Archimedes, Archimedis De insidentibvs aqvae

Table of contents

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[11.] Theorema v. Propoſitio v.
[12.] Theorema vj. Propoſitio vj.
[13.] Theorema vij. Propoſitio vij.
[14.] Suppoſitio ſecunda.
[15.] Theorema viij. Propoſitio viij.
[16.] AR CHIM EDIS DE INSIDENTIBVS AQV AE.
[17.] LIBER SECVNDVS. TROIANO CVRTIO VENETIIS, APVD TROIANVM CVRTIVM. M D L X V
[18.] FABRITIO DENORES FILIO IACOBI COMITIS TRIPOLIS CVRTIVS TROIANVS S. P. D.
[19.] INSIDENTIBVS AQV AE. LIB. II. PRIMVS.
[20.] SECVNDVS.
[21.] TERTIVS.
[22.] QVARTVS.
[23.] QVINTVS.
[24.] SEXTVS.
[25.] SEPTIMVS.
[26.] OCTAVVS.
[27.] NONVS.
[28.] DECIMVS.
[29.] Archimedis de inſidentibus in bumido li-ber ſecundus explicit, ad laudem Dei.
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            <s xml:id="echoid-s154" xml:space="preserve">
              <pb file="0014" n="14" rhead="DE INSIDENTIBVS AQV AE"/>
            tem ſuperficies quædam humidi alicuius quæ a, b, g, d, periferia. </s>
            <s xml:id="echoid-s155" xml:space="preserve">Quoniam
              <lb/>
            igitur tanta mole shumidi. </s>
            <s xml:id="echoid-s156" xml:space="preserve">quanta eſt magnitudo a, habet grauitatem æqua-
              <lb/>
            lem cum magnitudinibus a, d, palam quod demerſum ipſius erit magnitudo
              <lb/>
            a, reliquum' autem in quo d, erit totum deſuper ſupra ſuperficiem humidi. </s>
            <s xml:id="echoid-s157" xml:space="preserve">Si
              <lb/>
            enim. </s>
            <s xml:id="echoid-s158" xml:space="preserve">Palàm igitur quòd quanta uimagnitudo a, refertur ad ſuperius tan-
              <lb/>
            ta ab eo quod ſupraſ, d, premitur ad inferius quoniam neutra a neutra ex-
              <lb/>
            pellitur, ſed d, ad deorſum premit tanta grauitate quanta eſt g, ſupponeba-
              <lb/>
            tur enim grauitas eius, in quo g, d, eſſe æqualem ipſi g, palàm igitur quod
              <lb/>
            oportebat demonſtrare.</s>
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        <div xml:id="echoid-div17" type="section" level="1" n="13">
          <head xml:id="echoid-head19" xml:space="preserve">Theorema vij. Propoſitio vij.</head>
          <p>
            <s xml:id="echoid-s160" xml:space="preserve">Grauiora humido demiſſa in humidum ferrentur deorſum
              <lb/>
            donec deſcendant, & </s>
            <s xml:id="echoid-s161" xml:space="preserve">erunt leuiora in humido tantum, quantum
              <lb/>
            habet grauitas humidi habentis tantam molẽ, quanta eſt moles
              <lb/>
            ſolidæ magnitudinis.</s>
            <s xml:id="echoid-s162" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s163" xml:space="preserve">QVod quidem feretur in deorſum donec deſcendat, palàm partes e-
              <lb/>
            nim humidi, quæ ſubipſius premuntur magis, quæ partes ex quo ipſas
              <lb/>
            iacentes, quoniam ſolida magnitudo ſupponitur grauior humido.
              <lb/>
            </s>
            <s xml:id="echoid-s164" xml:space="preserve">Quod autem leuiora erunt, ut dictum est, demostrabitur. </s>
            <s xml:id="echoid-s165" xml:space="preserve">Sit enim aliqua ma
              <lb/>
            gnitudo, quæ a, quæ grauior humido, grauitas autem magnitudinis, quidem
              <lb/>
            in qua a, ſitq́ b, g, humidi autem habentis molẽ æqualem ipſi a, grauitas
              <lb/>
            b, demonſtrandum, quòd magnitudo a, in humido exiſtens habebit grauita-
              <lb/>
            tem æqualem ipſig, accipiatur enim aliqua alia magnitudo in quad, leuior
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            humido moli æqualis cum ipſo. </s>
            <s xml:id="echoid-s166" xml:space="preserve">Sit autcm magnitudinis quidem in quad, gra
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            uitas æqualis grauitatib, humidi autem habentis molẽ ęqualẽ magnitudini
              <lb/>
            d, grauitas ſit æqualis grauitatib, g. </s>
            <s xml:id="echoid-s167" xml:space="preserve">Compoſiti, autem
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                <image file="0014-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0014-01"/>
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            magnitudmibus in quibus, a, d, magnitudo ſimul utra-
              <lb/>
            rumq́ erit ęque grauis humido, grauitas enim magnitu-
              <lb/>
            dinum ſimul utrarumq; </s>
            <s xml:id="echoid-s168" xml:space="preserve">est æqualis ambabus grauitati
              <lb/>
            bus, ſcilicet b, g, & </s>
            <s xml:id="echoid-s169" xml:space="preserve">b, grauitas humidi buius habentis
              <lb/>
            molẽ æqualem ambabus magnitudinibus, eſt æqualis eiſ-
              <lb/>
            dem grauitatibus. </s>
            <s xml:id="echoid-s170" xml:space="preserve">Dimißis igitur magnitudinibus, & </s>
            <s xml:id="echoid-s171" xml:space="preserve">
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            proiectis in humidum æquerepentes erunt humido & </s>
            <s xml:id="echoid-s172" xml:space="preserve">
              <lb/>
            nec ad ſurſum ferentur, neque ad deorſum: </s>
            <s xml:id="echoid-s173" xml:space="preserve">quoniam
              <lb/>
            magnitudo quidem in qua a, exiſtens grauior humido
              <lb/>
            feretur ad deorſum, & </s>
            <s xml:id="echoid-s174" xml:space="preserve">tanta uia magnitudine in qua
              <lb/>
            d, retrabitur. </s>
            <s xml:id="echoid-s175" xml:space="preserve">Magnitudo autem, in qua d, quoniam eſt
              <lb/>
            leuior humido, eleuabitur ſurſum tanta ui quanta eſt grauitas g. </s>
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