Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
[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.
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            <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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