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

Table of contents

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[101.] PRAGMATIA.
Page: 25 (25)
[102.] 7 PROBLEMA. 12 PROPOSITIO.
Page: 25 (25)
[103.] 1 Exemplum.
Page: 25 (25)
[104.] PRAGMATIA.
Page: 26 (26)
[105.] DEMONSTRATIO.
Page: 26 (26)
[106.] 2 Exemplum.
Page: 26 (26)
[107.] PRAGMATIA.
Page: 26 (26)
[108.] DEMONSTRATIO.
Page: 27 (27)
[109.] 6 THEOREMA. 13 PROPOSITIO.
Page: 27 (27)
[110.] I Exemplum rectorum ponderum.
Page: 27 (27)
[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)
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              <pb o="163" file="527.01.163" n="163" rhead="*DE* S*PARTOSTATICA*."/>
            ductaq́ue M N parallela contra B C, concludes ut B N ad B M, ſic Gadpon-
              <lb/>
            dus ſuſtentatum ab A B.</s>
            <s xml:id="echoid-s4752" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4753" xml:space="preserve">Item ut B M ad B N, ſic pondus G ad pondus quod ſuſtinetur à B C.</s>
            <s xml:id="echoid-s4754" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4755" xml:space="preserve">Secundò continuata etiam H C ſurſum vorſum in O, & </s>
            <s xml:id="echoid-s4756" xml:space="preserve">B P parallela du-
              <lb/>
            cta contra C D: </s>
            <s xml:id="echoid-s4757" xml:space="preserve">concludes ſimiliter ſuperiori, ut C P ad C B, ſic H ad pondus
              <lb/>
            ſui partem quod pertiner ad C B. </s>
            <s xml:id="echoid-s4758" xml:space="preserve">Ex quo perſpicitur idem quod ſupra pro
              <lb/>
            B C concluſum eſt nunc redire. </s>
            <s xml:id="echoid-s4759" xml:space="preserve">Factio cæterarum concluſionum his ſimiliter
              <lb/>
            inſtituetur. </s>
            <s xml:id="echoid-s4760" xml:space="preserve">In his & </s>
            <s xml:id="echoid-s4761" xml:space="preserve">aliis ſimilibus I*LLVSTRISSIMVS* P*RINCEPS* cer-
              <lb/>
            tiſſimis experimentis cognovit, Praxin Theoriæ exactiſſimè conſentire.</s>
            <s xml:id="echoid-s4762" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4763" xml:space="preserve">Proportionem 17 propoſitione à nobis deſcriptam, aliter quoq; </s>
            <s xml:id="echoid-s4764" xml:space="preserve">efferre & </s>
            <s xml:id="echoid-s4765" xml:space="preserve">effa-
              <lb/>
            ri poſſumus, unde uſus paulo facilior emanet Cujus explicationi diagramma id
              <lb/>
            oculis hic ſubjeci. </s>
            <s xml:id="echoid-s4766" xml:space="preserve">ubi pro eo quodita enuntia-
              <lb/>
            tur, ut põdus oblique attollĕs ad pondus attol-
              <lb/>
              <figure xlink:label="fig-527.01.163-01" xlink:href="fig-527.01.163-01a" number="220">
                <image file="527.01.163-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.163-01"/>
              </figure>
            lens rectè, ſic propriũ cujuſq́; </s>
            <s xml:id="echoid-s4767" xml:space="preserve">pondus obliquè
              <lb/>
            tollĕs ad pondus tollĕs rectè ut aliter efferam,
              <lb/>
            unde factio expeditior derivetur: </s>
            <s xml:id="echoid-s4768" xml:space="preserve">agatur LP,
              <lb/>
            inter lineas rectè & </s>
            <s xml:id="echoid-s4769" xml:space="preserve">obliquè attollentes, paral
              <lb/>
            lela contra F M, his poſitis, dico ut linea rectè
              <lb/>
            attollens, ad tollentem oblique, ſic totius co-
              <lb/>
            lumnæ pondus ad pondus ipſum tollens obli-
              <lb/>
            què, hoc eſt, ut EP ad EL, ſic pondus columnę
              <lb/>
            totius ad G. </s>
            <s xml:id="echoid-s4770" xml:space="preserve">& </s>
            <s xml:id="echoid-s4771" xml:space="preserve">rurſum ut E P ad P L, ſic pon-
              <lb/>
            dus columnæ ad H. </s>
            <s xml:id="echoid-s4772" xml:space="preserve">qua via ignotorum ter-
              <lb/>
            minorum inventio multò fit brevior & </s>
            <s xml:id="echoid-s4773" xml:space="preserve">ſuccin-
              <lb/>
            ctior. </s>
            <s xml:id="echoid-s4774" xml:space="preserve">Animadvertas item pro LP potuiſſe duci M Q, inter alteras rectè & </s>
            <s xml:id="echoid-s4775" xml:space="preserve">obli-
              <lb/>
            què extollentes lineas, parallelam contra EL, quâ ratiocinium, ut ſupra cum
              <lb/>
            L E, inire liceat. </s>
            <s xml:id="echoid-s4776" xml:space="preserve">namq́ue ut P E ad EL, ſic Q F ad FM, cùm triangula
              <lb/>
            FMQ & </s>
            <s xml:id="echoid-s4777" xml:space="preserve">L P E ſimilia ſint, ob parallelas Q F PE, MF LP.</s>
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          <head xml:id="echoid-head496" xml:space="preserve">7 C*ONSECTARIUM*.</head>
          <p>
            <s xml:id="echoid-s4779" xml:space="preserve">Hactenus pondera è duabus lineis de-
              <lb/>
            pendĕtia expoſita ſunt, ſequuntur deinceps
              <lb/>
              <figure xlink:label="fig-527.01.163-02" xlink:href="fig-527.01.163-02a" number="221">
                <image file="527.01.163-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.163-02"/>
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            quæ pluribus lineis ſuſpenduntur. </s>
            <s xml:id="echoid-s4780" xml:space="preserve">Cui fini
              <lb/>
            quinti conſectarii diagramma aſſumamus,
              <lb/>
            hâc tantùm difſerentiâ, utrecta C G troch-
              <lb/>
            leam K hîc ſtrictim tangat, utrecta K C F
              <lb/>
            horizonti ſit obliqua, cæterum pondus AB
              <lb/>
            idem eſto, iidemq́ue anguli aſſumantur
              <lb/>
            D C F, F CE. </s>
            <s xml:id="echoid-s4781" xml:space="preserve">jam per 5 conſectarium patet
              <lb/>
            C I ad C H eſſe, ut pondus A B ad id quod
              <lb/>
            ſuſtinetur à D. </s>
            <s xml:id="echoid-s4782" xml:space="preserve">porro ut CI ad I H, ſic A B
              <lb/>
            ad id quod pertinet ad E. </s>
            <s xml:id="echoid-s4783" xml:space="preserve">Denique ut C H
              <lb/>
            ad H I, ſic id quod ab D ad id quod ab E
              <lb/>
            ſuſtinetur.</s>
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          </p>
          <p>
            <s xml:id="echoid-s4785" xml:space="preserve">Ex quo efficitur ſi ab D C E, tanquam
              <lb/>
            fune, dependeat pondus A B manifeſtum
              <lb/>
            eſſe quantum pars quæq́ue D C, C E ſuffe-
              <lb/>
            rant.</s>
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