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

Table of contents

< >
[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)
[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)
< >
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