              tur velocitatis momenta
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              per Ax.2. & per Th.36. </s>
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            <p id="N1683F" type="main">
              <s id="N16841">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              39.
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              </s>
            </p>
            <p id="N1684D" type="main">
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              Maius ſpatium acquiritur ſecundo inſtanti, quàm primo, quia ſecundo
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              inſtanti motus eſt velocior per Th.36. igitur maius conficitur ſpatium,
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              tempore ſcilicet æquali per Def. 2. l. 1. idem dico de tertio, quar­
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              to, &c. </s>
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            <p id="N16860" type="main">
              <s id="N16862">
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              Theorema
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              40.
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              </s>
            </p>
            <p id="N1686E" type="main">
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              Spatium quod acquiritur ſecundò instanti eſt ad ſpatium quod acquiritur
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              primo vt velocitas, quæ eſt ſecundo ad velocitatem, quæ eſt primo.
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              </s>
              <s id="N16879"> Patet per
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              Th.28. quia cum tempora illa ſint æqualia, ſpatia ſunt neceſſariò vt ve­
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              locitates; quippe æquali velocitati æquale ſpatium reſpondet tempore
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              æquali, igitur inæquale inæquali, igitur maius maiori, idem dico de
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              aliis inſtantibus. </s>
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            <p id="N16885" type="main">
              <s id="N16887">
                <emph type="center"/>
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              Theorema
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              41.
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              </s>
            </p>
            <p id="N16893" type="main">
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              Hinc ſpatium qucd acquiritur ſecundo inſtanti eſt duplum illius, quod ac­
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              quiritur primo.
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              </s>
              <s id="N1689E"> Probatur, quia velocitas eſt dupla per Th 38. igitur ſpa­
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              tium duplum, & triplum tertio, quadruplum quarto, &c. </s>
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            <p id="N168A3" type="main">
              <s id="N168A5">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              42.
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              </s>
            </p>
            <p id="N168B1" type="main">
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              Hinc quodlibet ſpatium creſcit æqualiter ſingulis inſtantibus æqualibus
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              ; </s>
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              quia ſpatia creſcunt vt motus, ſeu vt velocitates; hæ creſcunt æqualiter
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              ſingulis inſtantibus æqualibus per Th.36. igitur æqualiter creſcunt ſin­
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              gula ſpatia per Th.40. </s>
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            <p id="N168C5" type="main">
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                <emph type="center"/>
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              Theorema
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              43.
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              </s>
            </p>
            <p id="N168D3" type="main">
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              Hinc ſpatia creſcunt ſingulis inſtantibus æqualibus ſecundùm progreſſio­
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              nem arithmeticam
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              ; quia creſcit vt velocitas per Th.40. hæc vt impetus
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              per Th.38. hic demum iuxta progreſſionem arithmeticam per Th. 37.
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              igitur ſi ſpatium acquiſitum primo inſtanti ſit 1. acquiſitum ſecundo erit
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              2. tertio 3. quarto 4. &c. </s>
              <s id="N168E6">hinc ſpatia acquiſita ſingulis inſtantibus ſunt
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              vt ſeries numerorum, qui componunt progreſſionem ſimplicem, ſcilicet
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              1.2.3.4.5.6. &c. </s>
              <s id="N168ED">dixi ſingulis inſtantibus æqualibus, quod eſt apprimè
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              tenendum; ſi enim aſſumantur partes temporis maiores, perturbatur
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              hæc progreſſio, de quo infrà. </s>
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          </chap>
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