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

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        <div xml:id="echoid-div342" type="section" level="1" n="244">
          <head xml:id="echoid-head258" xml:space="preserve">12 PROBLEMA. 18 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2343" xml:space="preserve">Centrum gravitatis pyramidis axem ita ſecat ut ſegmen-
              <lb/>
            tum vertici vicinius reliqui ſit triplum.</s>
            <s xml:id="echoid-s2344" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2345" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s2346" xml:space="preserve">Pyramidis ABCD baſis triangulæ, vertex A, baſis BCD, axis
              <lb/>
            à B ad E centrum gravitatis trianguli ADC eſto BE, hinc ab A ad cen-
              <lb/>
            trum gravitatis oppoſitæ hedræ BCD eſto AF quæ per antecedentem pro-
              <lb/>
            poſ. </s>
            <s xml:id="echoid-s2347" xml:space="preserve">ſecet priorem BE in G centro gravitatis pyramidis.</s>
            <s xml:id="echoid-s2348" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div343" type="section" level="1" n="245">
          <head xml:id="echoid-head259" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2349" xml:space="preserve">Recta AH, angulum A & </s>
            <s xml:id="echoid-s2350" xml:space="preserve">punctum H baſis me-
              <lb/>
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            dium connectens, ita ſecatur ab E trianguli ADC
              <lb/>
            gravitatis centro per 4 propoſ. </s>
            <s xml:id="echoid-s2351" xml:space="preserve">ut AE ſegmentum
              <lb/>
            vertici conterminum reliqui E H ſit duplum, pari ra-
              <lb/>
            tione BF dupla erit rectæ FH. </s>
            <s xml:id="echoid-s2352" xml:space="preserve">Quod cum ita ſit, ra-
              <lb/>
            tio B F ad FH, per Ptolemaicam {δι}αςρεσιν lib. </s>
            <s xml:id="echoid-s2353" xml:space="preserve">1. </s>
            <s xml:id="echoid-s2354" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s2355" xml:space="preserve">12.
              <lb/>
            </s>
            <s xml:id="echoid-s2356" xml:space="preserve">μεγάλης σ{μν}θαξ. </s>
            <s xml:id="echoid-s2357" xml:space="preserve">componetur è ratione BG ad GE
              <lb/>
            & </s>
            <s xml:id="echoid-s2358" xml:space="preserve">EA ad AH, ſubducta igitur ratione EA 2 ad
              <lb/>
            AH 3 de ratione B F 2 ad FH 1 reliqua erit ratio
              <lb/>
            BG 3 ad GE 1.</s>
            <s xml:id="echoid-s2359" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2360" xml:space="preserve">Verumenimverò in pyramide baſis quadrangulæ demonſtratio hinc deriva-
              <lb/>
            ta hujuſmodi erit: </s>
            <s xml:id="echoid-s2361" xml:space="preserve">Etenim ABCDE pyramis
              <lb/>
              <figure xlink:label="fig-527.01.072-02" xlink:href="fig-527.01.072-02a" number="117">
                <image file="527.01.072-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.072-02"/>
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            aſſurgat à baſi BCDE, & </s>
            <s xml:id="echoid-s2362" xml:space="preserve">axis ſit AF. </s>
            <s xml:id="echoid-s2363" xml:space="preserve">Diviſa
              <lb/>
            igitur hac in pyramides componentes quarum
              <lb/>
            baſes ECB, ECD & </s>
            <s xml:id="echoid-s2364" xml:space="preserve">axes AG, AH, centra
              <lb/>
            item gravitatis I, K, etiam totius pyramidis cen-
              <lb/>
            trum fuerit per 16 propoſ. </s>
            <s xml:id="echoid-s2365" xml:space="preserve">in jugo IK, videlicet in
              <lb/>
            L cõmuni axis & </s>
            <s xml:id="echoid-s2366" xml:space="preserve">jugi interſectione, ſed in trian-
              <lb/>
            gulo AGH, recta IK baſi GH parallela eſt, la-
              <lb/>
            tera enim A G, AH proportionaliter ſecantur in
              <lb/>
            I & </s>
            <s xml:id="echoid-s2367" xml:space="preserve">K per priorem partem, itaque AL quoque
              <lb/>
            tripla erit ipſius L F nam ob ſimilitudinem ut AI
              <lb/>
            ad IG, ſic AL ad LF, ſimillima in ceteris à
              <lb/>
            quamlibet multangula baſi aſſurgentibus pyrami-
              <lb/>
            dibus ratio quoque fuerit.</s>
            <s xml:id="echoid-s2368" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2369" xml:space="preserve">Denique coni tum circularis quam ellipticæ baſis demonſtratio eodem re-
              <lb/>
            dit, cum enim ex antecedente parte pyramis baſis quoquomodo polygonæ
              <lb/>
            axem gravitatis incîdat ratione tripla, in cono verò baſis ellipticæ vel cir-
              <lb/>
            cularis pyramis poteſt inſcribi quæ à dato cono quamcunque minimi ſolidi
              <lb/>
            differentia abſit, itaque intervallum centrorum gravitatis dati & </s>
            <s xml:id="echoid-s2370" xml:space="preserve">inſcripti ſolidi
              <lb/>
            minus erit quâcunque minima diſtantia, unde ſyllogiſmus talis inſtituitur.</s>
            <s xml:id="echoid-s2371" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2372" xml:space="preserve">Duorum distantium punctorum intervallo minus intervallum dari poteſt.
              <lb/>
            </s>
            <s xml:id="echoid-s2373" xml:space="preserve">Sed horum centrθrum intervallo minus dari nullum poteſt. </s>
            <s xml:id="echoid-s2374" xml:space="preserve">
              <lb/>
            Itaqueista puncta nullo intervallo à ſe mutuò abſunt.</s>
            <s xml:id="echoid-s2375" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2376" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s2377" xml:space="preserve">Quamobrem axis pyramidis cujuſcunque ratione tripla
              <lb/>
            à gravitatis centro ſecatur, videlicet utſummum & </s>
            <s xml:id="echoid-s2378" xml:space="preserve">vertici vicinius imiſit tri-
              <lb/>
            plum. </s>
            <s xml:id="echoid-s2379" xml:space="preserve">Quod facere oportuit.</s>
            <s xml:id="echoid-s2380" xml:space="preserve"/>
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