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

Table of contents

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[141.] 9 C*ONSECTARIUM*.
Page: 39 (39)
[142.] 10 C*ONSECTARIUM*.
Page: 40 (40)
[143.] 11 C*ONSECTARIUM*.
Page: 40 (40)
[144.] 12 C*ONSECTARIUM*.
Page: 40 (40)
[145.] 12 THE OREMA. 20 PROPOSITIO.
Page: 41 (41)
[146.] NOTATO
Page: 42 (42)
[147.] 13 THEOREMA. 21 PROPOSITIO.
Page: 42 (42)
[148.] DEMONSTRATIO.
Page: 42 (42)
[149.] 9 PROBLEMA. 22 PROPOSITIO.
Page: 43 (43)
[150.] PRAGMATIA.
Page: 43 (43)
[151.] DEMONSTRATIO.
Page: 44 (44)
[152.] 1 NOTA.
Page: 44 (44)
[153.] 2 NOTA.
Page: 44 (44)
[154.] 14 THE OREMA. 23 PROPOSITIO.
Page: 44 (44)
[155.] DEMONSTRATIO.
Page: 45 (45)
[156.] 15 THEOREMA. 24 PROPOSITIO.
Page: 45 (45)
[157.] DEMONSTRATIO.
Page: 45 (45)
[158.] C*ONSECTARIUM*.
Page: 46 (46)
[159.] 16 THEOREMA. 25 PROPOSITIO.
Page: 46 (46)
[160.] 1 Exemplum.
Page: 46 (46)
[161.] DEMONSTRATIO.
Page: 46 (46)
[162.] 2 Exemplum.
Page: 46 (46)
[163.] DEMONSTRATIO.
Page: 46 (46)
[164.] 3 Exemplum.
Page: 47 (47)
[165.] DEMONSTRATIO.
Page: 47 (47)
[166.] 4 Exemplum.
Page: 47 (47)
[167.] DEMONSTRATIO.
Page: 47 (47)
[168.] 17 THEOREMA. 26 PROPOSITIO.
Page: 47 (47)
[169.] DEMONSTRATIO.
Page: 48 (48)
[170.] 18 PROBLEMA. 27 PROPOSITIO.
Page: 48 (48)
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        <div xml:id="echoid-div208" type="section" level="1" n="151">
          <head xml:id="echoid-head163" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s1335" xml:space="preserve">Quemadmodũ AS ad S OE: </s>
            <s xml:id="echoid-s1336" xml:space="preserve">ita rectè extol-
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            lens põdus ad Y extollĕs obliquè, per 20 propoſ.
              <lb/>
            </s>
            <s xml:id="echoid-s1337" xml:space="preserve">Atqui triangulũ Æ OE Z triangulo OE S A ſimi-
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            le eſt, quorum homologa latera ſunt, OE Z cum
              <lb/>
            OE S, & </s>
            <s xml:id="echoid-s1338" xml:space="preserve">Z Æ, cum S A. </s>
            <s xml:id="echoid-s1339" xml:space="preserve">erit igitur quemadmo-
              <lb/>
            dum A S ad S OE: </s>
            <s xml:id="echoid-s1340" xml:space="preserve">ita Æ Z ad Z OE, & </s>
            <s xml:id="echoid-s1341" xml:space="preserve">con-
              <lb/>
            ſequenter quemadmodum Æ Z 2 ad Z OE 1: </s>
            <s xml:id="echoid-s1342" xml:space="preserve">ita
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            pondus rectè extollens 4 lib. </s>
            <s xml:id="echoid-s1343" xml:space="preserve">ad Y. </s>
            <s xml:id="echoid-s1344" xml:space="preserve">Innotuit igi-
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            tur Y 2 ℔ pendere, quod probandum ſuit. </s>
            <s xml:id="echoid-s1345" xml:space="preserve">Si-
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            militer in quibuſvis aliis exemplis proceditur.</s>
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          <p>
            <s xml:id="echoid-s1347" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s1348" xml:space="preserve">Datis igitur, notâ columnâ
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            punctis q́ue in axe ſirmo, &</s>
            <s xml:id="echoid-s1349" xml:space="preserve">c.</s>
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        <div xml:id="echoid-div210" type="section" level="1" n="152">
          <head xml:id="echoid-head164" xml:space="preserve">1 NOTA.</head>
          <p style="it">
            <s xml:id="echoid-s1351" xml:space="preserve">Etiamiſto pacto concludere licuiſſet: </s>
            <s xml:id="echoid-s1352" xml:space="preserve">AS 2 dat S OE 1: </s>
            <s xml:id="echoid-s1353" xml:space="preserve">ego pondus 4 ℔ rectè
              <unsure/>
            ex-
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            t
              <unsure/>
            ollens dabit γ 2 ℔. </s>
            <s xml:id="echoid-s1354" xml:space="preserve">Verum ut operatio ipſirei & </s>
            <s xml:id="echoid-s1355" xml:space="preserve">natur æ magis conformis ſit (intra
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            ſolidx
              <unsure/>
            m corpus enim AS & </s>
            <s xml:id="echoid-s1356" xml:space="preserve">S OE delineari nequeunt ) externam perpendicularen
              <unsure/>
            s
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            in exemplo pro internâ aſſumere placuit.</s>
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        <div xml:id="echoid-div211" type="section" level="1" n="153">
          <head xml:id="echoid-head165" xml:space="preserve">2 NOTA.</head>
          <p style="it">
            <s xml:id="echoid-s1358" xml:space="preserve">Quomodo autem terminus ignotus, ut pondus rectè extollens, linea tam rectè. </s>
            <s xml:id="echoid-s1359" xml:space="preserve">quàns
              <lb/>
            obliquè extollens, columna, datis tribus inversâ & </s>
            <s xml:id="echoid-s1360" xml:space="preserve">alternâ proportione innoteſcat, igno-
              <lb/>
            tum eſſe non poteſt, quapropter brevitati ſtudentes, omittemus.</s>
            <s xml:id="echoid-s1361" xml:space="preserve"/>
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          <head xml:id="echoid-head166" xml:space="preserve">14 THE OREMA. 23 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s1362" xml:space="preserve">Æqualia pondera ſuſpenſa de ductariis lineis, quæ ex
              <lb/>
            eodem axis puncto in contrarias partes ductę æquales cum
              <lb/>
            axe angulos faciunt: </s>
            <s xml:id="echoid-s1363" xml:space="preserve">in columnam æqualem vim poten-
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            tia mq́ue exercent.</s>
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          <p>
            <s xml:id="echoid-s1365" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s1366" xml:space="preserve">A B columna, C D axis, E firmum, F mobile punctum eſto,
              <lb/>
            unde G obliquè extollens pondus dependeat, in ſuo ſitu columnam ſervans,
              <lb/>
            cujus obliqua linea F H. </s>
            <s xml:id="echoid-s1367" xml:space="preserve">Indi
              <unsure/>
            dem à puncto
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                <image file="527.01.044-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.044-02"/>
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            ſcilicet F, & </s>
            <s xml:id="echoid-s1368" xml:space="preserve">pondus I itidem obliquum,
              <lb/>
            aliovorſum depĕdeat
              <unsure/>
            , ejuſdem cum G pon-
              <lb/>
            deris, cujus obliqua linea F K, æquans K F D
              <lb/>
            angulum H F C angulo.</s>
            <s xml:id="echoid-s1369" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1370" xml:space="preserve">Q*VAESITVM*. </s>
            <s xml:id="echoid-s1371" xml:space="preserve">Demonſtrandũ eſt pon-
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            deris I tantundĕ potentiæ eſſe in columnam
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            A B, quantum eſt ponderis G, id eſt, & </s>
            <s xml:id="echoid-s1372" xml:space="preserve">I
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            pondus (coërcito eſt amoto G) columnam
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            eodem in ſitu tenere.</s>
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          <p>
            <s xml:id="echoid-s1374" xml:space="preserve">P*RAEPARATIO*. </s>
            <s xml:id="echoid-s1375" xml:space="preserve">Adidem punctum F, pondus L rectè extollens adda-
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            tur, quod non minus, in illo ſitu columnam ſuſpendat, cujus recta extol-
              <lb/>
            lens eſt F M.</s>
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