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

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        <div xml:id="echoid-div378" type="section" level="1" n="271">
          <pb o="87" file="527.01.087" n="87" rhead="DE S*TATICÆ PRAXI*."/>
        </div>
        <div xml:id="echoid-div379" type="section" level="1" n="272">
          <head xml:id="echoid-head287" xml:space="preserve">CONSTRVCTIO</head>
          <p>
            <s xml:id="echoid-s2670" xml:space="preserve">Remotis lancibus, uncis, & </s>
            <s xml:id="echoid-s2671" xml:space="preserve">agina tantum librilis cum examine gravitatis
              <lb/>
            diametrum illam, per 1 prop. </s>
            <s xml:id="echoid-s2672" xml:space="preserve">hujus lib. </s>
            <s xml:id="echoid-s2673" xml:space="preserve">inveſtigato, quæ aciei axis tranſverſi E
              <lb/>
            æquidiſtet, ſitq́ue F, deinde jugi & </s>
            <s xml:id="echoid-s2674" xml:space="preserve">uncorum confinia connectito recta G H,
              <lb/>
            ejusq́ue medium ſit F, hinc ſecato F I ratione quam gravitas librilis cum exa-
              <lb/>
            mine puta 1 ℔ habetad lances, uncos, & </s>
            <s xml:id="echoid-s2675" xml:space="preserve">funes è quibus dependent quæ item
              <lb/>
            1 ℔ ponderent, biſecta igitur F I in K, ipſum K erit punctum unde libra ſuſpen-
              <lb/>
            ſa quamcunque dederis theſin retinebit, tum jungito K G, hanc pendula dia-
              <lb/>
            metro E L per E ducta interſeces in M. </s>
            <s xml:id="echoid-s2676" xml:space="preserve">Ajo, pondus illud cujus ratio ad 2 ℔
              <lb/>
            (etenim 1 ℔ pro jugo altera pro lancibus additæ 2 ℔ valent) eadem ſit, quæ
              <lb/>
            M K ad M G, lanci D impoſitum, libram tali ſitu retinere. </s>
            <s xml:id="echoid-s2677" xml:space="preserve">Dicis gratia fue-
              <lb/>
            rit M K pars quinta & </s>
            <s xml:id="echoid-s2678" xml:space="preserve">vigeſima radii M G, etiam {1/23} duarum ℔ efficiet ne li-
              <lb/>
            bra ab iſta theſi recedat, cujus cauſa è 12 propoſ. </s>
            <s xml:id="echoid-s2679" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s2680" xml:space="preserve">evidens eſt; </s>
            <s xml:id="echoid-s2681" xml:space="preserve">attamen
              <lb/>
            majoris perſpicuitatis ergô paucula hic in medium afferemus.</s>
            <s xml:id="echoid-s2682" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div380" type="section" level="1" n="273">
          <head xml:id="echoid-head288" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2683" xml:space="preserve">Siquidem K centrum gravitatis ſit dati, etiam perpendicularis per K edu-
              <lb/>
            cta erit ejuſdem gravitatis diameter, ſed perpendicularis per G eſt item ponde-
              <lb/>
            ris in lancem injecti diameter, ideoq́ue K G ipſorum jugum, quod in M pun-
              <lb/>
            cto ita partiti ſumus, ut ratio ſegmentorum M G, M K ea ſit quæ ponderum
              <lb/>
            reciprocè quare perpendicularis per M demiſſâ, erit utriuſque communis gra-
              <lb/>
            vitatis diameter ſeu anſa, atqueideo librile iſtum ſervabit ſitum.</s>
            <s xml:id="echoid-s2684" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2685" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2686" xml:space="preserve">Itaque data libra cujus librile horizonti æquidiſtet, pon-
              <lb/>
            dus invenimus quod alteræ lanci impoſitum ipſum librile in optata theſi con-
              <lb/>
            ſervet. </s>
            <s xml:id="echoid-s2687" xml:space="preserve">Quod facere oportebat.</s>
            <s xml:id="echoid-s2688" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div381" type="section" level="1" n="274">
          <head xml:id="echoid-head289" xml:space="preserve">4 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2689" xml:space="preserve">Dato librili quod lancibus appenſis horizonti æquidi-
              <lb/>
            ſtet, ſine quibus aciei axis tranſverſi inniti non poſsit; </s>
            <s xml:id="echoid-s2690" xml:space="preserve">lan-
              <lb/>
            ces invenire ut ipſum librile datum retineat ſitum.</s>
            <s xml:id="echoid-s2691" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2692" xml:space="preserve">Experientia edocemur nonnulla librilia aciei axis tranſverſi inhærere non
              <lb/>
            poſſe, ſed declinare, additis autem lancibus rectè inniti, cujus rei cauſa pragma-
              <lb/>
            ticè nobis inveſtiganda eſt.</s>
            <s xml:id="echoid-s2693" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2694" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2695" xml:space="preserve">Librile A B cujuſmodi propoſitio depoſcit, axis tranſverſi
              <lb/>
            acies C. </s>
            <s xml:id="echoid-s2696" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s2697" xml:space="preserve">Geminas lances (ſuis uncis & </s>
            <s xml:id="echoid-s2698" xml:space="preserve">funibus perfectas in-
              <lb/>
            telligito) ejus ponderis invenire, quæ jugum eo quem dederis ſitu conſervent.</s>
            <s xml:id="echoid-s2699" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div382" type="section" level="1" n="275">
          <head xml:id="echoid-head290" xml:space="preserve">CONSTRVCTIO.</head>
          <p>
            <s xml:id="echoid-s2700" xml:space="preserve">Etjugi, & </s>
            <s xml:id="echoid-s2701" xml:space="preserve">examinis gravitatis diametrum, aciei tranſverſi axis C parallelam
              <lb/>
            per 1 propoſ. </s>
            <s xml:id="echoid-s2702" xml:space="preserve">inquirito, hæc eſto D, ſupra ipſam C, nam neque in C necin-
              <lb/>
            t
              <unsure/>
            ra cadet, ſiquidem ex hypotheſi librile in C quieſcere nequit, atque adeò mul-
              <lb/>
            tò minus inſra C. </s>
            <s xml:id="echoid-s2703" xml:space="preserve">tum confinia uncorum & </s>
            <s xml:id="echoid-s2704" xml:space="preserve">jugi connectar recta E F, videli-
              <lb/>
            cet infra C, ſecus enim ſi vel in C vel ſupra caderet, nullæ lances quantum-
              <lb/>
            cunque graves jugi datum ſitum aut ad horizontem æquidiſtantiam tueri poſ-
              <lb/>
            ſent, deinde G biſecet E F & </s>
            <s xml:id="echoid-s2705" xml:space="preserve">jungatur recta D C G, & </s>
            <s xml:id="echoid-s2706" xml:space="preserve">fiat ut C G, ad C D,
              <lb/>
            ſic librile ad quæſitarum lancium gravitatem, dicis gratia ſi C D æquetur C </s>
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