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

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          <pb o="106" file="527.01.106" n="106" rhead="*3 LIBER STATICÆ*"/>
        </div>
        <div xml:id="echoid-div432" type="section" level="1" n="307">
          <head xml:id="echoid-head322" xml:space="preserve">ASSERTIO EORVM QVÆ SVPRA
            <lb/>
          DEMONSTRATVROS NOS RECEPIMVS.</head>
          <p>
            <s xml:id="echoid-s3120" xml:space="preserve">PAncration hoc firmius ſolidiusq́ue & </s>
            <s xml:id="echoid-s3121" xml:space="preserve">impenſæ minoris quam Chariſtion
              <lb/>
            Archimedeum mihi videri initio hujus propoſitionis dixeram; </s>
            <s xml:id="echoid-s3122" xml:space="preserve">quoque mi-
              <lb/>
            nori temporis ſpatio plus efficeretur; </s>
            <s xml:id="echoid-s3123" xml:space="preserve">potentiamq́; </s>
            <s xml:id="echoid-s3124" xml:space="preserve">infinitam ipſi ad extremum
              <lb/>
            tribueram.</s>
            <s xml:id="echoid-s3125" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3126" xml:space="preserve">Operis quidem firmitudinem per ſe claram (meliora tamen non cõtemnens)
              <lb/>
            cuilibet eſſe exiſtimo, quid enim huic machinationi ſolidius excogitari poteſt
              <lb/>
            ſolido arboris trunco? </s>
            <s xml:id="echoid-s3127" xml:space="preserve">cujus partes arctius longe tenaciusq́ue cohærent, quam
              <lb/>
            trabes inter ſe compactæ & </s>
            <s xml:id="echoid-s3128" xml:space="preserve">coagmentatæ. </s>
            <s xml:id="echoid-s3129" xml:space="preserve">Impenſæ quantulæ? </s>
            <s xml:id="echoid-s3130" xml:space="preserve">quas ne verbis
              <lb/>
            quidem explicare opus eſt.</s>
            <s xml:id="echoid-s3131" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3132" xml:space="preserve">Quid, temporis ſpatium cujuſmodi?</s>
            <s xml:id="echoid-s3133" xml:space="preserve">. manubrium, quod proratione opera-
              <lb/>
            rum ipſum verſantium cuilibetaſteriſco inſertare licet, nobis argumento erit; </s>
            <s xml:id="echoid-s3134" xml:space="preserve">le-
              <lb/>
            vioribus enim oneribus ducendis altius, ponderoſioribus verò humilius inſer-
              <lb/>
            to manubrio, onus trahendum quamlibet ponderofum convenienti labore ju-
              <lb/>
            giq́ue motu commovetur. </s>
            <s xml:id="echoid-s3135" xml:space="preserve">Cui abſimilis eſt iſte Chariſtii & </s>
            <s xml:id="echoid-s3136" xml:space="preserve">tympanorũ motus,
              <lb/>
            nam leviculæ navi etiam adhibetur potentia majoribus ponderibus congrua,
              <lb/>
            quæque ideo temporis moram prolatat; </s>
            <s xml:id="echoid-s3137" xml:space="preserve">imò cum trahendum pondus majus
              <lb/>
            ſit quam ut commodè commoveri poſſit, magna hominum equorumq́ue ma-
              <lb/>
            nus adhibenda, quæ nonnunquam laboriosè procedit, quandoq́; </s>
            <s xml:id="echoid-s3138" xml:space="preserve">ſubſiſtit atq;
              <lb/>
            </s>
            <s xml:id="echoid-s3139" xml:space="preserve">ita tempus ducitur, navibus autem damnum infertur: </s>
            <s xml:id="echoid-s3140" xml:space="preserve">nam una è maximis tre-
              <lb/>
            decem aut quatuordecim modiorum capax, quę per Lugodinenſem
              <note symbol="*" position="left" xlink:label="note-527.01.106-01" xlink:href="note-527.01.106-01a" xml:space="preserve">Iepbtfchen
                <lb/>
              Dam.</note>
            obicem traducuntur, viginti hominibus tympanum calcando verſantibus opus
              <lb/>
            habet, qui ſæpè facta ſtatione ſimul ſe demittunt, navesq́ue ſubjecto ſtrato gra-
              <lb/>
            viter illidunt. </s>
            <s xml:id="echoid-s3141" xml:space="preserve">Quod in Pancratio ſecus eſt, quia navis jugiter æquabiliterq́ue
              <lb/>
            impellitur.</s>
            <s xml:id="echoid-s3142" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3143" xml:space="preserve">Sed potentia, quam pancratio infinitam aſſignavimus, hic tanta eſt in D,
              <lb/>
            quanta Tympani diametro 324 pedum. </s>
            <s xml:id="echoid-s3144" xml:space="preserve">Enimverò per centrum tympani tan-
              <lb/>
            iæ diametri inducatur axis æqualis ipſi S diametri ſeſquipedalis, unde ratio ſe-
              <lb/>
            midiametrorum exiſtet ea quæ eſt 216 ad 1, atque ideò per 9 propof. </s>
            <s xml:id="echoid-s3145" xml:space="preserve">pondus ab
              <lb/>
            axe ęquilibre ponderi, è tympani diametro horizonti parallela dependenti, ha-
              <lb/>
            bebit ad ipſum rationem eandem quam 216 ad 1; </s>
            <s xml:id="echoid-s3146" xml:space="preserve">atqui eadent ratio eſt poten-
              <lb/>
            tiæ manubrii M N ad pondus ab axe S: </s>
            <s xml:id="echoid-s3147" xml:space="preserve">itaque manubrii ad D efficientia in
              <lb/>
            axem S tanta erit, quanta tympani diametri 324 pedum, qui ne in maximo qui-
              <lb/>
            dem tympano 30 pedes æquat nedum excedit, unde expeditè concludere li-
              <lb/>
            cet quanto Pancratii efficientia potior ſit potentia tympanorum, & </s>
            <s xml:id="echoid-s3148" xml:space="preserve">quamvis
              <lb/>
            iympanum minorelabore à calcante verſetur, non tamen, ut jam ediſſeruimus,
              <lb/>
            ideo utiliſſimum quoque fuerit. </s>
            <s xml:id="echoid-s3149" xml:space="preserve">At ſi quis commoditatem iſtam calcandi in
              <lb/>
            pancratio majoribus molibus ſubvectantis promovendisq́; </s>
            <s xml:id="echoid-s3150" xml:space="preserve">deſideret, a
              <unsure/>
            eriſco-
              <lb/>
            rum D, F, H, K, T axiculo cuicunque libebit pro manubrio rotulam, quam
              <lb/>
            majus tympanum dentanti ambitus verſet affigere quidem licebit, ſed utilita-
              <lb/>
            tem ſuperante impenſa.</s>
            <s xml:id="echoid-s3151" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3152" xml:space="preserve">Atquiſi potentia jam deformati pancratii oneri trahendo cedat, non tamen
              <lb/>
            labor, non impenſæ perierint: </s>
            <s xml:id="echoid-s3153" xml:space="preserve">alter enim aſteriſcus triplicans numerum poten-
              <lb/>
            tiæ dictæ 216 ipſi D ſubjiciatur, tum manubrium ejus axiculo affixum efficiet
              <lb/>
            hic potentiam unius libræ ponderi 648 librarum ab S dependentium æquili-
              <lb/>
            brem, qua via ad optatam efficientiam tandem adſcenditur.</s>
            <s xml:id="echoid-s3154" xml:space="preserve"/>
          </p>
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