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

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              <pb o="66" file="527.01.066" n="66" rhead="L*IBER* S*TATICÆ*"/>
            ad baſis terminos eductas biſecet F G, in G & </s>
            <s xml:id="echoid-s2088" xml:space="preserve">F, & </s>
            <s xml:id="echoid-s2089" xml:space="preserve">diametrum A D in H, & </s>
            <s xml:id="echoid-s2090" xml:space="preserve">
              <lb/>
            ab ipſis biſectionum punctis ſint F I, G K parallelæ contra A D, quarum ver-
              <lb/>
            tices cum verticeſectionis & </s>
            <s xml:id="echoid-s2091" xml:space="preserve">termino baſis proximo connectantur rectis I A,
              <lb/>
            I B, K A, K C; </s>
            <s xml:id="echoid-s2092" xml:space="preserve">deinde eædem illæ F I, G K æquales (parallelæ diameter enim
              <lb/>
            A D, parallelarum I F, K G ſi ad B C baſin educantur ſeſquitertia eſſet per
              <lb/>
            19 propoſ. </s>
            <s xml:id="echoid-s2093" xml:space="preserve">Archimed. </s>
            <s xml:id="echoid-s2094" xml:space="preserve">de quad. </s>
            <s xml:id="echoid-s2095" xml:space="preserve">parab. </s>
            <s xml:id="echoid-s2096" xml:space="preserve">& </s>
            <s xml:id="echoid-s2097" xml:space="preserve">ſublatis æqualibus, reliquæ I F, K G
              <lb/>
            æquales erunt) fecentur ratione dupla in L & </s>
            <s xml:id="echoid-s2098" xml:space="preserve">M, tum recta L M connexa, in
              <unsure/>
            -
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              <figure xlink:label="fig-527.01.066-01" xlink:href="fig-527.01.066-01a" number="108">
                <image file="527.01.066-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.066-01"/>
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            terſecet diametrum A D in N, & </s>
            <s xml:id="echoid-s2099" xml:space="preserve">I K eandem in O. </s>
            <s xml:id="echoid-s2100" xml:space="preserve">Præterea tota diameter
              <lb/>
            A D ſecetur dupla ratione in P, parallela autem I F continuata occurrat baſi
              <lb/>
            B C in Q. </s>
            <s xml:id="echoid-s2101" xml:space="preserve">Quandoquidem igitur A P dupla eſt ipſius P D, P erit trianguli
              <lb/>
            A B C gravitatis centrum, eadem ratione L, M, erunt centra gravitatis trian-
              <lb/>
            gulorum A B I, A C K, Ideoq́ue N (ſunt enim triangula æqualia) utriuſque
              <lb/>
            commune centrum, quare N P jugum erit, quod ſecetur in R, ut ratio N R
              <lb/>
            ad R P ſit eadem quæ trianguli A B C ad duo triangula A B I, A C K, hoc
              <lb/>
            eſt ut 4 ad 1 (parabola enim trianguli æquealti in eadem baſi ſeſquitertia eſt,
              <lb/>
            demonſtrante Archimede propoſ. </s>
            <s xml:id="echoid-s2102" xml:space="preserve">24. </s>
            <s xml:id="echoid-s2103" xml:space="preserve">de quadratura paraboles. </s>
            <s xml:id="echoid-s2104" xml:space="preserve">Simili planè viâ
              <lb/>
            fecetur parabola a b c.</s>
            <s xml:id="echoid-s2105" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div315" type="section" level="1" n="225">
          <head xml:id="echoid-head238" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2106" xml:space="preserve">Vt A D ad A O, ſic per 20 prop. </s>
            <s xml:id="echoid-s2107" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s2108" xml:space="preserve">Apoll. </s>
            <s xml:id="echoid-s2109" xml:space="preserve">quadratum D B ad quadra-
              <lb/>
            tum O I, hoc eſtad Q D, ſed Q D dimidia eſt ipſius B D, nam F Q parallela
              <lb/>
            contra A D biſecat inſcriptam A B, quadratum itaque D Q hoc eſt O I ſub-
              <lb/>
            quadruplum erit quadrati B D, & </s>
            <s xml:id="echoid-s2110" xml:space="preserve">ſegmentum igitur A O {1/4} erit totius A D, cui
              <lb/>
            O H æqualis eſt, nam integra A D biſecatur in H, & </s>
            <s xml:id="echoid-s2111" xml:space="preserve">N H {1/12} ejuſdem, quæ
              <lb/>
            ad H D {1/2} addita exhibet N D {7/12} de qua deducta P D {1/3} relinquet P N {1/4}, fed
              <lb/>
            R P ſubquadrupla eſt ipſius N R, & </s>
            <s xml:id="echoid-s2112" xml:space="preserve">totius igitur A D ſubvigecupla, quæ ad-
              <lb/>
            dita ad P D {1/3} dabit D R {23/60} & </s>
            <s xml:id="echoid-s2113" xml:space="preserve">reliquam R A {37/60}. </s>
            <s xml:id="echoid-s2114" xml:space="preserve">Quamobrem ut 37 ad 23 ſic
              <lb/>
            A R ad R D. </s>
            <s xml:id="echoid-s2115" xml:space="preserve">eodem modo evincetur ſegmenta alterius parabolæ a r, r d, eſſe
              <lb/>
            ut 37 ad 23. </s>
            <s xml:id="echoid-s2116" xml:space="preserve">Itaque rectilinea ſimili ratione in diſſimilibus parabolis inſcripta
              <lb/>
            centrum gravitatis habent in diametris, à quibus ipſæ diametri in homologa
              <lb/>
            ſegmenta dividuntur. </s>
            <s xml:id="echoid-s2117" xml:space="preserve">Ac denique ſi in parabolæ ſegmentis B I, I A, A K, K C
              <lb/>
            triangula itidem ut in ſegmentis B I A, A K C inſcribantur, & </s>
            <s xml:id="echoid-s2118" xml:space="preserve">rectilineorum
              <lb/>
            gravitatis centra S & </s>
            <s xml:id="echoid-s2119" xml:space="preserve">ſ inveniantur, tandem ſimiliter concludes A S, S R, ſeg-
              <lb/>
            mentis aſ, ſr proportionalia eſſe, verum infinita hujuſmodi inſcriptione con-
              <lb/>
            tinuô ad E & </s>
            <s xml:id="echoid-s2120" xml:space="preserve">e propius acceditur. </s>
            <s xml:id="echoid-s2121" xml:space="preserve">Itaque hujuſmodi rectilineorum γνωζί-
              <lb/>
              <note position="left" xlink:label="note-527.01.066-01" xlink:href="note-527.01.066-01a" xml:space="preserve">Deſinit
                <lb/>
              Archimed.
                <lb/>
              prop. 1. lib. 2.
                <lb/>
              iſerrhopiewr
                <unsure/>
              .</note>
            μως ſcitè (ut cum Archimeàe loquar) in parabolas inſcriptorum gravitatis cen-
              <lb/>
            tra, diametros A D & </s>
            <s xml:id="echoid-s2122" xml:space="preserve">a d in ſegmenta homologa perpetuò tribuent; </s>
            <s xml:id="echoid-s2123" xml:space="preserve">atque
              <lb/>
            adeò ipſæ quibus inſcribuntur parabolæ A B C, a b c, ſegmenta diametri </s>
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