Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <p>
            <s xml:id="echoid-s1239" xml:space="preserve">
              <pb file="0054" n="54" rhead="ARCHIMEDIS"/>
            modo hum idi ſuperficiem continget.</s>
            <s xml:id="echoid-s1240" xml:space="preserve">] _In translatione le-_
              <lb/>
            _gebatur ut baſis ipſius non tangat ſuperficiem humidi ſecundum_
              <lb/>
            _unum ſignum. </s>
            <s xml:id="echoid-s1241" xml:space="preserve">nos autem ita uertere maluimus, & </s>
            <s xml:id="echoid-s1242" xml:space="preserve">hic & </s>
            <s xml:id="echoid-s1243" xml:space="preserve">in ijs,_
              <lb/>
            _quæ ſequuntur, quoniam græci οὐδὲ \~εις, οὐδὲ ἓν, pro οὐ δεὶς, &_</s>
            <s xml:id="echoid-s1244" xml:space="preserve">
              <lb/>
            _οὐδε ν frequenter utútur. </s>
            <s xml:id="echoid-s1245" xml:space="preserve">ut οὐδ ε ςιν οὐ δεὶς, nullus eſt: </s>
            <s xml:id="echoid-s1246" xml:space="preserve">οὐ \’δ ὑφ
              <unsure/>
            ἑ νὸς,_
              <lb/>
            _ànullo & </s>
            <s xml:id="echoid-s1247" xml:space="preserve">alia eiuſmodi._</s>
            <s xml:id="echoid-s1248" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div89" type="section" level="1" n="35">
          <head xml:id="echoid-head40" xml:space="preserve">PROPOSITIO VII.</head>
          <p>
            <s xml:id="echoid-s1249" xml:space="preserve">
              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            leuior humido axem habuerit maiorem quidem
              <lb/>
            quàm ſeſquialtérum eius, quæ uſque ad axem;
              <lb/>
            </s>
            <s xml:id="echoid-s1250" xml:space="preserve">minorem uero, quàm ut ad eam, quæ uſque ad
              <lb/>
            axem proportionem habeat, quam quindecim
              <lb/>
            ad quatuor: </s>
            <s xml:id="echoid-s1251" xml:space="preserve">in humidum demiſſa, adeo ut baſis
              <lb/>
            ipſius tota ſitin humido; </s>
            <s xml:id="echoid-s1252" xml:space="preserve">nunquam conſiſtet ita,
              <lb/>
            ut baſis contingat humidi ſuperficiem: </s>
            <s xml:id="echoid-s1253" xml:space="preserve">ſed ut to-
              <lb/>
            ta in humido ſit, & </s>
            <s xml:id="echoid-s1254" xml:space="preserve">nullo modo eius ſuperficiem
              <lb/>
            contingat.</s>
            <s xml:id="echoid-s1255" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1256" xml:space="preserve">SIT portio qualis dicta eſt: </s>
            <s xml:id="echoid-s1257" xml:space="preserve">& </s>
            <s xml:id="echoid-s1258" xml:space="preserve">demittatur in humidũ,
              <lb/>
            ut diximus, adeo ut baſis ipſius in uno puncto contingat
              <lb/>
            humidi ſuperficiem. </s>
            <s xml:id="echoid-s1259" xml:space="preserve">Demonſtrandum eſt non manere ip-
              <lb/>
            ſam: </s>
            <s xml:id="echoid-s1260" xml:space="preserve">ſed reuolui ita ut baſis fuperficiem humidi nullo mo-
              <lb/>
            do contingat. </s>
            <s xml:id="echoid-s1261" xml:space="preserve">Secta enim ipſa plano per axem, recto ad ſu
              <lb/>
            perficiem humidi, ſectio ſit a p o l rectanguli coni ſectio:
              <lb/>
            </s>
            <s xml:id="echoid-s1262" xml:space="preserve">ſuperficiei humidi ſectio ſit s 1: </s>
            <s xml:id="echoid-s1263" xml:space="preserve">axis portionis, & </s>
            <s xml:id="echoid-s1264" xml:space="preserve">ſectio-
              <lb/>
            nis diameter p f: </s>
            <s xml:id="echoid-s1265" xml:space="preserve">ſeceturq; </s>
            <s xml:id="echoid-s1266" xml:space="preserve">p f in r quidem ita ut r p ſit
              <lb/>
            dupla ipſius r f; </s>
            <s xml:id="echoid-s1267" xml:space="preserve">in ω autem ut p f ad r ω proportionem
              <lb/>
            habeat, quam quindecim ad quatuor: </s>
            <s xml:id="echoid-s1268" xml:space="preserve">& </s>
            <s xml:id="echoid-s1269" xml:space="preserve">ω k ipſi p f ad re-
              <lb/>
            ctos angulos ducatur erit r ω minor, quàm quæ uſque ad
              <lb/>
            axem. </s>
            <s xml:id="echoid-s1270" xml:space="preserve">Itaque accipiatur ei, quæ uſque ad axem æqualis rh:</s>
            <s xml:id="echoid-s1271" xml:space="preserve"/>
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