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

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          <pb o="40" file="527.01.040" n="40" rhead="1 L*IBER* S*TATICÆ*"/>
        </div>
        <div xml:id="echoid-div195" type="section" level="1" n="142">
          <head xml:id="echoid-head154" xml:space="preserve">10 C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s1218" xml:space="preserve">Eſto exemplat 9 conſectarii fimile, eo
              <lb/>
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            tantũ diſſimile, quod F H ultra F I, ver-
              <lb/>
            ſus C declinet, quodq́; </s>
            <s xml:id="echoid-s1219" xml:space="preserve">H F C angulus
              <lb/>
            R P O angulo ſit æqualis, quapropter
              <lb/>
            põderi G in columnam A M tantumdĕ
              <lb/>
            potentiæ eſt, quantũ ponderi Q: </s>
            <s xml:id="echoid-s1220" xml:space="preserve">& </s>
            <s xml:id="echoid-s1221" xml:space="preserve">pro-
              <lb/>
            pter cauſas 9 cõſect. </s>
            <s xml:id="echoid-s1222" xml:space="preserve">cõmemoratas (quas
              <lb/>
            brevitatis causâ omittimus) G tantam
              <lb/>
            vim columnæ A B adfert: </s>
            <s xml:id="echoid-s1223" xml:space="preserve">quantam Q
              <lb/>
            columnæ L M. </s>
            <s xml:id="echoid-s1224" xml:space="preserve">Itaque ut T P ad P R: </s>
            <s xml:id="echoid-s1225" xml:space="preserve">ita
              <lb/>
            S ad Q, per 9 conſectarium: </s>
            <s xml:id="echoid-s1226" xml:space="preserve">at qui I F
              <lb/>
            æquatur T P, & </s>
            <s xml:id="echoid-s1227" xml:space="preserve">F H ipſi P R, pondusq́;
              <lb/>
            </s>
            <s xml:id="echoid-s1228" xml:space="preserve">K ponderi S, & </s>
            <s xml:id="echoid-s1229" xml:space="preserve">G ipſi Q. </s>
            <s xml:id="echoid-s1230" xml:space="preserve">Quemadmo-
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            dum igitur I F ad F H: </s>
            <s xml:id="echoid-s1231" xml:space="preserve">ita K ad G.</s>
            <s xml:id="echoid-s1232" xml:space="preserve"/>
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        <div xml:id="echoid-div197" type="section" level="1" n="143">
          <head xml:id="echoid-head155" xml:space="preserve">11 C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s1233" xml:space="preserve">ESto & </s>
            <s xml:id="echoid-s1234" xml:space="preserve">10 conſectarii ſimile exemplũ,
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            eo tantũ diſſimile quod P R in alterũ
              <lb/>
            latus à P T declinet & </s>
            <s xml:id="echoid-s1235" xml:space="preserve">P R ad F H pa-
              <lb/>
            rallela ſit, ut Q & </s>
            <s xml:id="echoid-s1236" xml:space="preserve">G columnæ A M æ-
              <lb/>
            qualem vim inferant, &</s>
            <s xml:id="echoid-s1237" xml:space="preserve">, propter cauſas 9
              <lb/>
            conſectario dictas, quantum potentię eſt
              <lb/>
            ponderi G in columnam A B, tantundĕ
              <lb/>
            & </s>
            <s xml:id="echoid-s1238" xml:space="preserve">põdus Q obtinet in columnam L M.
              <lb/>
            </s>
            <s xml:id="echoid-s1239" xml:space="preserve">Vtigitur I F ad F H: </s>
            <s xml:id="echoid-s1240" xml:space="preserve">ita, per 6 conſecta-
              <lb/>
            rium, K ad G. </s>
            <s xml:id="echoid-s1241" xml:space="preserve">Atqui T P æquatur I F, & </s>
            <s xml:id="echoid-s1242" xml:space="preserve">
              <lb/>
            P R ipſi F H, & </s>
            <s xml:id="echoid-s1243" xml:space="preserve">pondus S ponderi K, & </s>
            <s xml:id="echoid-s1244" xml:space="preserve">
              <lb/>
            Q ipſi G. </s>
            <s xml:id="echoid-s1245" xml:space="preserve">Quemadmodum igitur TP ad
              <lb/>
            P R: </s>
            <s xml:id="echoid-s1246" xml:space="preserve">ita S ad Q. </s>
            <s xml:id="echoid-s1247" xml:space="preserve">Similiter aliorum
              <lb/>
            omnium ſituum proportio ex contrario demonſtrabitur.</s>
            <s xml:id="echoid-s1248" xml:space="preserve"/>
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        <div xml:id="echoid-div199" type="section" level="1" n="144">
          <head xml:id="echoid-head156" xml:space="preserve">12 C*ONSECTARIUM*.</head>
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            <s xml:id="echoid-s1249" xml:space="preserve">HAncautem proportionem etiam in illis
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            locum obtinere ubi axis horizõti paral-
              <lb/>
            lelus eſt, ita demõſtratur. </s>
            <s xml:id="echoid-s1250" xml:space="preserve">A B columna eſto,
              <lb/>
            ejusq́; </s>
            <s xml:id="echoid-s1251" xml:space="preserve">axis C D ad horizontem parallelus, E
              <lb/>
            punctũ firmum, F mobile, G põdus obliquè
              <lb/>
            extollens, quod columnam eo in ſitu ſervat,
              <lb/>
            cujus obliqua linea F H, I vero pondus rectè
              <lb/>
            extollens, columnam itidem eodem ſervans
              <lb/>
            in ſitu, ejusq́; </s>
            <s xml:id="echoid-s1252" xml:space="preserve">linea recta F K. </s>
            <s xml:id="echoid-s1253" xml:space="preserve">His poſitis, diſ-
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            ſimilis ratio eſto (ſi fieri poteſt) K F ad F H,
              <lb/>
            atq; </s>
            <s xml:id="echoid-s1254" xml:space="preserve">I ad G: </s>
            <s xml:id="echoid-s1255" xml:space="preserve">exempli gratià, ratio K F ad F H
              <lb/>
            ſit 1 ad 2: </s>
            <s xml:id="echoid-s1256" xml:space="preserve">ratio verò I ad G 3 ad 7. </s>
            <s xml:id="echoid-s1257" xml:space="preserve">Et hoc ita
              <lb/>
            poſito, prioris exempli columna demittitor,
              <lb/>
            aut poſterioris extollitor, uſq; </s>
            <s xml:id="echoid-s1258" xml:space="preserve">dum ratio K F
              <lb/>
            ad F H, ſit 3 ad 7: </s>
            <s xml:id="echoid-s1259" xml:space="preserve">tunc G contra columnam
              <lb/>
            æquilibre erit, per antecedentia conſectaria,
              <lb/>
            ut columna ſive altius elata, ſive humilius de-
              <lb/>
            preſſa contra G æquilibris manſura ſit: </s>
            <s xml:id="echoid-s1260" xml:space="preserve">At-
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            qui illud @@ ἀδύναπις eſſe manifeſtum </s>
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