Fabri, Honoré, Tractatus physicus de motu locali, 1646

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    <archimedes>
      <text>
        <body>
          <chap id="N15AC3">
            <pb pagenum="107" xlink:href="026/01/139.jpg"/>
            <p id="N177E0" type="main">
              <s id="N177E2">Si verò in noſtra hypotheſi ſpatium, quod reſpondet primæ parti tem­
                <lb/>
              poris AC ſit idem cum illo, quod reſpondet eidem parti in ſententia
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              Galilei, id eſt æquale triangulo CAG, ſumma ſpatiorum erit minor in
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              noſtra hypotheſi triangulo AFN ſex triangulis æqualibus triangulo
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              ACG; igitur erit vt 10.ad 16. igitur minor 1/8. </s>
              <s id="N177EE">ſi verò diuidantur in 8.
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              temporis partes, triangulum AFN continebit 64. triangula æqualia
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              AXQ: </s>
              <s id="N177F6">at verò ſumma quæ reſpondet noſtræ hypotheſi 36.igitur minor
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              (7/16). denique ſi diuidantur in 16. partes, triangulum AFN continebit
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              256. triangula æqualia AYZ; at verò ſumma noſtra 136. igitur minor
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              (15/52) ſed nunquam erit minor 1/2. </s>
            </p>
            <p id="N17800" type="main">
              <s id="N17802">Obſeruabis obiter dictum eſſe ſuprà ſummam rectangulorum CB CI
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              EK EN eſſe maiorem triangulo AFN, 2.quadratis æqualibus CB; </s>
              <s id="N17808">ſi
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              verò diuidatur tempus in 8. partes, ſumma rectangulorum eſt minor præ­
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              cedenti ſummâ, toto quadrato æquali CB, id eſt 4.quadratis æqualibus
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              XB, id eſt 1/2 primæ differentiæ, quæ eſt ſumma duorum quadratorum
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              æqualium CB; </s>
              <s id="N17814">at ſi diuidatur in 16. partes, tempus AF, ſumma rectan­
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              gulorum eſt minor præcedente 8. quadratis æqualibus QZ, vel ſubdu­
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              plo quadrati CB, id eſt 1/4 primæ differentiæ quæ eſt ſumma duorum
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              quadratorum æqualium CB; </s>
              <s id="N1781E">ſi 4. partes temporis diuidantur in 8. de­
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              trahitur 1/2 differentiæ, quæ eſt inter ſummam primam rectangulorum,
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              & triangulum AFN; </s>
              <s id="N17826">ſi diuidantur in 16. detrahitur 1/4 eiuſdem diffe­
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              rentiæ; </s>
              <s id="N1782C">ſi diuidantur in 32. detrahitur 1/8, ſi in 64. (1/16); </s>
              <s id="N17830">atque ita deinceps,
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              & nunquam hæ minutiæ ſubtractæ in infinitum totam differentiam ex­
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              haurient; hinc minutiæ iſtæ 1/2 1/4 1/8 (1/16) (1/32) (1/64) &c. </s>
              <s id="N17838">in infinitum non fa­
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              ciunt vnum integrum; ſed hæc ſunt facilia. </s>
            </p>
            <p id="N1783E" type="main">
              <s id="N17840">Quarta ratio, quam afferunt aliqui, eſt; </s>
              <s id="N17844">quia ſi cum eadem velocita­
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              te acquiſita in fine temporis dati ſine augmento nouo moueatur mobi­
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              le; </s>
              <s id="N1784C">haud dubiè acquiret duplum ſpatium tempore æquali tempori dato; </s>
              <s id="N17850">
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              v. g. ſit triangulum AFE; </s>
              <s id="N17859">ſitque velocitas acquiſita EF in 4. parti­
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              bus temporis AE, vt iam ſuprà dictum eſt, ne cogar repetere: </s>
              <s id="N1785F">certè ſi du­
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              catur velocitas EF in tempus AE, vel EL æquale; </s>
              <s id="N17865">habebitur rectan­
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              gulum EK duplum trianguli AFE: </s>
              <s id="N1786B">ſed triangulum AFE eſt ſumma
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              ſpatiorum motus accelerati tempore AE, & rectangulum EK eſt ſum­
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              ma ſpatiorum motus æquabilis cum velocitate EF; igitur duplum eſt
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              ſpatium motus æquabilis, quod erat demonſtrandum. </s>
              <s id="N17875">Præterea ſi diui­
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              datur velocitas EF, & eius ſubdupla ducatur in tempus AE; habebitur
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              rectangulum æquale triangulo AFE, vt conſtat. </s>
              <s id="N1787D">Reſpondeo facilè ex di­
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              ctis, hoc ipſum etiam ex noſtra hypotheſi proxime ſequi; </s>
              <s id="N17883">ſint enim duo
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              inſtantia; </s>
              <s id="N17889">haud dubie ſi non creſcit velocitas, ſecundo inſtanti æquale
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              ſpatium percurretur; </s>
              <s id="N1788F">ſi vero ſecundo inſtanti creſcat, percurrentur illo
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              motu 3.ſpatia; </s>
              <s id="N17895">& cùm velocitas
                <expan abbr="ſecũdi">ſecundi</expan>
                <expan abbr="inſtãtis">inſtantis</expan>
              ſit dupla velocitatis primi
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              inſtantis, primo inſtanti ſit 1.gradus v.g. ſecundo erunt 2. gradus; </s>
              <s id="N178A5">igi­
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              tur moueatur per duo inſtantia motu æquabili veloci vt 2. percurrentur
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              4. ſpatia; </s>
              <s id="N178AD">igitur totum ſpatium, quod percurritur motu veloci vt 2. per
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              2.inſtantia eſt ad totum ſpatium, quod percurritur æquali tempore mo-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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