Archimedes, Archimedis De insidentibvs aqvae

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            <s xml:id="echoid-s432" xml:space="preserve">
              <pb file="0030" n="30" rhead="DE INSIDENTIBVS AQVAE"/>
            K, recta ducatur ſuper p, f, erit autem minor, quæ r, ***, quàm e, a, quæ
              <lb/>
            uſque ad axem. </s>
            <s xml:id="echoid-s433" xml:space="preserve">Accipiatur igitur ei quæ uſque ad axem æqũas quæ
              <lb/>
            r, h, & </s>
            <s xml:id="echoid-s434" xml:space="preserve">quæ quidem c, o, ducatur contingens ſectiones penes o, exiſtens
              <lb/>
            _æquedistans_ ipſi a, s, & </s>
            <s xml:id="echoid-s435" xml:space="preserve">quæ n, o, & </s>
            <s xml:id="echoid-s436" xml:space="preserve">_æquedistans_ ipſi p, f. </s>
            <s xml:id="echoid-s437" xml:space="preserve">Secet autem
              <lb/>
            quæ n, o, ipſam K, ***, prius ſecundum i. </s>
            <s xml:id="echoid-s438" xml:space="preserve">Conſimiliter autem præcedenti
              <lb/>
            demõſtrabitur, quòd quæn, o, aut hemiolia eſt ipſius o, i, aut maior quàm
              <lb/>
            bemiolia, ſit autẽ, quæ o, t, ipſi t, n, minor, quàm dupla. </s>
            <s xml:id="echoid-s439" xml:space="preserve">Sit igitur quæ o,
              <lb/>
            b, dupla ipſius b, n, & </s>
            <s xml:id="echoid-s440" xml:space="preserve">diſponantur tandem prioribus. </s>
            <s xml:id="echoid-s441" xml:space="preserve">Similiter igitur de
              <lb/>
            monstrabitur, quæ r, f, faciens angulos rectos ad c, o, & </s>
            <s xml:id="echoid-s442" xml:space="preserve">ad ſuperficiem
              <lb/>
            humidi, & </s>
            <s xml:id="echoid-s443" xml:space="preserve">ab ipſis b, g, productæ æquedistanter ipſi r, f, erunt perpendi
              <lb/>
            culares ſuper ſuperficiem humidi. </s>
            <s xml:id="echoid-s444" xml:space="preserve">Portio igitur, quę quidem extra hu-
              <lb/>
            midum deorſum ferretur in humidum, ſecundum eam, quæ per b, perpen
              <lb/>
            dicularem. </s>
            <s xml:id="echoid-s445" xml:space="preserve">Quæ autem inter humidum ſurſum ferretur, ſecũdum eam,
              <lb/>
            quàm per g. </s>
            <s xml:id="echoid-s446" xml:space="preserve">Maximum igitur, quod ad uoluit ſolidum ita, ut baſis ip-
              <lb/>
            ſius, necſecundum vnum contingat ſuperficiem humidi, quoniam nunc,
              <lb/>
            ſecundum vnum tangens ad deorſum, ferret ex parte a. </s>
            <s xml:id="echoid-s447" xml:space="preserve">Manifestum
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            autem quòd & </s>
            <s xml:id="echoid-s448" xml:space="preserve">ſi quæ n, o, non ſecuerit ***, K, eandem demonſtrabũtur.</s>
            <s xml:id="echoid-s449" xml:space="preserve"/>
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        <div xml:id="echoid-div36" type="section" level="1" n="26">
          <head xml:id="echoid-head36" xml:space="preserve">OCTAVVS.</head>
          <p>
            <s xml:id="echoid-s450" xml:space="preserve">Recta portio rectanguli conoy dalis, quando axem habue
              <lb/>
            rit maiorem, quàm hemiolium eius, quæ uſque ad axem mi-
              <lb/>
            norem, autem ut ad eam, quæ ad axem habeat proportionẽ,
              <lb/>
            quam habet quindecim ad quatuor. </s>
            <s xml:id="echoid-s451" xml:space="preserve">Si grauis ad humidum
              <lb/>
            habeat proportionem minorem proportione, quam habet
              <lb/>
            tetragonum, quod ab ex ceſſu, quo axis eſt maior, quàm he-
              <lb/>
            miolius eius, quæ uſque ad axem ad tetragonum, quod ab
              <lb/>
            axe dimiſſa in humidum, it a ut baſis ipſius non tangat humi
              <lb/>
            dum, nec in rectum reſtituetur, nec manebit inclinata, niſi
              <lb/>
            quando axis ipſius ad ſuperficiem humidi fecerit angulum
              <lb/>
            æqualem ei qui dicendus eſt.</s>
            <s xml:id="echoid-s452" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s453" xml:space="preserve">_S_It portio qualis dicta est : </s>
            <s xml:id="echoid-s454" xml:space="preserve">& </s>
            <s xml:id="echoid-s455" xml:space="preserve">ſit quæ b, d,@ æquales axi, & </s>
            <s xml:id="echoid-s456" xml:space="preserve">quæ qui-
              <lb/>
            dem b, K, ſit duplaipſius k, d. </s>
            <s xml:id="echoid-s457" xml:space="preserve">Quæ autem r, k, æqualis ei, quæ uſ-
              <lb/>
            que ad axem. </s>
            <s xml:id="echoid-s458" xml:space="preserve">Sit autem, & </s>
            <s xml:id="echoid-s459" xml:space="preserve">quæ quidem e, b, hemiolia ipſius b, r.
              <lb/>
            </s>
            <s xml:id="echoid-s460" xml:space="preserve">Quam autem proportionem habet portio in grauitate ad bumidum hãc
              <lb/>
            quod a, b, f, q, tetragonum ad id, quod a, d, b. </s>
            <s xml:id="echoid-s461" xml:space="preserve">Sit autem, & </s>
            <s xml:id="echoid-s462" xml:space="preserve">quæ f, dupla
              <lb/>
            ipſius q, palam, igitur quòd quæ f, g, ad ipſam d, b, proportionem habet
              <lb/>
            minorem proportione, quàm habet, quæ t, b, ad ipſam b, d, exceſſus enim
              <lb/>
            quòdg, d, eſt quo axis eſt. </s>
            <s xml:id="echoid-s463" xml:space="preserve">maior, quàm bemiolius eius, quæuſque </s>
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