Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

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          <pb o="104" file="527.01.104" n="104" rhead="*3 LIBER STATICÆ*"/>
        </div>
        <div xml:id="echoid-div428" type="section" level="1" n="303">
          <head xml:id="echoid-head318" xml:space="preserve">RATIO VERSATIONVM MANVBRII
            <lb/>
          AD AXEM.</head>
          <p>
            <s xml:id="echoid-s3069" xml:space="preserve">QVia manubrum L M N ter rotatum ſemel circumagit tympanum F, at no-
              <lb/>
            vies ſemel in orbem aget H, & </s>
            <s xml:id="echoid-s3070" xml:space="preserve">27 tympanum K, hinc 162 circumductum
              <lb/>
            convertet ipſum T hoc eſt axem S. </s>
            <s xml:id="echoid-s3071" xml:space="preserve">Eodemq́ue modo manubrium L M N
              <lb/>
            affixum ad F id tympanum 54 circumducendum erit ut axis S ſemel converta-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s3072" xml:space="preserve">ad H 18, K ſexies, T autem toties in orbem vertitur quoties ipſemet axis S.
              <lb/>
            </s>
            <s xml:id="echoid-s3073" xml:space="preserve">Cum autem manubrium altius inſeres quam in D, verbi gratiâ in K, ne infe-
              <lb/>
            riora tympana, quæ difficultatem operi inducunt, unà convertere ſit opus, pro-
              <lb/>
            ximè inferius quod in expoſito caſu eſt G loco ſuo depelles ne dentes ejus den-
              <lb/>
            tibus I amplius implicentur, atque ita inferior machinæ pars univerſa immota
              <lb/>
            conſiſtet.</s>
            <s xml:id="echoid-s3074" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div429" type="section" level="1" n="304">
          <head xml:id="echoid-head319" xml:space="preserve">RATIO POTENTIÆ MANVBRIVM VER-
            <lb/>
          SANTIS AD PONDVS TRACTVM,
            <lb/>
          QUALE EST NAVIS X.</head>
          <p>
            <s xml:id="echoid-s3075" xml:space="preserve">CVm flexura LM ex hypotheſi pedem longa, octupla ſit aſteriſci C, etiam
              <lb/>
            potentia quâ C agit in E æquivalens potentiæ impellentis manubrium
              <lb/>
            LM erit ut 8 ad I, eodemq́ue modo propter efficientiam H in F, ut 24 ad I
              <lb/>
            atque deinceps ab I in G, ut 72 ad I, denique à T in K ut 216 ad I. </s>
            <s xml:id="echoid-s3076" xml:space="preserve">Sed or-
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            biculus T æquivalet axi S, (æquivalere dixi, reverâ enim diameter axis
              <lb/>
            S eſt ſeſquipedalis, T autem bipedalis ex hypotheſi, ſed quia dentes aſte-
              <lb/>
            riſci T ſextupli ſunt ipſius K, etiam diameter ſextuplum peterit diametri K
              <lb/>
            quæ propterea erit 3 digitorum, & </s>
            <s xml:id="echoid-s3077" xml:space="preserve">quiad T digitorum 18, ſive ſeſquipedalis,
              <lb/>
            quemadmodum diameter axis S) quare pondus ab axe S rectà deſcendens
              <lb/>
            eandem habebit rationem ad pondus ſitu ſibi æquipondium, ſeu potentiam
              <lb/>
            æquivalentem in M N quam 216 ad I. </s>
            <s xml:id="echoid-s3078" xml:space="preserve">Ratiocinium hoc ab axe S deſcenden-
              <lb/>
            do deorſum inire licebit, eodem modo quo ſurſum adſcendendo nunc nobis
              <lb/>
            inſtitutum fuit.</s>
            <s xml:id="echoid-s3079" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3080" xml:space="preserve">Sedidem etiam hoc pacto explicari poterit. </s>
            <s xml:id="echoid-s3081" xml:space="preserve">Cum manubrum M N 162 in
              <lb/>
            orbem gyratum ſemel circumducat axem S, ut ſupra jam aſſertum eſt, & </s>
            <s xml:id="echoid-s3082" xml:space="preserve">ra-
              <lb/>
            tio diametri circuli à verſura manubrii M N deſcripti ad radium axis S ſit ſeſ-
              <lb/>
            quitertia (namque LM ſcapus pedalis eſt, ſemidiameter autem axis S {3/4} pedis)
              <lb/>
            exporrecti ambitus 162 verſationum manubrii M N, ad ambitum circuli in
              <lb/>
            axe S ſe habet ut 216 ad I, atque in iſta ratione quoque ſunt ſemidiametri 216
              <lb/>
            iſtius circuli ad hujus circuli ſemidiametrum. </s>
            <s xml:id="echoid-s3083" xml:space="preserve">quare per I propoſ. </s>
            <s xml:id="echoid-s3084" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s3085" xml:space="preserve">pondus
              <lb/>
            iſtius ad pondus hujus rationem habebit eandem quam 216 ad I. </s>
            <s xml:id="echoid-s3086" xml:space="preserve">Vnde effici-
              <lb/>
            tur ſi M N tantâ verſetur potentiâ quanta eſt 25 librarum deſcendendo, quæ
              <lb/>
            nobis v. </s>
            <s xml:id="echoid-s3087" xml:space="preserve">g. </s>
            <s xml:id="echoid-s3088" xml:space="preserve">hominis viribus æſtimetur, & </s>
            <s xml:id="echoid-s3089" xml:space="preserve">major ubi collibitum erit (quamvis
              <lb/>
            enim longè infra viri vires ſubſiſtat expoſita potentia, ita tamen exempli gra-
              <lb/>
            tia ſumpſiſſe placuit) iſta inquam potentia æquivalebit, 5400 libris (nam 216
              <lb/>
            ſumpta 25 hanc ſummam efficiunt) ab axerectà deorſum tendentibus. </s>
            <s xml:id="echoid-s3090" xml:space="preserve">Iam ve-
              <lb/>
            rò navis X ſit ſextupla ponderis ab axe S rectà dimiſſi, itaque X navis 32400
              <lb/>
            librarum (quod pondus eſt 9 modiorum, ſi 3600 libras ſingulis modiis tribua-
              <lb/>
            mus) æquiponderabit priori ponderi ſeu quod idem eſt potentiæ manubrium
              <lb/>
            MN continuè verſantis.</s>
            <s xml:id="echoid-s3091" xml:space="preserve"/>
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