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

Page concordance

< >
Scan Original
131 131
132 132
133 133
134 134
135 135
136 136
137 137
138 138
139 139
140 140
141 141
142
143
144 144
145 145
146 146
147 147
148 148
149 149
150 150
151 151
152 152
153 153
154 154
155 155
156
157
158
159
160
< >
page |< < (97) of 197 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div406" type="section" level="1" n="293">
          <pb o="97" file="527.01.097" n="97" rhead="DE S*TATICÆ* PRAXI."/>
        </div>
        <div xml:id="echoid-div409" type="section" level="1" n="294">
          <head xml:id="echoid-head309" xml:space="preserve">9 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s2905" xml:space="preserve">Axium in peritrochio & </s>
            <s xml:id="echoid-s2906" xml:space="preserve">tractorum ponderum rationes
              <lb/>
            inquirere.</s>
            <s xml:id="echoid-s2907" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2908" xml:space="preserve">Pondus movens & </s>
            <s xml:id="echoid-s2909" xml:space="preserve">motum ſemidiametris tympani & </s>
            <s xml:id="echoid-s2910" xml:space="preserve">axis proportionales
              <lb/>
            ſunt, unde majoris evidentiæ gratia, theorema tale inſtituimus.</s>
            <s xml:id="echoid-s2911" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div410" type="section" level="1" n="295">
          <head xml:id="echoid-head310" xml:space="preserve">THEOREMA.</head>
          <p style="it">
            <s xml:id="echoid-s2912" xml:space="preserve">Si & </s>
            <s xml:id="echoid-s2913" xml:space="preserve">ab axe & </s>
            <s xml:id="echoid-s2914" xml:space="preserve">ab extremâ tympani ſemidiametro horizonti par allelâ.
              <lb/>
            </s>
            <s xml:id="echoid-s2915" xml:space="preserve">ponder a ſitu æquipondia dependeant, hæc erunt ſemidiametris reciproce pro-
              <lb/>
            portionalia.</s>
            <s xml:id="echoid-s2916" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2917" xml:space="preserve">D*ATVM.</s>
            <s xml:id="echoid-s2918" xml:space="preserve">* Eſto tympanum A B C D E F G, quod verſetur circa axem
              <lb/>
            E F G cujus diameter E F, centrum H, pondus I ab axe dependeat, A B C D
              <lb/>
            ſit ipſa rota ſeu tympanum, cujus ſemidiameter horizonti parallela A C, & </s>
            <s xml:id="echoid-s2919" xml:space="preserve">à
              <lb/>
            termino A pondus K dependeat ſitu æquipondium ipſi I; </s>
            <s xml:id="echoid-s2920" xml:space="preserve">L autem axis & </s>
            <s xml:id="echoid-s2921" xml:space="preserve">
              <lb/>
            ſuſtentaculi ſui infimus contactus. </s>
            <s xml:id="echoid-s2922" xml:space="preserve">Q*VAESITVM.</s>
            <s xml:id="echoid-s2923" xml:space="preserve">* Demonſtrato, H A, H F,
              <lb/>
            & </s>
            <s xml:id="echoid-s2924" xml:space="preserve">I, K, in eadem analogia eſſe.</s>
            <s xml:id="echoid-s2925" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div411" type="section" level="1" n="296">
          <head xml:id="echoid-head311" xml:space="preserve">DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s2926" xml:space="preserve">Enimverò tympanum A B C D librilis iſtar eſto, cujus anſa L B, ut ſublatis
              <unsure/>
              <lb/>
            ponderibus K, I, partes tympa-
              <lb/>
              <figure xlink:label="fig-527.01.097-01" xlink:href="fig-527.01.097-01a" number="142">
                <image file="527.01.097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.097-01"/>
              </figure>
            ni B D A, B D C ſint æquili-
              <lb/>
            bres. </s>
            <s xml:id="echoid-s2927" xml:space="preserve">Siigitur pondus I ab F de-
              <lb/>
            pendere fingas, quia hic tantæ
              <lb/>
            eſt potentiæ quantæ ſuo loco, K
              <lb/>
            autem è loco ſuo A, per 1 prop.
              <lb/>
            </s>
            <s xml:id="echoid-s2928" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s2929" xml:space="preserve">eadem ratio erit radii lon-
              <lb/>
            gioris H A, ad breviorem H F,
              <lb/>
            quæ ponderis majoris I ad mi-
              <lb/>
            nus K. </s>
            <s xml:id="echoid-s2930" xml:space="preserve">Quamobrem ſi H A ſex-
              <lb/>
            tuplus ſit ipſius H F, etiam I
              <lb/>
            ſextuplum fuerit ipſius K, ut ſi
              <lb/>
            I ponatur 600 librarum, K erit
              <lb/>
            100, ideo q́ue potentia hominis
              <lb/>
            ad A æquivalens 100 libris, ſitu
              <lb/>
            æquipondia foret 600 libris ad
              <lb/>
            I, & </s>
            <s xml:id="echoid-s2931" xml:space="preserve">quo attolli poſſit (propter
              <lb/>
            impedimenta contactus axis & </s>
            <s xml:id="echoid-s2932" xml:space="preserve">ſuſtentaculi C) paulo potentius quam 100 ℔
              <lb/>
            agat neceſſe erit.</s>
            <s xml:id="echoid-s2933" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div413" type="section" level="1" n="297">
          <head xml:id="echoid-head312" xml:space="preserve">2 Exemplum.</head>
          <p>
            <s xml:id="echoid-s2934" xml:space="preserve">Hinc tympanorum qui Græcis γέζανθι ſimiliumq́ue rotarum ratio, quæ à
              <lb/>
            calcantibus hominibus verſantur, manifeſta eſt. </s>
            <s xml:id="echoid-s2935" xml:space="preserve">Exponatur enim tympanum
              <lb/>
            A B C D, diametro A C horizonti parallela, cujus axis craſſities ad tornum
              <lb/>
            rotundati ſit E F, centrum G, pondus ab axe H; </s>
            <s xml:id="echoid-s2936" xml:space="preserve">homo ad I ſitu æquilibris
              <lb/>
            ponderi H, & </s>
            <s xml:id="echoid-s2937" xml:space="preserve">I K gtavitatis ejus perpendicularis in A C. </s>
            <s xml:id="echoid-s2938" xml:space="preserve">Notumautem G K,
              <lb/>
            ad G F eſt
              <unsure/>
            e, ſicut pondus H ad gravitatem hominis qui ad I, ſi igitur G K </s>
          </p>
        </div>
      </text>
    </echo>
Impressum