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

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          <pb o="68" file="527.01.068" n="68" rhead="L*IBER* S*TATICÆ*"/>
        </div>
        <div xml:id="echoid-div321" type="section" level="1" n="229">
          <head xml:id="echoid-head242" xml:space="preserve">NOTA.</head>
          <p style="it">
            <s xml:id="echoid-s2178" xml:space="preserve">Videtur Archimedes, @altero horum modorum problematis hujus inventionens
              <lb/>
            aſſecutus, ut dum aut parabolici ſui ſpeculi exemplar fabricatur, aut alterius gratia pa-
              <lb/>
            rabolam ſolidam, boc eſt conoïdale rectangulum efformat, reapſe edoctus ſit, ſegmentums
              <lb/>
            vertici co nterminum reliqui eſſe ſeſquialterum, in cujus cauſam hâc viâ inquiſierit & </s>
            <s xml:id="echoid-s2179" xml:space="preserve">
              <lb/>
            quaſi inſpexerit: </s>
            <s xml:id="echoid-s2180" xml:space="preserve">Cum ambæ B A I, B A C parabolæ ſint, diametros I F, A D àgra-
              <lb/>
            vitatis centris in homologa ſegmenta per 11 propoſ. </s>
            <s xml:id="echoid-s2181" xml:space="preserve">ſecari neceſſe erit, ideo{q́ue} I L, L F,
              <lb/>
            hoc eſt O N, N H ipſis æquales, rectis A E, E D proportionales erunt: </s>
            <s xml:id="echoid-s2182" xml:space="preserve">ſed ſi N com-
              <lb/>
            mune utriuſque par abolicæ portionis gravitatis centrum foret, P verò centrum trian-
              <lb/>
            guli A B C, quia triangulum ſimulutriuſque portionis eſt triplum, etiam jugum N E
              <lb/>
            jugi E P quoque triplum erit. </s>
            <s xml:id="echoid-s2183" xml:space="preserve">Vnde propoſitio iſtiuſmodi exiſtit. </s>
            <s xml:id="echoid-s2184" xml:space="preserve">Invenire duo puncta
              <lb/>
            N, E, quæ ſegmentorum O N, N H rationem faciant eandem quam A E habet
              <lb/>
            ad E D. </s>
            <s xml:id="echoid-s2185" xml:space="preserve">aſſumpta deinde A E {3/5} totius A D, & </s>
            <s xml:id="echoid-s2186" xml:space="preserve">E D {2/5}, facto{q́ue} periculo, quid ex his dedu-
              <lb/>
            catur; </s>
            <s xml:id="echoid-s2187" xml:space="preserve">tandem iſtudipſum veritati congruere comperit. </s>
            <s xml:id="echoid-s2188" xml:space="preserve">Aut ſi coniectur â huius ſeſ-
              <lb/>
            quialteræ rationis id ipſum aſſecutus non ſit, verùm arte duce in hæc penetralia pene-
              <lb/>
            traverit, videtur numeris hæc primùm expertus: </s>
            <s xml:id="echoid-s2189" xml:space="preserve">Dati duo numeri O H {1/4}, H P {1/6} am-
              <lb/>
            bo ita dividuntor, ut minus ſegmentum rectæ O H cum majore ipſius H P, tri-
              <lb/>
            plum ſit ſegmenti minoris rectæ H P cum majore ipſius H O, ea lege ut majus
              <lb/>
            ſegmentum rectæ O H ad minus habeat rationem, quam majus ſegmentum
              <lb/>
            H P + {1/3} habet ad minus ſegmentum H P + {1/3}.</s>
            <s xml:id="echoid-s2190" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div322" type="section" level="1" n="230">
          <head xml:id="echoid-head243" xml:space="preserve">5 PROBLEMA. 15 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2191" xml:space="preserve">Datâ parabolâ curtâ, gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2192" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2193" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2194" xml:space="preserve">A B C D parabola curta, oppoſitas rectas habeat parallelas, quas
              <lb/>
            biſecat diameter E F. </s>
            <s xml:id="echoid-s2195" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2196" xml:space="preserve">Gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2197" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div323" type="section" level="1" n="231">
          <head xml:id="echoid-head244" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s2198" xml:space="preserve">Parabolam curtam abſolvito, defectu A B G addito, hinc G E ſecetur in
              <lb/>
            H ut ſegmentum G H vertici vicinum reliqui H E ſit ſeſquialterum, itemq́uc
              <lb/>
            G I ipſius I F; </s>
            <s xml:id="echoid-s2199" xml:space="preserve">denique fiat ut A B C D ad A B G ſic H I ad I K: </s>
            <s xml:id="echoid-s2200" xml:space="preserve">Ajo K
              <lb/>
            optatu m gravitatis centrum eſſe.</s>
            <s xml:id="echoid-s2201" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div324" type="section" level="1" n="232">
          <head xml:id="echoid-head245" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2202" xml:space="preserve">Integræ parabolæ gravitatis cen-
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            trum eſt I, & </s>
            <s xml:id="echoid-s2203" xml:space="preserve">H portionis, quia verò
              <lb/>
              <figure xlink:label="fig-527.01.068-01" xlink:href="fig-527.01.068-01a" number="110">
                <image file="527.01.068-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.068-01"/>
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            eſt H I ad I K ut parabola curta ad
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            dictam portionem, K curtæ parabolæ
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            centrum erit.</s>
            <s xml:id="echoid-s2204" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2205" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2206" xml:space="preserve">Itaque, ut opor-
              <lb/>
            tuit, curtæ parabolæ centrum gravita-
              <lb/>
            tis invenimus, Generaliter autem ſive
              <lb/>
            A B parallela ſit contra D C, ſive an-
              <lb/>
            nuat ita efficies. </s>
            <s xml:id="echoid-s2207" xml:space="preserve">inveniatur H centrum
              <lb/>
            gravitatis parabolæ A G B & </s>
            <s xml:id="echoid-s2208" xml:space="preserve">I centrum totius D G C quæ connectantur ju-
              <lb/>
            go H I & </s>
            <s xml:id="echoid-s2209" xml:space="preserve">fiat H I ad continuationem I K ſicut parabola curta A B C D ad
              <lb/>
            complementum ſui A G B. </s>
            <s xml:id="echoid-s2210" xml:space="preserve">utriuſque autem ratio ad rectilineas figuras revo-
              <lb/>
            cari poteſt, cum utraque D G C, A G B trianguli quæ ipſis & </s>
            <s xml:id="echoid-s2211" xml:space="preserve">baſin & </s>
            <s xml:id="echoid-s2212" xml:space="preserve">altitu-
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            dinem habet æqualem ſeſquitertia ſit; </s>
            <s xml:id="echoid-s2213" xml:space="preserve">Et demonſtratio antecedens huic omni-
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            no congruet.</s>
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