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

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        <div xml:id="echoid-div608" type="section" level="1" n="439">
          <pb o="145" file="527.01.145" n="145" rhead="5 L*IBER* S*TAT. DE INITIIS PRAXIS* H*YDROSTAT*."/>
          <p>
            <s xml:id="echoid-s4300" xml:space="preserve">QVomodo navis rerumq́ue quas vehit, aut cujuſlibet ſolidi aquæ innatan-
              <lb/>
            tis pondus, è data parte demerſa inveniri & </s>
            <s xml:id="echoid-s4301" xml:space="preserve">concludi queat, jam ſupra 6
              <lb/>
            propoſitione apertè ſatis ediſſerui; </s>
            <s xml:id="echoid-s4302" xml:space="preserve">his igitur omiſſis paucula quædam 7 propo-
              <lb/>
            ſitioni cognata & </s>
            <s xml:id="echoid-s4303" xml:space="preserve">ab ea dependentia etiam hic proponemus.</s>
            <s xml:id="echoid-s4304" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div609" type="section" level="1" n="440">
          <head xml:id="echoid-head458" xml:space="preserve">1 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s4305" xml:space="preserve">Invenire quantò idem corpus materiæ levioris quàm
              <lb/>
            aqua, in hacaltiùs demergatur, quàm in illa.</s>
            <s xml:id="echoid-s4306" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4307" xml:space="preserve">Verbigratia, Quæritur quantò altiùs navis Lugodini Batavorum in Rheno
              <lb/>
            flumine immergatur quam in mari propè Cattorum vicum haud lõgè iſtinc.</s>
            <s xml:id="echoid-s4308" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-527.01.145-01" xlink:href="note-527.01.145-01a" xml:space="preserve">@ att
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            Primum aquæ utriuſque, Rhenanæ ſcilicet & </s>
            <s xml:id="echoid-s4309" xml:space="preserve">marinæ, materiæ gravitatem in-
              <lb/>
            quirito, ea erit ut 42 ad 43, ita enim menſe Sextili experientia approbante edo-
              <lb/>
            ctus ſum. </s>
            <s xml:id="echoid-s4310" xml:space="preserve">Sumptis enim duobus corporibus parili magnitudine, Rhenanum
              <lb/>
            pendebat ſcruptula 4260, marinum autem 4362, quorum ratio in minoribus
              <lb/>
            terminis, ut 42 ad 43 ſatis vicina eſt.</s>
            <s xml:id="echoid-s4311" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4312" xml:space="preserve">Vnde concludes partem in Rheno demerſam, ad eam quæ in mari juxta
              <lb/>
            Catto-vicum mergeretur eſſe, ut 43 ad 42, hinc Geometra pro datæ navis for-
              <lb/>
            mâ rationem altitudinis hujus ad illam judicabit. </s>
            <s xml:id="echoid-s4313" xml:space="preserve">Cujus concluſionis neceſſitas
              <lb/>
            è 7 propoſ. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">hydroſtat. </s>
            <s xml:id="echoid-s4315" xml:space="preserve">perſpicitur.</s>
            <s xml:id="echoid-s4316" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div611" type="section" level="1" n="441">
          <head xml:id="echoid-head459" xml:space="preserve">2 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s4317" xml:space="preserve">Exemplis pragmaticis 10 propoſitionis Hydroſtatices
              <lb/>
            veritatem comprobare.</s>
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          <p>
            <s xml:id="echoid-s4319" xml:space="preserve">Quinto conſectario 10 propoſ. </s>
            <s xml:id="echoid-s4320" xml:space="preserve">Hydroſtat. </s>
            <s xml:id="echoid-s4321" xml:space="preserve">mathematicè demonſtratum no-
              <lb/>
            bis eſt, fundum aquæ characteribus E F iſtic inſignitum, aqua copioſiore, pau-
              <lb/>
            cioreq́ue in eadem altitudine perindeaffici. </s>
            <s xml:id="echoid-s4322" xml:space="preserve">Quia tamen non nemo hoc à vero
              <lb/>
            alienum & </s>
            <s xml:id="echoid-s4323" xml:space="preserve">naturæ contrarium ſuſpicari poſſet, Mathematicam illam demon-
              <lb/>
            ſtrationem quinque exemplis, cujus experientia cuilibet in procinctuſit, dein-
              <lb/>
            ceps ſumus illuſtraturi.</s>
            <s xml:id="echoid-s4324" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div612" type="section" level="1" n="442">
          <head xml:id="echoid-head460" xml:space="preserve">1 Exemplum.</head>
          <p>
            <s xml:id="echoid-s4325" xml:space="preserve">Fundum A B fundo C D ſimilis eſto & </s>
            <s xml:id="echoid-s4326" xml:space="preserve">æqualis, itemq́ue altitudo E F al-
              <lb/>
            titudini G H; </s>
            <s xml:id="echoid-s4327" xml:space="preserve">ſed pars I E inſiſtens ſujectæ aquæ K L B A minor ſit, quam pars
              <lb/>
            ipſius G C D ſibi reſpondens, pendatq́ue aqua E A B
              <lb/>
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                <image file="527.01.145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.145-01"/>
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            1 ℔, G C D 10 ℔, ſitq́ue G C D cylindrus, is igitur
              <lb/>
            ipſius E A B erit decuplus, hujus tamen in fundum
              <lb/>
            A B impreſſum eſſe tantum aſſerimus, quantus ſit to-
              <lb/>
            tius G C D in fundum C D. </s>
            <s xml:id="echoid-s4328" xml:space="preserve">Quod reapſe pragma-
              <lb/>
            tica machinatione ita demonſtratur.</s>
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