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

Table of contents

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[111.] DEMONSTRATIO.
Page: 27 (27)
[112.] 2 Exemplum obliquorum ponderum.
Page: 28 (28)
[113.] DEMONSTRATIO.
Page: 28 (28)
[114.] 3 Exemplum.
Page: 28 (28)
[115.] DEMONSTRATIO.
Page: 28 (28)
[116.] 8 PROBLEMA. 14 PROPOSITIO.
Page: 29 (29)
[117.] PRAGMATIA.
Page: 29 (29)
[118.] DEMONSTRATIO.
Page: 29 (29)
[119.] NOTATO
Page: 29 (29)
[120.] 1 C*ONSECTARIUM*.
Page: 29 (29)
[121.] 2 C*ONSECTARIUM*.
Page: 30 (30)
[122.] 7 THEOREMA. 15 PROPOSITIO.
Page: 31 (31)
[123.] DECLARATIO.
Page: 31 (31)
[124.] 8 THEOREMA. 16 PROPOSITIO.
Page: 31 (31)
[125.] DEMONSTRATIO.
Page: 31 (31)
[126.] 9 THEOREMA. 17 PROPOSITIO.
Page: 32 (32)
[127.] DEMONSTRATIO.
Page: 32 (32)
[128.] C*ONSECTARIUM*.
Page: 33 (33)
[129.] 10 THEOREMA. 18 PROPOSITIO.
Page: 33 (33)
[130.] C*ONSECTARIUM*.
Page: 34 (34)
[131.] HACTENVS RECTORVM PONDERVM GENERA DICTA SVNT; OBLI-QVORVM PROPRIETATES DEINCEPS deſcribendæ ſunt, quarum omnium genera-lem veritatem tanquam fundamentum istud theoremata complectitur. 11 THEOREMA. 19 PROPOSITIO.
Page: 34 (34)
[132.] DEMONSTRATIO.
Page: 35 (35)
[133.] 1 C*ONSECTARIUM*.
Page: 35 (35)
[134.] 2 C*ONSECTARIUM*.
Page: 35 (35)
[135.] 3 C*ONSECTARIUM*.
Page: 35 (35)
[136.] 4 C*ONSECTARIUM*.
Page: 36 (36)
[137.] 5 C*ONSECTARIUM*.
Page: 36 (36)
[138.] 6 C*ONSECTARIUM*.
Page: 36 (36)
[139.] 7 C*ONSECTARIUM*.
Page: 38 (38)
[140.] 8 C*ONSECTARIUM*.
Page: 38 (38)
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          <head xml:id="echoid-head148" xml:space="preserve">4 C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s1072" xml:space="preserve">QVandoquidem 3 confectarii globus li-
              <lb/>
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                <image file="527.01.036-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.036-01"/>
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            neam A B tangit in puncto G, tanquam
              <lb/>
            firmo, globi axis G H perpendicularis eſt ad
              <lb/>
            A B: </s>
            <s xml:id="echoid-s1073" xml:space="preserve">quapropter amoto globo, loco ejus co-
              <lb/>
            lumna D ejuſdem ponderis cum globo po-
              <lb/>
            natur, ut axis G H (cujus punctum firmũ G)
              <lb/>
            perpendicularis ſit lateri A B, & </s>
            <s xml:id="echoid-s1074" xml:space="preserve">D F linea
              <lb/>
            obliquè extollens ad A B parallela ſecans la-
              <lb/>
            tus columnæ in I; </s>
            <s xml:id="echoid-s1075" xml:space="preserve">erit etiam nunc, quemad-
              <lb/>
            modum A B ad B C (ratio autem eſt dupla,
              <lb/>
            utante) ita columna D ad pondus E.</s>
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          <head xml:id="echoid-head149" xml:space="preserve">5 C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s1077" xml:space="preserve">PErpendiculari D K è columnæ centro D productâ, ut ejus latus in L ſe-
              <lb/>
            cet, triangulum LDI ſimile erit triangulo A B C, anguli enim A C B & </s>
            <s xml:id="echoid-s1078" xml:space="preserve">
              <lb/>
            L I D recti ſunt, & </s>
            <s xml:id="echoid-s1079" xml:space="preserve">rectæ L D, D I, pa-
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              <figure xlink:label="fig-527.01.036-02" xlink:href="fig-527.01.036-02a" number="59">
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            rallelæ ſunt ad BC, AB. </s>
            <s xml:id="echoid-s1080" xml:space="preserve">Vtigitur AB
              <lb/>
            ad B C: </s>
            <s xml:id="echoid-s1081" xml:space="preserve">ita L D ad D I. </s>
            <s xml:id="echoid-s1082" xml:space="preserve">Atquiut A B
              <lb/>
            ad B C: </s>
            <s xml:id="echoid-s1083" xml:space="preserve">ita columna ad pondus E, per
              <lb/>
            4 confectarium, & </s>
            <s xml:id="echoid-s1084" xml:space="preserve">propterea ut L D
              <lb/>
            ad D I: </s>
            <s xml:id="echoid-s1085" xml:space="preserve">ita columna eſt ad E. </s>
            <s xml:id="echoid-s1086" xml:space="preserve">Ad li-
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            neam K D ſi pondus M, quod rectè
              <lb/>
            extollat, & </s>
            <s xml:id="echoid-s1087" xml:space="preserve">columnæ ſitu æquilibre eſt,
              <lb/>
            adjungatur, ad columnam etiam æqui-
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            pondium erit, per 14 propoſit. </s>
            <s xml:id="echoid-s1088" xml:space="preserve">utigitur
              <lb/>
            L D ad D I: </s>
            <s xml:id="echoid-s1089" xml:space="preserve">ita M ad E.</s>
            <s xml:id="echoid-s1090" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div182" type="section" level="1" n="138">
          <head xml:id="echoid-head150" xml:space="preserve">6 C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s1091" xml:space="preserve">B N ducatur, ſecans A C continuatam in N, conſimiliter D O ſecans
              <lb/>
            continuatam L I, hoc eſt, latus columnæ in O, ut angulus I D O æqualis ſit
              <lb/>
            angulo C B N. </s>
            <s xml:id="echoid-s1092" xml:space="preserve">Appendatur quoque ad D O pondus P obliquè attollens,
              <lb/>
            quod (amotis M, E ponderibus) columnam in ſuo ſitu conſervet. </s>
            <s xml:id="echoid-s1093" xml:space="preserve">Quia vero
              <lb/>
            D L & </s>
            <s xml:id="echoid-s1094" xml:space="preserve">B A, item D I & </s>
            <s xml:id="echoid-s1095" xml:space="preserve">B C latera trian-
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            gulorum D L I & </s>
            <s xml:id="echoid-s1096" xml:space="preserve">B A C homologa
              <lb/>
            ſunt, hujuſmodi concluſio inde dedu-
              <lb/>
            citur. </s>
            <s xml:id="echoid-s1097" xml:space="preserve">Quemadmodum B A ad B C:
              <lb/>
            </s>
            <s xml:id="echoid-s1098" xml:space="preserve">ita ſacoma lateris B A ad antiſacoma
              <lb/>
            lateris B C (per 2 conſectarium.) </s>
            <s xml:id="echoid-s1099" xml:space="preserve">item
              <lb/>
            quemadmodum D L ad D I: </s>
            <s xml:id="echoid-s1100" xml:space="preserve">ita ſaco-
              <lb/>
            ma lateris D L ad antiſacoma lateris
              <lb/>
            D I, hoc eſtita M ad E. </s>
            <s xml:id="echoid-s1101" xml:space="preserve">Sed homolo-
              <lb/>
            ga latera triãgulorum ſimilium A B N,
              <lb/>
            L D O ſunt A B & </s>
            <s xml:id="echoid-s1102" xml:space="preserve">D L, item B N, & </s>
            <s xml:id="echoid-s1103" xml:space="preserve">
              <lb/>
            D O. </s>
            <s xml:id="echoid-s1104" xml:space="preserve">Itaque ut ſupra, quemadmodum B A ad B N: </s>
            <s xml:id="echoid-s1105" xml:space="preserve">ir
              <unsure/>
            a ſacoma B A ad an-
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            tiſacoma B N (per 1 confectarium) Et quemadmodum D L ad D O: </s>
            <s xml:id="echoid-s1106" xml:space="preserve">ita il-
              <lb/>
            lius ſacoma ad hujus antiſacoma, id eſt, M ad P. </s>
            <s xml:id="echoid-s1107" xml:space="preserve">Si linea B N à puncto B
              <lb/>
            aliovorſum; </s>
            <s xml:id="echoid-s1108" xml:space="preserve">A ſcilicet verſus, ultra B C fuiſſet ducta, etiam recta D O à </s>
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