Archimedes, Archimedis De insidentibvs aqvae

Table of contents

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[21.] TERTIVS.
Page: 23 (4)
[22.] QVARTVS.
Page: 24
[23.] QVINTVS.
Page: 25 (5)
[24.] SEXTVS.
Page: 27 (6)
[25.] SEPTIMVS.
Page: 29 (7)
[26.] OCTAVVS.
Page: 30
[27.] NONVS.
Page: 33 (9)
[28.] DECIMVS.
Page: 36
[29.] Archimedis de inſidentibus in bumido li-ber ſecundus explicit, ad laudem Dei.
Page: 47 (16)
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            <s xml:id="echoid-s358" xml:space="preserve">
              <pb o="6" file="0027" n="27" rhead="LIBER II."/>
            proportionem quam habet tetragonum, quod ab n, o, ad id quod a, p, f,
              <lb/>
            non maiorem ergo proportionem habet, quæ ab n, o, ad id a, p, f, quàm
              <lb/>
            quòd ab n, o, ad id, quod ab m, o, non minor ergo fit, quæ p, f, quàm quæ
              <lb/>
            o, m, quare nec quæ p, b, quàm n, o. </s>
            <s xml:id="echoid-s359" xml:space="preserve">Quæ ergo ab m, producitur ipſi r, o,
              <lb/>
            æquidiſtans concidet ipſi b, p, intra p, & </s>
            <s xml:id="echoid-s360" xml:space="preserve">b, concidat ſecundum t, & </s>
            <s xml:id="echoid-s361" xml:space="preserve">quo
              <lb/>
            niam in rectanguli coni, Sectione quæ p, f, eſt æquidiſtanter dyametto r,
              <lb/>
            o. </s>
            <s xml:id="echoid-s362" xml:space="preserve">Quæ autem n, t, perpendicularis ſuper dyametrum, quæ autem r, m,
              <lb/>
            æqualis ei quæ uſque ad axem. </s>
            <s xml:id="echoid-s363" xml:space="preserve">Palam quòd quæ r, t, educta facit angu-
              <lb/>
            los rectos ad K, p, ***, quare & </s>
            <s xml:id="echoid-s364" xml:space="preserve">ad i, s. </s>
            <s xml:id="echoid-s365" xml:space="preserve">Quæ ergo r, t, eſt perpendicula-
              <lb/>
            ris ad ſuperficiem humidi, & </s>
            <s xml:id="echoid-s366" xml:space="preserve">per ſigna b, g, æquediſtanter ipſi r, t, produ
              <lb/>
            ctæ erunt perpendiculares ad ſuperficiem bumidi: </s>
            <s xml:id="echoid-s367" xml:space="preserve">quæ quidem igitur ex
              <lb/>
            tra humidum portio deorſum ferretur in humidum ſecundum producta
              <lb/>
            per b, perpendicularem. </s>
            <s xml:id="echoid-s368" xml:space="preserve">Quæ autem intra humidum ſurſum ferretur ſe
              <lb/>
            cundum perpendicularem, quæ per g, & </s>
            <s xml:id="echoid-s369" xml:space="preserve">non manet ſolida portio apol.
              <lb/>
            </s>
            <s xml:id="echoid-s370" xml:space="preserve">ſed intra humidum erit in motum, donec utique quæ n, o, fiat ſecundum
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            perpendicularem.</s>
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          <head xml:id="echoid-head34" xml:space="preserve">SEXTVS.</head>
          <p>
            <s xml:id="echoid-s372" xml:space="preserve">Recta portio rectanguli conoydalis quando humido le-
              <lb/>
            uior exiſtens axem habuerit maiorem quidem quam hemio
              <lb/>
            lium minorem autem quam ut habet hãc proportionem ad
              <lb/>
            eam, quæ uſque ad axem quam habent quindecim ad quat-
              <lb/>
            tuor dimiſſa in humidum ita, ut baſis ipſius contingat humi-
              <lb/>
            dum, nunquam ſtabit inclinata ita, ut baſis ipſius ſecundum
              <lb/>
            vnum ſignum conting at humidum</s>
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            <s xml:id="echoid-s373" xml:space="preserve">_S_It portio qualis dicta eſt, & </s>
            <s xml:id="echoid-s374" xml:space="preserve">dimiſſa in humidum conſiſtat, ſicut ſtẽ
              <lb/>
            ſum eſt : </s>
            <s xml:id="echoid-s375" xml:space="preserve">ita ut baſis ipſius ſecundum vnum ſignum contingat hu-
              <lb/>
            midum. </s>
            <s xml:id="echoid-s376" xml:space="preserve">Secta autem ipſa per axem plano recto ad ſuperficiem hu
              <lb/>
            midi: </s>
            <s xml:id="echoid-s377" xml:space="preserve">ſectio ſuperficiei portionis ſit, quæ apol. </s>
            <s xml:id="echoid-s378" xml:space="preserve">rectanguli coni ſectio : </s>
            <s xml:id="echoid-s379" xml:space="preserve">ſu
              <lb/>
            perficiei autem humidi quæ a, s, axis autem portionis, & </s>
            <s xml:id="echoid-s380" xml:space="preserve">dyameter ſit
              <lb/>
            quæ n, o, & </s>
            <s xml:id="echoid-s381" xml:space="preserve">ſecetur ſecundum f, quidem ita quæ o, f, ſit quæ dupla ipſius
              <lb/>
            f, n, ſecundum ***, autem ita, ut quæ n, o, ad f, ***, habe at proportionem
              <lb/>
            quam quindecim ad quattuor, & </s>
            <s xml:id="echoid-s382" xml:space="preserve">ipſi n, o, adducatur quæ ***, K. </s>
            <s xml:id="echoid-s383" xml:space="preserve">Quæ
              <lb/>
            autem n, o, maiorem proportionẽ habet ad f, ***, quàm ad ea, ꝗ̃ uſq; </s>
            <s xml:id="echoid-s384" xml:space="preserve">ad
              <lb/>
            axem. </s>
            <s xml:id="echoid-s385" xml:space="preserve">Sit quæ f, b, æqualis ei, quæ uſque ad axem, & </s>
            <s xml:id="echoid-s386" xml:space="preserve">ducatur quæ qui-
              <lb/>
            dem p, c, æquediſtanter ipſi a s contingens, ſectionem. </s>
            <s xml:id="echoid-s387" xml:space="preserve">apol. </s>
            <s xml:id="echoid-s388" xml:space="preserve">ſecundum p.
              <lb/>
            </s>
            <s xml:id="echoid-s389" xml:space="preserve">Quæ autem p, i, æquediſtanter ipſi n, o, Secet autem quæ p, i, prius ipſam
              <lb/>
            K, ***. </s>
            <s xml:id="echoid-s390" xml:space="preserve">Quoniam igitur in portione apol contenta a recta, & </s>
            <s xml:id="echoid-s391" xml:space="preserve"/>
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