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

Page concordance

< >
Scan Original
31 31
32 32
33 33
34 34
35 35
36 36
37 37
38 38
39 39
40 40
41 41
42 42
43 43
44 44
45 45
46 46
47 47
48 48
49 49
50 50
51 51
52
53
54
55 55
56 56
57 57
58 58
59 59
60 60
< >
page |< < (104) of 197 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div426" type="section" level="1" n="302">
          <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>
        </div>
        <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-
              <lb/>
            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"/>
          </p>
        </div>
      </text>
    </echo>
Impressum