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

Table of Notes

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              <pb o="130" file="527.01.130" n="130" rhead="4 L*IBER* S*TATICÆ*"/>
            æquales, & </s>
            <s xml:id="echoid-s3826" xml:space="preserve">ſumma latera E, G in ſuperna aquæ ſuperficie collocentur.</s>
            <s xml:id="echoid-s3827" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3828" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3829" xml:space="preserve">Longitudines EF, G H preſſibus aquæ, quibus fundã
              <lb/>
            EF, GH afficiuntur æquales eſſe.</s>
            <s xml:id="echoid-s3830" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div531" type="section" level="1" n="382">
          <head xml:id="echoid-head399" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3831" xml:space="preserve">Pondus aquæ fundo E F inſidentis æquatur per 11 propoſ. </s>
            <s xml:id="echoid-s3832" xml:space="preserve">aqueæ columnæ
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            cujus altitudo I F, baſis autem fundum E F. </s>
            <s xml:id="echoid-s3833" xml:space="preserve">ſimiliter pondus aquæ quod in-
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            ſidet fundo G H æquatur columnæ aqueæ altitudinis K H baſis G H fundo
              <lb/>
              <note symbol="*" position="right" xlink:label="note-527.01.130-01" xlink:href="note-527.01.130-01a" xml:space="preserve">32. p. 11.
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              t. E.</note>
            æqualis. </s>
            <s xml:id="echoid-s3834" xml:space="preserve"> quarę ſunt ut baſes: </s>
            <s xml:id="echoid-s3835" xml:space="preserve">ſed baſis ſeu fun- dum E F eſt ad fundum G H, ut recta E F ad re-
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              <figure xlink:label="fig-527.01.130-01" xlink:href="fig-527.01.130-01a" number="181">
                <image file="527.01.130-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.130-01"/>
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            ctam G H, nam perhypotheſin æqualem habent
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            latitudinem: </s>
            <s xml:id="echoid-s3836" xml:space="preserve">ex æquo itaque longitudo E F erit
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            ad longitudinem G H ut illius columna, ad co-
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            lumnam hujus, & </s>
            <s xml:id="echoid-s3837" xml:space="preserve">conſequenter ut pondus aquæ
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            illi inſidentis, ad pondus huic inſidentis. </s>
            <s xml:id="echoid-s3838" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s3839" xml:space="preserve">Itaque ſi duo pa-
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            rallelogramma ęqualis latitudinis ab aquæ ſuperficie deorlum altitudine æqua-
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            li recedunt, ipſorum longitudines preſſibus aquæ ipſi inſidentis proportionales
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            erunt. </s>
            <s xml:id="echoid-s3840" xml:space="preserve">Quod demonſtrandum fuit.</s>
            <s xml:id="echoid-s3841" xml:space="preserve"/>
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        <div xml:id="echoid-div533" type="section" level="1" n="383">
          <head xml:id="echoid-head400" xml:space="preserve">4 THEOREMA. 15 PROPOSITIO.</head>
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            <s xml:id="echoid-s3842" xml:space="preserve">Si parallelogrammi ad horizontem inclinati, cujus
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            ſupremum latus in aquæ ſuperficie ſumma conſiſtat, duæ
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            perpendiculares altera in latus imum, altera in planum per
              <lb/>
            imum latus horizonti parallelum notæ ſint; </s>
            <s xml:id="echoid-s3843" xml:space="preserve">aquæ ipſi inſi-
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            dentis pondus invenire.</s>
            <s xml:id="echoid-s3844" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div534" type="section" level="1" n="384">
          <head xml:id="echoid-head401" xml:space="preserve">NOTATO.</head>
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            <s xml:id="echoid-s3845" xml:space="preserve">Parallelogrammum eſſe aut rectangulum aut obliquangulum, cum{q́ue} ſummo latere
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            in aquæ ſuperficie collocato ipſa ad horizontem inclinabuntur, id fiet in angulo recto, vel
              <lb/>
            obliquo. </s>
            <s xml:id="echoid-s3846" xml:space="preserve">unde quadruplex exemplorum ratio exiſtit, cuius varietatis tam in hoc, quam
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            duabus ſequentibus propoſitionibus quatuor dabimus exempla. </s>
            <s xml:id="echoid-s3847" xml:space="preserve">Primum rectanguli ad
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            horizontem recti, ubi alterum laterum horizonti annuentium & </s>
            <s xml:id="echoid-s3848" xml:space="preserve">perpendicularis duæ
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            altera in imum latus, altera in planũ per imum latus horizonti parallelum, una eodem{q́ue}
              <lb/>
            recta ſunt. </s>
            <s xml:id="echoid-s3849" xml:space="preserve">Secundum parallelogrammi obliquanguli itidem ad horizontirecti ubi duæ
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            perpendiculares altera à ſummo latere in imum, altera indidem in planum per imum
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            latus horizonti parallelum, eadem ſunt linea. </s>
            <s xml:id="echoid-s3850" xml:space="preserve">Tertium parallelogrammi rectanguli ad
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            horizontem obliquati ubi latus unam horizonti annuens & </s>
            <s xml:id="echoid-s3851" xml:space="preserve">perpendicularis a latere
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            ſummo in imum eadem ſunt recta. </s>
            <s xml:id="echoid-s3852" xml:space="preserve">Quartum denique parallelogrammi obliquanguli,
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            ubi dictæ tres lineæ inter ſe diverſae; </s>
            <s xml:id="echoid-s3853" xml:space="preserve">ſunt.</s>
            <s xml:id="echoid-s3854" xml:space="preserve"/>
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        <div xml:id="echoid-div535" type="section" level="1" n="385">
          <head xml:id="echoid-head402" xml:space="preserve">1 Exemplum.</head>
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            <s xml:id="echoid-s3855" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s3856" xml:space="preserve">Rectanguli A B C D ad horizontem recti latus extimum A B
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            inaquæ ſuperficie 4 eſto pedum, A D 3.</s>
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          </p>
          <p>
            <s xml:id="echoid-s3858" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3859" xml:space="preserve">Aquæ inſidentis fundo A B C D pondus invenire.</s>
            <s xml:id="echoid-s3860" xml:space="preserve"/>
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