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

Table of contents

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[31.] DECLARATIO.
Page: 8 (8)
[32.] 13 DEFINITIO.
Page: 8 (8)
[33.] 14 DEFINITIO.
Page: 9 (9)
[34.] DECLARATIO.
Page: 9 (9)
[35.] NOTATO.
Page: 9 (9)
[36.] *POSTVLATA.*
Page: 10 (10)
[37.] 1 POSTVLATVM.
Page: 10 (10)
[38.] 2 POSTVLATVM.
Page: 10 (10)
[39.] 3 POSTVLATVM.
Page: 10 (10)
[40.] DECLARATIO.
Page: 10 (10)
[41.] 4 POSTVLATVM.
Page: 11 (11)
[42.] 5 POSTVLATVM.
Page: 11 (11)
[43.] DECLARATIO.
Page: 11 (11)
[44.] PARS ALTERA DE PROPOSITIONIBVS. 1 THE OREMA. I PROPOSITIO.
Page: 12 (12)
[45.] 1 Exemplum.
Page: 12 (12)
[46.] DEMONSTRATIO.
Page: 12 (12)
[47.] 2 Exemplum.
Page: 12 (12)
[48.] DEMONSTRATIO. 1 MEMBRVM.
Page: 13 (13)
[49.] 2 MEMBRVM.
Page: 13 (13)
[50.] 3 MEMBRVM.
Page: 13 (13)
[51.] 3 Exemplum.
Page: 14 (14)
[52.] C*ONSECTARIUM*.
Page: 14 (14)
[53.] 1 PROBLEMA. 2 PROPOSITIO.
Page: 14 (14)
[54.] 1 Exemplum.
Page: 15 (15)
[55.] PRAGMATIA.
Page: 15 (15)
[56.] 2 Exemplum.
Page: 15 (15)
[57.] *PRAGMATIA*.
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[58.] 3 Exemplum.
Page: 15 (15)
[59.] *PRAGMATIA.*
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[60.] *PRAGMATIA ALIVSMODI.*
Page: 15 (15)
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              <pb o="123" file="527.01.123" n="123" rhead="*DE* H*YDROSTATICES ELEMENTIS*."/>
            minus inſidere pondus quàm A C ζ γ V R, fundo R V X S minus quàm
              <lb/>
            R V Z δ X S, item fundo S X Y T minus quam S X α ε Y T, denique ſundo
              <lb/>
            T Y D E minus quàm T Y β H D E, toti quoq; </s>
            <s xml:id="echoid-s3577" xml:space="preserve">fundo A C D E minus inſide-
              <lb/>
            bit ponere omniũ horũ, hoc eſt, corpore circumſcripto A C ζ γ Z δ α ε β H D E.
              <lb/>
            </s>
            <s xml:id="echoid-s3578" xml:space="preserve">Atqui fundo A C D E, qui in diagrammate quadrãtibus diſtinguitur, ſic in octo
              <lb/>
            æqualia ſegmenta divio palam eſt corporum dimidiæ columnæ A C H E D
              <lb/>
            hujus inſcripti illius circumſcripti ab ipſa differentiam dimidio minorem fore
              <lb/>
            quàm nunc ſit: </s>
            <s xml:id="echoid-s3579" xml:space="preserve">quare hujuſmodi fundi ſectione infinita eo devenitur, ut differĕ-
              <lb/>
            tia ponderis (ſi qua tamen hîc ſit) fundo A C D E incumbĕtis a põdere dimidiæ
              <lb/>
            columnæ A C D E quolibet minimo põdere adhuc minor ſit. </s>
            <s xml:id="echoid-s3580" xml:space="preserve">Vnde ita ediſſero.</s>
            <s xml:id="echoid-s3581" xml:space="preserve"/>
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            <s xml:id="echoid-s3582" xml:space="preserve">Gravitas cujus à pondere fundo A C D E inſidente differentia minor eſt quolibet
              <lb/>
            pondere dato, æquatur ponderi fundo A C D E inſidenti.</s>
            <s xml:id="echoid-s3583" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3584" xml:space="preserve">Sed pondus dimidiæ columnæ A C H D E eſt gravitas minus differens à pondere
              <lb/>
            fundo A C D E inſidente quam quodlibet datum.</s>
            <s xml:id="echoid-s3585" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3586" xml:space="preserve">Itaque pondus dimidiæ columnæ A C H D E æquatur ponderi in baſe A C D E.</s>
            <s xml:id="echoid-s3587" xml:space="preserve"/>
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        </div>
        <div xml:id="echoid-div507" type="section" level="1" n="365">
          <head xml:id="echoid-head382" style="it" xml:space="preserve">2 Exemplum.</head>
          <p>
            <s xml:id="echoid-s3588" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s3589" xml:space="preserve">Exponatur ſecundo A B vas plenum aquæ, fundumq́ue A C D E
              <lb/>
            quadrangulum ad horizontem in angulo obliquo inclinatum, ejusq́ue ſupre-
              <lb/>
            mum latus A C conſiſtar in A C F G aquæ ſuperficie ſumma. </s>
            <s xml:id="echoid-s3590" xml:space="preserve">Iam aqua
              <lb/>
            ipſiusq́ue fundum dividatur conſimiliter antecedenti 1 exemplo, & </s>
            <s xml:id="echoid-s3591" xml:space="preserve">A υ per-
              <lb/>
            pendicularis ſit àſummo fundi latere in planum, per inſimum latus E D ad ho-
              <lb/>
            rizontis paralleliſmum eductum, demiſſa. </s>
            <s xml:id="echoid-s3592" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s3593" xml:space="preserve">Pondus aquæ
              <lb/>
            fundo A C D E ſubnixum dimidiæ columnæ cujus baſis A C D E, altitudo
              <lb/>
            A υ, æquari demonſtrato. </s>
            <s xml:id="echoid-s3594" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s3595" xml:space="preserve">Perpendicularis A υ à tribus
              <lb/>
            punctis ο, π, ρ in quatuor æquas partes diſſecator.</s>
            <s xml:id="echoid-s3596" xml:space="preserve"/>
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        <div xml:id="echoid-div508" type="section" level="1" n="366">
          <head xml:id="echoid-head383" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3597" xml:space="preserve">Fundo A C V R, cum nõ ſit in
              <lb/>
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                <image file="527.01.123-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.123-01"/>
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            aquę ſummitate, inſidet aliquod
              <lb/>
            pondus, minus tamen quàm co-
              <lb/>
            lumna aquea baſis A C V R, alti-
              <lb/>
            tudinis A ο, nam ſi per R V planũ
              <lb/>
            horizonti æquidiſtanter duce-
              <lb/>
            retur per 10 propof id hoc pon-
              <lb/>
            deris ſuſtineret, nuncverò cum
              <lb/>
            ſublimiori ſit loco minus ſuffert
              <lb/>
            quam columnam iſta baſi & </s>
            <s xml:id="echoid-s3598" xml:space="preserve">al-
              <lb/>
            titudine, hoc eſt, A C ζ γ V R.
              <lb/>
            </s>
            <s xml:id="echoid-s3599" xml:space="preserve">Simili deductione ut in primo exemplo
              <lb/>
            cætera proſequeris; </s>
            <s xml:id="echoid-s3600" xml:space="preserve">unde tandem con-
              <lb/>
              <figure xlink:label="fig-527.01.123-02" xlink:href="fig-527.01.123-02a" number="172">
                <image file="527.01.123-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.123-02"/>
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            cludes fundo A C D E inſidere corpus
              <lb/>
            æquale ipſi A C H D E, hoc eſt, colum-
              <lb/>
            næ baſis A C D E, altitudinis A υ (nam
              <lb/>
            A υ æqualis eſt perpendiculari ab H
              <lb/>
            in planum A C D E) tandem inquam
              <lb/>
            concludes fundo A C D E inſidere a-
              <lb/>
            queam molem magnitudine æqualem
              <lb/>
            columnæ cujus baſis A C D E, altitu-
              <lb/>
            do A υ.</s>
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