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

Table of contents

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[81.] DEMONSTRATIO.
Page: 19 (19)
[82.] NOTATO.
Page: 19 (19)
[83.] 2 THEOREMA. 6 PROPOSITIO.
Page: 19 (19)
[84.] DEMONSTRATIO.
Page: 19 (19)
[85.] 3 THEOREMA. 7 PROPOSITIO.
Page: 20 (20)
[86.] DEMONSTRATIO.
Page: 20 (20)
[87.] 4 THEOREMA. 8 PROPOSITIO.
Page: 20 (20)
[88.] DEMONSTRATIO.
Page: 21 (21)
[89.] 1 NOTA.
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[90.] 2 NOTA.
Page: 21 (21)
[91.] 5 THEOREMA. 9 PROPOSITIO.
Page: 22 (22)
[92.] DEMONSTRATIO.
Page: 22 (22)
[93.] 1 C*ONSECTARIUM.*
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[94.] 2 C*ONSECTARIUM.*
Page: 22 (22)
[95.] 5 PROBLEMA. 10 PROPOSITIO.
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[96.] PRAGMATIA.
Page: 23 (23)
[97.] DEMONSTRATIO.
Page: 23 (23)
[98.] 6 PROBLEMA. 11 PROPOSITIO.
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[99.] 1 NOTA.
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[100.] 2 NOTA.
Page: 24 (24)
[101.] PRAGMATIA.
Page: 25 (25)
[102.] 7 PROBLEMA. 12 PROPOSITIO.
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[103.] 1 Exemplum.
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[104.] PRAGMATIA.
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[105.] DEMONSTRATIO.
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[106.] 2 Exemplum.
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[107.] PRAGMATIA.
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[108.] DEMONSTRATIO.
Page: 27 (27)
[109.] 6 THEOREMA. 13 PROPOSITIO.
Page: 27 (27)
[110.] I Exemplum rectorum ponderum.
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              <pb o="98" file="527.01.098" n="98" rhead="3 L*IBER* S*TATICÆ*"/>
            drupla ſit ipſius G F etiam pondus H quadruplum erit ipſius hominis, quare
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            poſita gravitate hominis I librarum 150, atque H 600 ℔, eo ſitu æquiponde-
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              <figure xlink:label="fig-527.01.098-01" xlink:href="fig-527.01.098-01a" number="143">
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            r
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            abunt, neque H quoquam impelletur, ſed ſi ulterius tendat verſus A, etiam
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            H neceſſariò attolletur, quia ratio ipſius G K ad G F tum major foret quam in
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            theſi. </s>
            <s xml:id="echoid-s2939" xml:space="preserve">Si plures tympanum calcent, vicinior ipſi A aget potentius remotiore;
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            </s>
            <s xml:id="echoid-s2940" xml:space="preserve">atque per 3 prop. </s>
            <s xml:id="echoid-s2941" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s2942" xml:space="preserve">cum ſingulorum tum etiam univerſorum potentia con-
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            cludetur.</s>
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          <head xml:id="echoid-head313" xml:space="preserve">3 Exemplums.</head>
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            <s xml:id="echoid-s2944" xml:space="preserve">Atqui ponderum quæ rectà attolluntur, ut ſunt onera quæcunque, ſarcinæ,
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            vaſa, quæ tympanorum ſubſidio è navibus eximuntur, ratio hujuſmodi eſt.
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            </s>
            <s xml:id="echoid-s2945" xml:space="preserve">Pondera verò obliquè adſcendentia, cujus generis ſunt naves quæ in Belgio ſæ-
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            pe trans aggeres & </s>
            <s xml:id="echoid-s2946" xml:space="preserve">aquarum obices traducuntur, rationem non paulò diver-
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            ſam habent. </s>
            <s xml:id="echoid-s2947" xml:space="preserve">Enimverò ſit agger A, B navis trans aggerem pertrahenda, C D
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            tympanum, diameter C D horizonti parallela, homo navi B ſitu ἰ{σό}ῤῥοπ & </s>
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            ſeu æquilibris habeat gravitatis diametrum F E, funis ductarius G H, axis ſo-
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            liditas I K. </s>
            <s xml:id="echoid-s2949" xml:space="preserve">& </s>
            <s xml:id="echoid-s2950" xml:space="preserve">centrum L: </s>
            <s xml:id="echoid-s2951" xml:space="preserve">deinde eſto M N normalis aggeris clivo, horizonti
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            autem perpendicularis ad idem punctum N ſit N O. </s>
            <s xml:id="echoid-s2952" xml:space="preserve">præterea L F ſextupla
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            eſt ſemidiametri L K; </s>
            <s xml:id="echoid-s2953" xml:space="preserve">& </s>
            <s xml:id="echoid-s2954" xml:space="preserve">N O tripla ipſius M O, pondus autem hominis tym-
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            panum calcantis ℔ 150. </s>
            <s xml:id="echoid-s2955" xml:space="preserve">Quæ cum ita ſint, erit ut L F ad L K, ſic ex antece-
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            dente I
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            heoremate pondus è fune ductario ſuſpenſum rectà deſcendens, ad
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            gravitatem hominis 150 ℔, L F autem ex hypotheſi ſextupla eſt ipſius L K,
              <lb/>
            quamobrem pondus è fune H G recta deſcendens ſextuplum quoque eſſet
              <lb/>
            150 ℔, quæ ſunt 900 libræ, & </s>
            <s xml:id="echoid-s2956" xml:space="preserve">homo tympanum verſans tam potenter agit
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            quam 900 ℔ obliquâ trutinâ ſuſpenſæ. </s>
            <s xml:id="echoid-s2957" xml:space="preserve">Itaque per 20 propoſ. </s>
            <s xml:id="echoid-s2958" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s2959" xml:space="preserve">pondus na-
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            vis B ita ſe habet ad 900 ℔, ut N O ad O M, ſed N O tripla eſt ipſius O </s>
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