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

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        <div xml:id="echoid-div118" type="section" level="1" n="95">
          <p>
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              <pb o="23" file="527.01.023" n="23" rhead="*DE* S*TATICÆ ELEMENTIS.*"/>
            medio inter E, Gloco, è columnâ
              <lb/>
              <figure xlink:label="fig-527.01.023-01" xlink:href="fig-527.01.023-01a" number="34">
                <image file="527.01.023-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.023-01"/>
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            autem duo pondera I, K, depen-
              <lb/>
            dento, ſingula 4 ℔, & </s>
            <s xml:id="echoid-s670" xml:space="preserve">diametro-
              <lb/>
            rum firmitudinis puncta C, D,
              <lb/>
            axis L M, horizon N O.</s>
            <s xml:id="echoid-s671" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s672" xml:space="preserve">Q*VAESITVM.</s>
            <s xml:id="echoid-s673" xml:space="preserve">* Inveniendum
              <lb/>
            nobis, an axis L M ad horizon-
              <lb/>
            tem N O parallelus futurus ſit;
              <lb/>
            </s>
            <s xml:id="echoid-s674" xml:space="preserve">an quicunque datus fuerit ſitus,
              <lb/>
            retinebit; </s>
            <s xml:id="echoid-s675" xml:space="preserve">an denique invertet ſe
              <lb/>
            donec, E centrum gravitatis in
              <lb/>
            pendulâ gravitatis diametro ſit,
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            quæ eſt per H, quæ diverſitates
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            evenire poſſunt, pro variâ ratio-
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            ne gravitatis columnæ ad ponde-
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            ra, quæ inde dependent.</s>
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          </p>
        </div>
        <div xml:id="echoid-div120" type="section" level="1" n="96">
          <head xml:id="echoid-head105" xml:space="preserve">PRAGMATIA.</head>
          <p>
            <s xml:id="echoid-s677" xml:space="preserve">Ducatur P Q pendula gravi-
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            tatis diameter columnæ per E,
              <lb/>
            hinc per G pĕdula diameter R S
              <lb/>
            ponderum I, K, jugum erit E G, deinde ſecundæ propoſit. </s>
            <s xml:id="echoid-s678" xml:space="preserve">adjumento, quo
              <lb/>
            firmum anſae; </s>
            <s xml:id="echoid-s679" xml:space="preserve">punctum incidat, cognoſcetur. </s>
            <s xml:id="echoid-s680" xml:space="preserve">Si enim infra H ſit locus ejus,
              <lb/>
            movet ſe L M donec ad horizontem N O parallelus ſit; </s>
            <s xml:id="echoid-s681" xml:space="preserve">ſi in H, quicunque
              <lb/>
            datus fuerit ſitus retinetur; </s>
            <s xml:id="echoid-s682" xml:space="preserve">ſin ſupra H, omnia invertuntur. </s>
            <s xml:id="echoid-s683" xml:space="preserve">Atqui columna
              <lb/>
            4 ℔ pendet, ponderum I, K, item ſingula 4 ℔, ut amborum totus 8 ℔ ſit ex
              <lb/>
            conceſſo, E G itaque ſecta in T, ut E T ad T G illam rationem habeat quæ
              <lb/>
            eſt 8 ad 4. </s>
            <s xml:id="echoid-s684" xml:space="preserve">Dico L M ſeſe moturum (quod T infra H ſit) donec ad horizon-
              <lb/>
            tem parallelus frierit. </s>
            <s xml:id="echoid-s685" xml:space="preserve">Columna 4 ℔ pendeat, pondera vero I, K binas, ſumma
              <lb/>
            utriuſque 4 ℔ fuerit: </s>
            <s xml:id="echoid-s686" xml:space="preserve">ſectâ igitur E Gín H (eſt autem H ex cõceſſo inter E G
              <lb/>
            medium) utratio E H ad H G eaſit: </s>
            <s xml:id="echoid-s687" xml:space="preserve">quæ eſt 4 ad 4; </s>
            <s xml:id="echoid-s688" xml:space="preserve">dico L M (quòd in H
              <lb/>
            incidit) quemcunque ſitum dederis ſervare. </s>
            <s xml:id="echoid-s689" xml:space="preserve">Deniq; </s>
            <s xml:id="echoid-s690" xml:space="preserve">columna 4 ℔ eſto, pon-
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            dera I, K, vero ſingula 1 ℔, ut ſimul utrumque ſit 2 ℔. </s>
            <s xml:id="echoid-s691" xml:space="preserve">quapropter E G ſecta
              <lb/>
            in V, ut E V eam rationem habeat ad V G: </s>
            <s xml:id="echoid-s692" xml:space="preserve">quæ eſt 2 ad 4: </s>
            <s xml:id="echoid-s693" xml:space="preserve">inquio columnam
              <lb/>
            & </s>
            <s xml:id="echoid-s694" xml:space="preserve">ſe, & </s>
            <s xml:id="echoid-s695" xml:space="preserve">omnia reliqua inverſuram (quòd V ſupra H ſit) uſque dum H in ſua
              <lb/>
            gravitatis diametro fuerit.</s>
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          </p>
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        <div xml:id="echoid-div121" type="section" level="1" n="97">
          <head xml:id="echoid-head106" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s697" xml:space="preserve">Primum L M movere ſe donec horizonti ſit parallela, I & </s>
            <s xml:id="echoid-s698" xml:space="preserve">K 4 ℔ penden-
              <lb/>
            tibus, ita liquet. </s>
            <s xml:id="echoid-s699" xml:space="preserve">Perpendicularis per T, ut T X, eſt pendula gravitatis diame-
              <lb/>
            ter totius, eâ igitur omiſsâ, totoq́ue ex perpendiculari per H, ut H Y, ſuſpen-
              <lb/>
            ſo (H autem firmitudinis punctum eſt) ſegmentum B A, K, verſus ponde-
              <lb/>
            roſius erit, quam quod A D, I, verſus eſt, ideòque B A, K, deorſum verget,
              <lb/>
            donec H in pendulâ gravitatis diametro totius fuerit, atque tunc L M ad ho-
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            rizontem N O parallela fuerit.</s>
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          <p>
            <s xml:id="echoid-s701" xml:space="preserve">Secundò, I & </s>
            <s xml:id="echoid-s702" xml:space="preserve">K binas ℔ pendentibus, L M quemvis datum ſitum ſerva-
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            re, iſto pacto arguitur. </s>
            <s xml:id="echoid-s703" xml:space="preserve">I & </s>
            <s xml:id="echoid-s704" xml:space="preserve">K in altitudinem elata eſſe fingamus, ut pro I & </s>
            <s xml:id="echoid-s705" xml:space="preserve">K,
              <lb/>
            D & </s>
            <s xml:id="echoid-s706" xml:space="preserve">C centra gravitatis ſint, nulla, ex 3 poſtulato, gravitatis mutatio </s>
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