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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              <pb o="37" file="527.01.037" n="37" rhead="*DE* S*TATICÆ ELEMENTIS*."/>
            u@@a D I cecidiſſet, hoc eſt, ut nunc citra: </s>
            <s xml:id="echoid-s1109" xml:space="preserve">ita tunc ultra cecidiſſet, & </s>
            <s xml:id="echoid-s1110" xml:space="preserve">præce-
              <lb/>
            dens demonſtratio etiam iſtiſitui accommoda fuiſſet, hoc eſt, quemadmodum
              <lb/>
            B A ad B N ita ſacoma lateris B A, ad antiſacoma lateris B N eſſet: </s>
            <s xml:id="echoid-s1111" xml:space="preserve">& </s>
            <s xml:id="echoid-s1112" xml:space="preserve">quem-
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            admodum D L ad D O: </s>
            <s xml:id="echoid-s1113" xml:space="preserve">ita ſacoma lateris D L, ad antiſacoma lateris D O.
              <lb/>
            </s>
            <s xml:id="echoid-s1114" xml:space="preserve">hoc eſt M ad P. </s>
            <s xml:id="echoid-s1115" xml:space="preserve">Vtiſta proportio non tantum in exemplis valeat, in quibus
              <lb/>
            linea attollens, ut D I, perpendicularis eſt axi, ſed etiam in aliis cujuſmodi-
              <lb/>
            cunque ſint anguli.</s>
            <s xml:id="echoid-s1116" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1117" xml:space="preserve">ISta etiam deglobo in lineâ, ut A B, jacente intelligi poſſunt, nam & </s>
            <s xml:id="echoid-s1118" xml:space="preserve">hic, ut
              <lb/>
            L D ad D O: </s>
            <s xml:id="echoid-s1119" xml:space="preserve">ita M ad P (modo C L ad A B perpendicularis ſit, hoc eſt,
              <lb/>
            patallela ad axem G H globi D) atqui pon-
              <lb/>
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            dus Mglobo D æquatur, ideo etiam ut L D
              <lb/>
            ad D O: </s>
            <s xml:id="echoid-s1120" xml:space="preserve">ita pondus globi ad pondus P. </s>
            <s xml:id="echoid-s1121" xml:space="preserve">Ve-
              <lb/>
            rumenimvero, quia L D & </s>
            <s xml:id="echoid-s1122" xml:space="preserve">D O intra glo-
              <lb/>
            biſoliditatem re ipſa delineari cõmodè non
              <lb/>
            poſſunt, perpendiculari C E ductâ, extra
              <lb/>
            globi ſolidum comprehĕdetur C E O trian-
              <lb/>
            gulum L D O triangulo ſimile, cujus latera
              <lb/>
            L D & </s>
            <s xml:id="echoid-s1123" xml:space="preserve">C E, item D O & </s>
            <s xml:id="echoid-s1124" xml:space="preserve">E O homologa
              <lb/>
            erunt. </s>
            <s xml:id="echoid-s1125" xml:space="preserve">Quemadmodum igitur L D ad D O:
              <lb/>
            </s>
            <s xml:id="echoid-s1126" xml:space="preserve">ita C E ad E O, & </s>
            <s xml:id="echoid-s1127" xml:space="preserve">per conſequens ut C E ad E O: </s>
            <s xml:id="echoid-s1128" xml:space="preserve">itaglobi pondus ad P.</s>
            <s xml:id="echoid-s1129" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1130" xml:space="preserve">VT major claritudo hujus ſit, ſublatis aliis li-
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              <figure xlink:label="fig-527.01.037-02" xlink:href="fig-527.01.037-02a" number="62">
                <image file="527.01.037-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.037-02"/>
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            neis omnibus dicatur ut C E ad C O: </s>
            <s xml:id="echoid-s1131" xml:space="preserve">ita
              <lb/>
            pondus globi D ad pondus P.</s>
            <s xml:id="echoid-s1132" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1133" xml:space="preserve">NEque illud de globis tantum verum eſt, ſed
              <lb/>
            etiam de quibuſvis corporibus, puncta vel li-
              <lb/>
            neas ſtringentibus, aut etiam per illa volutis, ut in-
              <lb/>
            fra videre eſt. </s>
            <s xml:id="echoid-s1134" xml:space="preserve">Sed de his in S*TATICES* praxi
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                <image file="527.01.037-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.037-03"/>
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            preſſius dicemus. </s>
            <s xml:id="echoid-s1135" xml:space="preserve">Nam & </s>
            <s xml:id="echoid-s1136" xml:space="preserve">hîc dicimus quemadmodum C E ad E O: </s>
            <s xml:id="echoid-s1137" xml:space="preserve">ita pon-
              <lb/>
            dus corporis D, ad pondus P.</s>
            <s xml:id="echoid-s1138" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1139" xml:space="preserve">VNde etiam hoc manifeſtum: </s>
            <s xml:id="echoid-s1140" xml:space="preserve">Si recta A B horizonti eſt parallela, qua-
              <lb/>
            lem figuram hic juxta poſitam videre eſt, rectas C E & </s>
            <s xml:id="echoid-s1141" xml:space="preserve">C O in unam & </s>
            <s xml:id="echoid-s1142" xml:space="preserve">
              <lb/>
            candem lineam coïre, ideoq́ue inter E & </s>
            <s xml:id="echoid-s1143" xml:space="preserve">O nullam longitudinĕ & </s>
            <s xml:id="echoid-s1144" xml:space="preserve">propterea
              <lb/>
            rectæ C E ad rectam E O nullam rationĕ fore. </s>
            <s xml:id="echoid-s1145" xml:space="preserve">Hinc intelligere in proclivi </s>
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