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

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          <pb o="194" file="527.01.194" n="194" rhead="A*DDITAMENTI* S*TATICÆ* P*ARS QUARTA*"/>
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            <s xml:id="echoid-s5300" xml:space="preserve">D*ATVM.</s>
            <s xml:id="echoid-s5301" xml:space="preserve">* A B ſcapus ſit præ-
              <lb/>
              <figure xlink:label="fig-527.01.194-01" xlink:href="fig-527.01.194-01a" number="244">
                <image file="527.01.194-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.194-01"/>
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            longus, A C prælongum ejuſdem
              <lb/>
            capitellum, in cõtinuata A B: </s>
            <s xml:id="echoid-s5302" xml:space="preserve">con-
              <lb/>
            tra A D ſcapus breviuſculus, & </s>
            <s xml:id="echoid-s5303" xml:space="preserve">
              <lb/>
            A E ejus capitellum breviuſculum;
              <lb/>
            </s>
            <s xml:id="echoid-s5304" xml:space="preserve">ſed ita, ut A E A D, A C A B. </s>
            <s xml:id="echoid-s5305" xml:space="preserve">
              <lb/>
            proportionales ſint. </s>
            <s xml:id="echoid-s5306" xml:space="preserve">agatur deinde
              <lb/>
            ipſi A B æqualis A F, & </s>
            <s xml:id="echoid-s5307" xml:space="preserve">A G ipſi
              <lb/>
            A C: </s>
            <s xml:id="echoid-s5308" xml:space="preserve">ſintq́ue ab F & </s>
            <s xml:id="echoid-s5309" xml:space="preserve">G in B C
              <lb/>
            perpendiculares, F H, G C. </s>
            <s xml:id="echoid-s5310" xml:space="preserve">
              <lb/>
            deinde A K æqualis rectæ A D
              <lb/>
            tantum attollatur ut K L perpen-
              <lb/>
            diculatis ſit æqualis ipſi H F. </s>
            <s xml:id="echoid-s5311" xml:space="preserve">ſimi-
              <lb/>
            liter ut altrinſecus A M, in con-
              <lb/>
            tinuata K A, æquetur ipſi A E,
              <lb/>
            & </s>
            <s xml:id="echoid-s5312" xml:space="preserve">ab M perpendicularis cadat
              <lb/>
            M N. </s>
            <s xml:id="echoid-s5313" xml:space="preserve">his conſtitutis, ponamus
              <lb/>
            annellum B ſcapi longioris ab B
              <lb/>
            adductum in F ut diſtantia à prio-
              <lb/>
            ri ſcapi ſitu ſit F A: </s>
            <s xml:id="echoid-s5314" xml:space="preserve">minoris au-
              <lb/>
            tem ſcapi annellum ab D didu-
              <lb/>
            ctum in K, ut diſtantia ſit L K. </s>
            <s xml:id="echoid-s5315" xml:space="preserve">his
              <lb/>
            ductibus ocellus majoris ſcapi mi-
              <lb/>
            grabit ab C in G, eritq́ue diſtan-
              <lb/>
            tia à priori ſitu I G: </s>
            <s xml:id="echoid-s5316" xml:space="preserve">ocellus verò E
              <lb/>
            capitelli minoris diſcedet in M, cu-
              <lb/>
            jus à capitelli primo ſitu diſtantia
              <lb/>
            eſt M N. </s>
            <s xml:id="echoid-s5317" xml:space="preserve">Sed motus intervalla H F
              <lb/>
            L K pro manus ductibus (quiaillis
              <lb/>
            æquantur) cenſenda ſunt: </s>
            <s xml:id="echoid-s5318" xml:space="preserve">item
              <lb/>
            IG M N pro pſelliorum motibus-
              <lb/>
            quod illis æquentur. </s>
            <s xml:id="echoid-s5319" xml:space="preserve">Quæ cum ita
              <lb/>
            ſint demonſtrandum eſt N M æ,
              <lb/>
            quari ipſi I G. </s>
            <s xml:id="echoid-s5320" xml:space="preserve">unde, quod propo-
              <lb/>
            ſitum nobis fuerat, par preſſus vio-
              <lb/>
            lentia neceſſariò concluditur.</s>
            <s xml:id="echoid-s5321" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div733" type="section" level="1" n="527">
          <head xml:id="echoid-head560" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s5322" xml:space="preserve">Triangulum A K L ſimile eſt triangulo A M N; </s>
            <s xml:id="echoid-s5323" xml:space="preserve">ideoq́ue latera quæ ſimili
              <lb/>
            ſitu reſpondent proportionalia,
              <lb/>
            Sic A K ad A M eſt, ut K L ad M N.</s>
            <s xml:id="echoid-s5324" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5325" xml:space="preserve">Triangulum A F H ſimile eſt triangulo A I G, ideoq́; </s>
            <s xml:id="echoid-s5326" xml:space="preserve">latera ſimiliter ſita
              <lb/>
            erunt proportionalia.</s>
            <s xml:id="echoid-s5327" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5328" xml:space="preserve">hoc eſt, A F ad A G, ut FH ad GI,
              <lb/>
            ſed ut A F ad A G, ſic A K ad A M. </s>
            <s xml:id="echoid-s5329" xml:space="preserve">itaque
              <lb/>
            ut A K ad A M, ſic F H ad G I.</s>
            <s xml:id="echoid-s5330" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5331" xml:space="preserve">atqui F H & </s>
            <s xml:id="echoid-s5332" xml:space="preserve">K L per hypotheſin æquantur. </s>
            <s xml:id="echoid-s5333" xml:space="preserve">erit igitur
              <lb/>
            ut A K ad A M, ſic K L ad GI.</s>
            <s xml:id="echoid-s5334" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5335" xml:space="preserve">Vt G I & </s>
            <s xml:id="echoid-s5336" xml:space="preserve">M N quartæ proportionales ſint, poſitis iiſdem tribus </s>
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