Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605
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          <p>
            <s xml:id="echoid-s2123" xml:space="preserve">
              <pb o="67" file="527.01.067" n="67" rhead="DE INVENTIONE GRAVITATIS CENTRO."/>
            portionalia habebunt. </s>
            <s xml:id="echoid-s2124" xml:space="preserve">Etenim ſi T ſumatur centrũ gravitatis parabolæ A B C,
              <lb/>
            hinc t ita quidem ftatuatur in a d, ut E T, T S, ipſis et, & </s>
            <s xml:id="echoid-s2125" xml:space="preserve">t s, proportionales
              <lb/>
            ſint, cùm multilaterarum figurarum inſcriptione in hac ad t deventum erit,
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            in illa itidem ad T devenietur, Quamobrem T centrum erit inſcripti multan-
              <lb/>
            guli, & </s>
            <s xml:id="echoid-s2126" xml:space="preserve">ipſius quoque parabolæ A B C, quod abſurdum eſt.</s>
            <s xml:id="echoid-s2127" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2128" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2129" xml:space="preserve">Itaque omnium parabolarum diametri à gravitatis centro
              <lb/>
            in homologa ſegmenta dividuntur. </s>
            <s xml:id="echoid-s2130" xml:space="preserve">Quod demonſtraſſe oportuit.</s>
            <s xml:id="echoid-s2131" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div317" type="section" level="1" n="226">
          <head xml:id="echoid-head239" xml:space="preserve">4 PROBLEMA. 12 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2132" xml:space="preserve">Datæ parabolæ gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2133" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2134" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2135" xml:space="preserve">A B C parabola, ejus diameter A D.</s>
            <s xml:id="echoid-s2136" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2137" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2138" xml:space="preserve">Gravitatis centrum invenire.</s>
            <s xml:id="echoid-s2139" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div318" type="section" level="1" n="227">
          <head xml:id="echoid-head240" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s2140" xml:space="preserve">Fiat ut 3 ad 2 ſic diametri ſegmentum A E ad E D.</s>
            <s xml:id="echoid-s2141" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2142" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s2143" xml:space="preserve">Biſectrix rectarum A B, A C, interſecet A D in H, hinc
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            F I, G K diametro parallelæ quasq́ue in antecedentis theorematis conſtructio-
              <lb/>
            ne æquales oſten dimus in L & </s>
            <s xml:id="echoid-s2144" xml:space="preserve">M, ita ſecentur ut I L, L F, item K M, M G,
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            diametri ſegmentis A E, E D proportionales ſint; </s>
            <s xml:id="echoid-s2145" xml:space="preserve">hinc I F continuata occur-
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            rat baſi B C in Q, & </s>
            <s xml:id="echoid-s2146" xml:space="preserve">fiat A P ſegmentum duplum P D, P erit trianguli A B C
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            gravitatis centrum: </s>
            <s xml:id="echoid-s2147" xml:space="preserve">ſiquidem M, L centra gravitatis ſint portionum A C K,
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            A B I, igitur N (nam per 4 propoſ. </s>
            <s xml:id="echoid-s2148" xml:space="preserve">Arch. </s>
            <s xml:id="echoid-s2149" xml:space="preserve">de Conoid. </s>
            <s xml:id="echoid-s2150" xml:space="preserve">& </s>
            <s xml:id="echoid-s2151" xml:space="preserve">Sphæroïd. </s>
            <s xml:id="echoid-s2152" xml:space="preserve">portiones
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            parabolicæ iſtæ inter ſe æquantur) harum commune gravitatis centrum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s2153" xml:space="preserve">Quamobrem Iugo P N, ſecundum rationem trianguli A B C ad duas para-
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            bolicas portiones, diviſo, habebimus optatum: </s>
            <s xml:id="echoid-s2154" xml:space="preserve">ſed integra parabola A B C eſt,
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            per 24 propoſ. </s>
            <s xml:id="echoid-s2155" xml:space="preserve">Archimed. </s>
            <s xml:id="echoid-s2156" xml:space="preserve">de quadr. </s>
            <s xml:id="echoid-s2157" xml:space="preserve">parab. </s>
            <s xml:id="echoid-s2158" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-527.01.067-01" xlink:href="fig-527.01.067-01a" number="109">
                <image file="527.01.067-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.067-01"/>
              </figure>
            ſeſquitertia trianguli A B C, quamobrem
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            A B C triangulum triplum erit duarum pa-
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            raboles portionum, ſecetur igitur P N in E
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            ratione tripla, hoc eſt ut ſegmentum N E
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            vertici vicinius triplum ſit reliqui E P. </s>
            <s xml:id="echoid-s2159" xml:space="preserve">Di-
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            co E optatum eſſe parabolæ centrum: </s>
            <s xml:id="echoid-s2160" xml:space="preserve">& </s>
            <s xml:id="echoid-s2161" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s2162" xml:space="preserve">ſegmenti A E ad E D rationem eſſe ſeſ-
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            quialteram, quod ex opere & </s>
            <s xml:id="echoid-s2163" xml:space="preserve">ſectionis ra-
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            tione patet.</s>
            <s xml:id="echoid-s2164" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div320" type="section" level="1" n="228">
          <head xml:id="echoid-head241" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2165" xml:space="preserve">A O, O H ſunt quartæ partes totius A D, quod 11 prop. </s>
            <s xml:id="echoid-s2166" xml:space="preserve">oſtendimus; </s>
            <s xml:id="echoid-s2167" xml:space="preserve">Ve-
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            rum ut 3 ad 2 ſic A E ad E D, ſic item I L ad L F, ſic quoque O N ad N H,
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            quamobrem N H erit {1/4}, hoc eſt ſubdecupla totius A D, hinc N H {1/10} addita
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            ad A D {1/2} exhibet N D {1/3} quæ multata P D {1/3} relinquit N P {4/23}. </s>
            <s xml:id="echoid-s2168" xml:space="preserve">Verum hæc
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            ex fabrica in E ita diviſa eſt ut N E tripla ſit ipſius E P. </s>
            <s xml:id="echoid-s2169" xml:space="preserve">Itaque E P valet {1/15} hæc
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            addita ad P D {1/3} dabit E D {2/3
              <unsure/>
            } diametri A D. </s>
            <s xml:id="echoid-s2170" xml:space="preserve">Et E A valebit ejuſdem {3/5}. </s>
            <s xml:id="echoid-s2171" xml:space="preserve">Quam-
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            obrem A E ad E D eſt ut 3 ad 2, & </s>
            <s xml:id="echoid-s2172" xml:space="preserve">conſequenter E gravitatis eſt centrum pa-
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            rabolæ A B C. </s>
            <s xml:id="echoid-s2173" xml:space="preserve">quod fuit propoſitum. </s>
            <s xml:id="echoid-s2174" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2175" xml:space="preserve">Itaque. </s>
            <s xml:id="echoid-s2176" xml:space="preserve">Data ellipſi
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            centrum gravitatis invenimus.</s>
            <s xml:id="echoid-s2177" xml:space="preserve"/>
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