Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N1C940">
            <p id="N1CC74" type="main">
              <s id="N1CCC0">
                <pb pagenum="199" xlink:href="026/01/231.jpg"/>
              retineret pondus in L; </s>
              <s id="N1CCC9">ducatur autem KLG Tangens parallela CT; </s>
              <s id="N1CCCD">certè
                <lb/>
              eadem potentia in L per LG retinebit pondus in L; </s>
              <s id="N1CCD3">quæ idem retine­
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              ret applicata in C per CT; </s>
              <s id="N1CCD9">cum enim RC & RL ſint æquales ſi ſint ap­
                <lb/>
              plicatæ duæ potentiæ æquales in C quidem per CT, & in L per LG; </s>
              <s id="N1CCDF">
                <lb/>
              haud dubiè erit perfectum æquilibrium; </s>
              <s id="N1CCE4">igitur ſi pondus A pendeat in
                <lb/>
              H fune LGH, retinebit pondus L in plano inclinato GLK; </s>
              <s id="N1CCEA">eſt autem
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              pondus H ad pondus LN SR ad RL; </s>
              <s id="N1CCF0">ſed triangula RSL, & GKI
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              ſunt proportionalia; </s>
              <s id="N1CCF6">igitur pondus in H eſt ad pondus L, vt GI ad G
                <lb/>
              K; </s>
              <s id="N1CCFC">igitur ſi vires, quæ retinent pondus in plano inclinato GK ſunt ad vi­
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              res, quæ retinent pondus in perpendiculari GI, vt GI ad GK; igitur im­
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              petus ſeu motus mobilis in plano GK eſt ad impetum, ſeu motum eiuſ­
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              dem in perpendiculo GI, vt GI ad GK. </s>
            </p>
            <p id="N1CD06" type="main">
              <s id="N1CD08">Hæc omnia veriſſima ſunt, ſemper tamen deſiderari videtur ratio phy­
                <lb/>
              ſica, cur idem pondus pendulum ex C in O, ſit eiuſdem momenti cum
                <lb/>
              pondere affixo puncto P, ſeu brachio libræ horizontalis PS. quod certè
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              Mechanica Axiomatis, vel hypotheſeos loco iure aſſumere poteſt; </s>
              <s id="N1CD12">at ve­
                <lb/>
              rò phyſica non ſatis habet de re cognoſcere quod ſit, niſi ſciat propter
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              quid ſit; igitur nos aliquam afferre conabimur. </s>
              <s id="N1CD1A">Suppono tantùm tunc
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              eſſe æquilibrium perfectum duorum ponderum æqualium cum
                <expan abbr="vtrimq;">vtrimque</expan>
                <lb/>
              æqualia illa pondera ita ſunt appenſa, vt linea directionis vnius æqua­
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              lis ſit lineæ directionis alterius, cur enim alterum præualeret ſi ſint æ­
                <lb/>
              qualia? </s>
              <s id="N1CD29">hoc poſito. </s>
            </p>
            <p id="N1CD2C" type="main">
              <s id="N1CD2E">Dico pondus affixum P æquale ponderi L facere æquilibrium; cum
                <lb/>
              enim linea directionis ſit PO, ſi deſcenderet liberè per PO. </s>
              <s id="N1CD34">L eodem
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              tempore attolleretur per LS, quod certè applicatis planis SL PO facilè
                <lb/>
              fieri poſſet; </s>
              <s id="N1CD3C">ſed eodem modo P grauitat, quo ſi deſcenderet per PO; </s>
              <s id="N1CD40">eſt
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              enim eius linea directionis; </s>
              <s id="N1CD46">atqui tunc faceret æquilibrium, quod oſten­
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              do; </s>
              <s id="N1CD4C">æquale ſpatium conficeret L, per LS aſcendendo, quod P per PO
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              deſcendendo; </s>
              <s id="N1CD52">igitur ſi attolleret L in S, ſimiliter pondus L æquale P in S
                <lb/>
              attolleret pondus P ex O in P, igitur neutrum præualere poteſt; ſed quia
                <lb/>
              hæc fuſiùs explicabimus cum de libra, nunc tantùm indicaſſe ſufficiat. </s>
            </p>
            <p id="N1CD5A" type="main">
              <s id="N1CD5C">Supereſt vt breuiter oſtendamus accipi non poſſe hanc proportio­
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              nem imminutionis motus in plano inclinato à Tangente BE tùm
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              quia; </s>
              <s id="N1CD64">iam à ſecante accipi oſtendimus, tùm quia ſit Tangens BD æqualis
                <lb/>
              ſumi toti ſeu perpendiculari AB; </s>
              <s id="N1CD6A">ſequeretur motum per AD æqualem
                <lb/>
              eſſe motui per AB; </s>
              <s id="N1CD70">Equidem in maxima diſtantia accedit Tangens ad
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              ſecantem; igitur eò plùs impeditur motus, quò maius ſpatium conficien­
                <lb/>
              dum eſt, &c. </s>
            </p>
            <p id="N1CD78" type="main">
              <s id="N1CD7A">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              6.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1CD87" type="main">
              <s id="N1CD89">
                <emph type="italics"/>
              Ex hoc ſequitur neceſſariò motum in plano inclinato eſſe ad motum in per­
                <lb/>
              pendiculari, vt ipſa perpendicularis ad ipſum planum inclinatum,
                <emph.end type="italics"/>
              v.g. velo­
                <lb/>
              citas motus per AE eſt ad velocitatem motus per AB, vt ipſa AB eſt
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              ad ipſam AE, ſit enim AE dupla AB, velocitas per AB eſt dupla veloci­
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              tatis per AE. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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