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

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        <div xml:id="echoid-div504" type="section" level="1" n="363">
          <p>
            <s xml:id="echoid-s3529" xml:space="preserve">
              <pb o="122" file="527.01.122" n="122" rhead="4 L*IBER* S*TATICÆ*"/>
            ventio 18 propoſ. </s>
            <s xml:id="echoid-s3530" xml:space="preserve">inſtituitur) pondus I aquæ preſſui erit æquilibre, fundum
              <lb/>
            A C D E (ſilabi poſſe fingas) eo ſtatu conſervans.</s>
            <s xml:id="echoid-s3531" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3532" xml:space="preserve">Vel, ut idem adhuc clarius illuſtrem. </s>
            <s xml:id="echoid-s3533" xml:space="preserve">M N O P fundum eſto, ipſi A C D E
              <lb/>
            æquale & </s>
            <s xml:id="echoid-s3534" xml:space="preserve">ſimile, lateribus M P, A C, M N, A E, homologis, cui inſidet ſolidum
              <lb/>
            M N O P Q ponderitate & </s>
            <s xml:id="echoid-s3535" xml:space="preserve">magnitudine dimidiæ
              <lb/>
              <figure xlink:label="fig-527.01.122-01" xlink:href="fig-527.01.122-01a" number="170">
                <image file="527.01.122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.122-01"/>
              </figure>
            columnæ A C H D E æquale ipſiq́ue ſimile, ac
              <lb/>
            recta Q O æqualis D H horizonti ad perpendi-
              <lb/>
            culum normata inſiſtat. </s>
            <s xml:id="echoid-s3536" xml:space="preserve">Ajo, quemadmodum ſo-
              <lb/>
            lidum M N O P Q baſin M N O P premit pon-
              <lb/>
            deroſiùs verſus N O quam ad M P, quia iſtic
              <lb/>
            corpus ipſum ſpiſſius graviuſq́ue ſit; </s>
            <s xml:id="echoid-s3537" xml:space="preserve">ita quoque
              <lb/>
            aquam A B ponderoſiore validioreq́ preſſu con-
              <lb/>
            niti contra E D quàm contra A C.</s>
            <s xml:id="echoid-s3538" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3539" xml:space="preserve">P*RÆPARATIO*. </s>
            <s xml:id="echoid-s3540" xml:space="preserve">Dirimito latus A E in qua
              <unsure/>
            -
              <lb/>
            tuor quadrantes, in R, S, T, unde parallelæ ſint
              <lb/>
            R V, S X, T Y contra A C; </s>
            <s xml:id="echoid-s3541" xml:space="preserve">ſint item V Z, X α, Y β parallelæ contra D H,
              <lb/>
            ſecentq́ue C H in γ, δ, ε, ut quælibet eductarum γ Z, δ α, ε β æquent rectam
              <lb/>
            V γ; </s>
            <s xml:id="echoid-s3542" xml:space="preserve">tum ζ η per γ parallela contra C D interſecet X α in θ & </s>
            <s xml:id="echoid-s3543" xml:space="preserve">V β in 1, ſi-
              <lb/>
            militer Z κ per δ educta ſecet Y β in λ, ad extremum eodem ordine ducan-
              <lb/>
            tur parallelæ α μ per ε, & </s>
            <s xml:id="echoid-s3544" xml:space="preserve">β H per H.</s>
            <s xml:id="echoid-s3545" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div506" type="section" level="1" n="364">
          <head xml:id="echoid-head381" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3546" xml:space="preserve">Primùm fundo A C V R aliquod pondus incumbit, quia tuncſolum one-
              <lb/>
            re vacaret ſi in aquæ ſuperficie ſumma conſiſteret; </s>
            <s xml:id="echoid-s3547" xml:space="preserve">at infra eſt; </s>
            <s xml:id="echoid-s3548" xml:space="preserve">non igitur ponde-
              <lb/>
            ris preſſu vacat. </s>
            <s xml:id="echoid-s3549" xml:space="preserve">Secundò minore quàm A C ζ γ V R, aquei corporis pondere
              <lb/>
            afficitur, etenim per 10 propoſ. </s>
            <s xml:id="echoid-s3550" xml:space="preserve">ſi horizonti æquidiſtaret iſtud pondus ſuſtine-
              <lb/>
            ret, at nunc altiorem locum obtinet, minus igitur ſuſtinet. </s>
            <s xml:id="echoid-s3551" xml:space="preserve">Conſimiliter fundo
              <lb/>
            R V X S majus quoddam pondus incumbit quàm corporis A C ζ γ V R; </s>
            <s xml:id="echoid-s3552" xml:space="preserve">ete-
              <lb/>
            nim ſi fundum iſtud per R V horizonti æquidiſtaret iſtic per 10 propoſ. </s>
            <s xml:id="echoid-s3553" xml:space="preserve">tan-
              <lb/>
            tum corpus ſuſtineret: </s>
            <s xml:id="echoid-s3554" xml:space="preserve">at nunc cùm loco ſit inferiore plus quoq; </s>
            <s xml:id="echoid-s3555" xml:space="preserve">ſufferet, quam
              <lb/>
            pondus corporis A C ζ γ V S hoceſt ſibi æqualis R V γ θ X S. </s>
            <s xml:id="echoid-s3556" xml:space="preserve">Et rurſum mi-
              <lb/>
            nus ipſi inſidet quam corpus A C ζ θ X S, quia per 10 propof. </s>
            <s xml:id="echoid-s3557" xml:space="preserve">opus eſſet fun-
              <lb/>
            dum id, per S X ad horizontis paralleliſmum eductum eſſe; </s>
            <s xml:id="echoid-s3558" xml:space="preserve">jam verò cum fun-
              <lb/>
            dum R V X S ſublimius ſit, minus ponderis perpetitur quàm A C ζ θ X S, hoc
              <lb/>
            eſt, ipſi æquale R V Z δ X S. </s>
            <s xml:id="echoid-s3559" xml:space="preserve">Eodem raticinio, adhibito 10 propof. </s>
            <s xml:id="echoid-s3560" xml:space="preserve">& </s>
            <s xml:id="echoid-s3561" xml:space="preserve">plano per
              <lb/>
            X S horizonti parallelo, cõcludes fundo S X Y T plus ponderis inſidere quàm
              <lb/>
            corporis A C ζ θ X S, hoc eſt ipſi æqualis S X δ λ Y T; </s>
            <s xml:id="echoid-s3562" xml:space="preserve">& </s>
            <s xml:id="echoid-s3563" xml:space="preserve">minus tamen (pro-
              <lb/>
            pter eandem 10 prop. </s>
            <s xml:id="echoid-s3564" xml:space="preserve">& </s>
            <s xml:id="echoid-s3565" xml:space="preserve">planũ per T Y horizonti parallelũ) quam A C ζ. </s>
            <s xml:id="echoid-s3566" xml:space="preserve">Y T
              <lb/>
            hoc eſt quam ipſi æquale S X α ε Y T. </s>
            <s xml:id="echoid-s3567" xml:space="preserve">Denique eadem via, ſubſidio 10 propof.
              <lb/>
            </s>
            <s xml:id="echoid-s3568" xml:space="preserve">& </s>
            <s xml:id="echoid-s3569" xml:space="preserve">plano per T Y horizonti parallelo, evincesfundo T Y D E inſidere pondus
              <lb/>
            majus corpore A C ζ. </s>
            <s xml:id="echoid-s3570" xml:space="preserve">Y T ſeu ipſi æquali T Y ε μ D E: </s>
            <s xml:id="echoid-s3571" xml:space="preserve">attamen (propter ean-
              <lb/>
            dem 10 propoſ. </s>
            <s xml:id="echoid-s3572" xml:space="preserve">& </s>
            <s xml:id="echoid-s3573" xml:space="preserve">planum per E D horizonti parallelum) minus corpore
              <lb/>
            A C ζ η D E hoc eſt ipſo T Y β H D E. </s>
            <s xml:id="echoid-s3574" xml:space="preserve">Iam autem cum his demonſtrationi-
              <lb/>
            bus effectum ſit fundo A C V R aliquod pondus inſidere neque vacare omni-
              <lb/>
            no, fundo R V X S plus corpore R V γ θ X S; </s>
            <s xml:id="echoid-s3575" xml:space="preserve">item fundo S X Y T plus cor-
              <lb/>
            pore S X δ λ Y T, ultimùm fundo T Y D E plus corpore T Y ε μ D E, toti
              <lb/>
            quoque fundo A C D E plus inſidet quàm pondus omnium iſtorum corpo-
              <lb/>
            rum, quæ addita cõſtituunt corpus R V γ θ δ λ ε μ D E in dimidiam columnam
              <lb/>
            inſcriptum. </s>
            <s xml:id="echoid-s3576" xml:space="preserve">Et cum iiſdem demonſtrationibus cõcl
              <unsure/>
            uſerimus fundo A C V </s>
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