Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[71.] THEOREMA VI. PROPOSITIO VI.
[72.] THE OREMA VII. PROPOSITIO VII.
[73.] THE OREMA VIII. PROPOSITIO VIII.
[74.] THE OREMA IX. PROPOSITIO IX.
[75.] PROBLEMA I. PROPOSITIO X.
[76.] PROBLEMA II. PROPOSITIO XI.
[77.] PROBLEMA III. PROPOSITIO XII.
[78.] PROBLEMA IIII. PROPOSITIO XIII.
[79.] THEOREMA X. PROPOSITIO XIIII.
[80.] THE OREMA XI. PROPOSITIO XV.
[81.] THE OREMA XII. PROPOSITIO XVI.
[82.] THE OREMA XIII. PROPOSITIO XVII.
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
[84.] THEOREMA XV. PROPOSITIO XIX.
[85.] THE OREMA XVI. PROPOSITIO XX.
[86.] THEOREMA XVII. PROPOSITIO XXI.
[87.] THE OREMA XVIII. PROPOSITIO XXII.
[88.] THEOREMA XIX. PROPOSITIO XXIII.
[89.] PROBLEMA V. PROPOSITIO XXIIII.
[90.] THEOREMA XX. PROPOSITIO XXV.
[91.] THEOREMA XXI. PROPOSITIO XXVI.
[92.] THEOREMA XXII. PROPOSITIO XXVII.
[93.] PROBLEMA VI. PROPOSITIO XX VIII.
[94.] THE OREMA XXIII. PROPOSITIO XXIX.
[95.] THEOREMA XXIIII. PROPOSITIO XXX.
[96.] THEOREMA XXV. PROPOSITIO XXXI.
[97.] FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.
< >
page |< < (14) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div55" type="section" level="1" n="25">
          <p>
            <s xml:id="echoid-s791" xml:space="preserve">
              <pb o="14" file="0039" n="39" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ſeſquialter eius, quæ uſque ad axem, quanta eſt linea m o.
              <lb/>
            </s>
            <s xml:id="echoid-s792" xml:space="preserve">Ponebatur autem portio ad humidum æqualis molis non
              <lb/>
            minorem in grauitate proportionem habere, quam qua-
              <lb/>
            dratum, quod fit ab exceſſu, quo axis eſt maior, quam ſeſ-
              <lb/>
            quialter eius, quæ uſque ad axem, ad quadratum, quod ab
              <lb/>
            axe. </s>
            <s xml:id="echoid-s793" xml:space="preserve">quare conſtat portionem ad humidum in grauitate
              <lb/>
            non minorem proportionem habere, quàm quadratum li
              <lb/>
            neæ m o ad quadratum ipſius n o. </s>
            <s xml:id="echoid-s794" xml:space="preserve">Sed quam proportio-
              <lb/>
            nem habet portio ad humidum in grauitate, eandem por-
              <lb/>
            tio ipſius demerla habet ad totam portionem: </s>
            <s xml:id="echoid-s795" xml:space="preserve">hoc enim
              <lb/>
              <note position="right" xlink:label="note-0039-01" xlink:href="note-0039-01a" xml:space="preserve">C</note>
            ſupra demonſtratum eſt: </s>
            <s xml:id="echoid-s796" xml:space="preserve">& </s>
            <s xml:id="echoid-s797" xml:space="preserve">quam proportionem habet de
              <lb/>
              <note position="right" xlink:label="note-0039-02" xlink:href="note-0039-02a" xml:space="preserve">D</note>
            merſa portio ad totam, eam quadratum p f habet ad n o
              <lb/>
            quadratum: </s>
            <s xml:id="echoid-s798" xml:space="preserve">cum demonſtratum ſit in iis, quæ de conoidi
              <lb/>
            bus, & </s>
            <s xml:id="echoid-s799" xml:space="preserve">ſphæroidibus, ſi à rectangulo conoide duæ portio-
              <lb/>
            nes planis quomodocunque ductis abſcindantur, portio-
              <lb/>
            nes inter ſe eandem habere proportionem, qnàm quadra-
              <lb/>
            ta, quæ ab ipſorum axibus conſtituuntur. </s>
            <s xml:id="echoid-s800" xml:space="preserve">non minorem
              <lb/>
            ergo proportionẽ habet quadratum pf ad quadratũ n o,
              <lb/>
            quàm quadratum m o ad idem n o quadratum. </s>
            <s xml:id="echoid-s801" xml:space="preserve">quare
              <lb/>
              <note position="right" xlink:label="note-0039-03" xlink:href="note-0039-03a" xml:space="preserve">E</note>
            p f non eſt minor ipſa m o; </s>
            <s xml:id="echoid-s802" xml:space="preserve">nec b p item minor h o. </s>
            <s xml:id="echoid-s803" xml:space="preserve">Si
              <lb/>
              <note position="right" xlink:label="note-0039-04" xlink:href="note-0039-04a" xml:space="preserve">F</note>
            igitur ab h ducatur linea ad rectos angulos ipſi n o, coi-
              <lb/>
              <note position="right" xlink:label="note-0039-05" xlink:href="note-0039-05a" xml:space="preserve">G</note>
            bit cum b p, atque inter b, & </s>
            <s xml:id="echoid-s804" xml:space="preserve">p cadet. </s>
            <s xml:id="echoid-s805" xml:space="preserve">coeat in t. </s>
            <s xml:id="echoid-s806" xml:space="preserve">& </s>
            <s xml:id="echoid-s807" xml:space="preserve">quo
              <lb/>
              <note position="right" xlink:label="note-0039-06" xlink:href="note-0039-06a" xml:space="preserve">H</note>
            niam p f quidem æquidiſtans eſt diametro, h t autem ad
              <lb/>
            diametrum perpendicularis; </s>
            <s xml:id="echoid-s808" xml:space="preserve">& </s>
            <s xml:id="echoid-s809" xml:space="preserve">r h æqualis ei, quæ uſque
              <lb/>
            ad axem: </s>
            <s xml:id="echoid-s810" xml:space="preserve">ducta linea ab r ad t & </s>
            <s xml:id="echoid-s811" xml:space="preserve">producta angulos rectos
              <lb/>
            faciet cum linea ſectionem in puncto p contingente. </s>
            <s xml:id="echoid-s812" xml:space="preserve">qua-
              <lb/>
            re & </s>
            <s xml:id="echoid-s813" xml:space="preserve">cum is, & </s>
            <s xml:id="echoid-s814" xml:space="preserve">cum humidi ſuperficie, quæ per is tran-
              <lb/>
            ſit. </s>
            <s xml:id="echoid-s815" xml:space="preserve">Itaque ſi per b g puncta lineæ ipſi r t æquidiſtantes du
              <lb/>
            cantur, angulos rectos facient cum ſuperficie humidi: </s>
            <s xml:id="echoid-s816" xml:space="preserve">& </s>
            <s xml:id="echoid-s817" xml:space="preserve">
              <lb/>
            quod quidem in humido eſt ſolidum conoidis feretur ſur-
              <lb/>
            ſum ſecundum eam, quæ per b ducta fuerit ipſi r t æquidi
              <lb/>
            ſtans: </s>
            <s xml:id="echoid-s818" xml:space="preserve">quod autem extra humidum, ſecundum eam, quæ
              <lb/>
            per g deorſum feretur. </s>
            <s xml:id="echoid-s819" xml:space="preserve">atque hoc tandiu fiet, quoad co-
              <lb/>
            noides rectum conſtituatur.</s>
            <s xml:id="echoid-s820" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>