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

Table of contents

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[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)
[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)
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          <pb o="151" file="527.01.151" n="151" rhead="S*TATICES.*"/>
        </div>
        <div xml:id="echoid-div631" type="section" level="1" n="452">
          <head xml:id="echoid-head472" xml:space="preserve">C*APVT I.*</head>
          <head xml:id="echoid-head473" style="it" xml:space="preserve">Cauſam æquilibritatis ſitus non eſſe in circulis ab extre=
            <lb/>
          mitatibus radiorum deſcriptis.</head>
          <p>
            <s xml:id="echoid-s4446" xml:space="preserve">CVr pondera æqualia in æqualibus radiis ſitu æquiponderent, communi
              <lb/>
            notioneſcitur: </s>
            <s xml:id="echoid-s4447" xml:space="preserve">at non perinde patet cauſa æquamenti ponderum inæ-
              <lb/>
            qualium in radiis diſparibus, quique ponderibus ſuis reciprocè propor-
              <lb/>
            tionales ſint. </s>
            <s xml:id="echoid-s4448" xml:space="preserve">hanc veteres circulis decircinatis à radiorum extremitatibus ineſſe
              <lb/>
            crediderunt, quemadmodum apud Ariſtotelem in Mechanicis ejusq́ueſectato-
              <lb/>
            res videre licet, quod falſum eſſehoc pacto redarguimus.</s>
            <s xml:id="echoid-s4449" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4450" xml:space="preserve">Quieſcens nullum deſcribit circulum:</s>
            <s xml:id="echoid-s4451" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4452" xml:space="preserve">Duo ſitu æquilibria quieſcunt:</s>
            <s xml:id="echoid-s4453" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4454" xml:space="preserve">Itaque duo ſitu æquilibria nullum deſcribunt circulum.</s>
            <s xml:id="echoid-s4455" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4456" xml:space="preserve">Et conſequenter nullus erit circulus; </s>
            <s xml:id="echoid-s4457" xml:space="preserve">atqui ſublato circulo etiam cauſa tolli-
              <lb/>
            tur quæ ipſi ſubeſt, quare cauſa æquilibritatis ſitus in circulis hîc non latet. </s>
            <s xml:id="echoid-s4458" xml:space="preserve">Mo-
              <lb/>
            tus autem iſte (ut aſſumptionem noſtri ſyllogiſmi confirmemus) ſivè circulo-
              <lb/>
            rum deſcriptio qui hic cernitur, æquiponderantibus propriè non ineſt; </s>
            <s xml:id="echoid-s4459" xml:space="preserve">ſed
              <lb/>
            cafu contingit, ut vento aliove impulſu quo non hæc ſolùm, ſed ἀνιοὀῤῥοπα
              <lb/>
            pondera quælibet etiam circulos deſcribent. </s>
            <s xml:id="echoid-s4460" xml:space="preserve">Quamobrem in his circulis cauſa
              <lb/>
            æquilibritatis nulla eſt: </s>
            <s xml:id="echoid-s4461" xml:space="preserve">ſed iis quæ 1 propoſ. </s>
            <s xml:id="echoid-s4462" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s4463" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s4464" xml:space="preserve">Staticor. </s>
            <s xml:id="echoid-s4465" xml:space="preserve">Mathematicè
              <lb/>
            demonſtravimus: </s>
            <s xml:id="echoid-s4466" xml:space="preserve">minimeq́ue mirum ſi ii, qui errores iſtiuſmodi pro veritate
              <lb/>
            uſurpabant, ad cauſarum cognitionem non penetrarint, aut nulla Statices for-
              <lb/>
            mâ inventa, à verò adeò diverſi abierint, multis falſis propoſitionibus ſeſe exer-
              <lb/>
            centes, quas ſigillatim, propter cauſas ſupra expoſitas, nuncnõ refellimus; </s>
            <s xml:id="echoid-s4467" xml:space="preserve">atque
              <lb/>
            eo magis quod à contraria veritatis norma facillimè coarguantur.</s>
            <s xml:id="echoid-s4468" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4469" xml:space="preserve">Propoſitiones item Cardani nonnullas lib. </s>
            <s xml:id="echoid-s4470" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4471" xml:space="preserve">Proportion. </s>
            <s xml:id="echoid-s4472" xml:space="preserve">de ponderibus
              <lb/>
            obliquatis, quarum judicium è certis quibuſdam angulis, lineis, planisq́ue in-
              <lb/>
            ſtituit, falſas & </s>
            <s xml:id="echoid-s4473" xml:space="preserve">à vero alienas eſſe, ne longior hic ſim, è 19 propoſ. </s>
            <s xml:id="echoid-s4474" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s4475" xml:space="preserve">Static.
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            </s>
            <s xml:id="echoid-s4476" xml:space="preserve">facillime perſpicitur.</s>
            <s xml:id="echoid-s4477" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div632" type="section" level="1" n="453">
          <head xml:id="echoid-head474" xml:space="preserve">C*APVT II.*</head>
          <head xml:id="echoid-head475" style="it" xml:space="preserve">Res motas impedimentis ſuis non eſſe propor-
            <lb/>
          tionales.</head>
          <p>
            <s xml:id="echoid-s4478" xml:space="preserve">IN Praxis Statices ad Lectorem præfatione diximus res motas ſuis impedi-
              <lb/>
            mentis non eſſe proportionales, ejusq́ue demonſtrationi hunc locum de-
              <lb/>
            ſtinavimus, ut argumenta aliter ſentientium refutemus. </s>
            <s xml:id="echoid-s4479" xml:space="preserve">Principiò Ariſtoteles
              <lb/>
            ejusq́ue ſectatores 4 Phyſic. </s>
            <s xml:id="echoid-s4480" xml:space="preserve">cap. </s>
            <s xml:id="echoid-s4481" xml:space="preserve">de inani exiſtimat corporibus duobus ſimili-
              <lb/>
            bus, & </s>
            <s xml:id="echoid-s4482" xml:space="preserve">materiâ æquipondiis per aërem delapſis eandem eſſe rationem ponde-
              <lb/>
            ris ad pondus quæ velocitatis illius ad velocitatem hujus, id eſt quæ ſit impe-
              <lb/>
            dimenti ad impedimentum. </s>
            <s xml:id="echoid-s4483" xml:space="preserve">Quam ſententiam variis locis clarius proponit, ut
              <lb/>
            6 Phyſic. </s>
            <s xml:id="echoid-s4484" xml:space="preserve">item 1, 2, 3 4 de Cælo, aliisq́ue compluribus. </s>
            <s xml:id="echoid-s4485" xml:space="preserve">ſententiam hanc Ioannes
              <lb/>
            Taiſnerus Hannonius oppugnavit, proportionem quidem hactenus admittens
              <lb/>
            ut corpora iſta æquali temporis ſpatio æqualia permeent intervallo. </s>
            <s xml:id="echoid-s4486" xml:space="preserve">Cui opi-
              <lb/>
            nioni Cardanus lib. </s>
            <s xml:id="echoid-s4487" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4488" xml:space="preserve">Proportion. </s>
            <s xml:id="echoid-s4489" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4490" xml:space="preserve">110. </s>
            <s xml:id="echoid-s4491" xml:space="preserve">conſentit. </s>
            <s xml:id="echoid-s4492" xml:space="preserve">Sed utroſque hallucinari
              <lb/>
            ipſa experientia demonſtrabimus, ac deinde ejus cauſam declarabimus. </s>
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