Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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        <div xml:id="echoid-div1166" type="section" level="1" n="381">
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            <s xml:id="echoid-s13630" xml:space="preserve">
              <pb o="410" file="0448" n="449" rhead="Archimedis"/>
            Veteri Libro Theoremata ſatis obſcura propter multitudinem errorum,
              <lb/>
            qui in eo ſunt, nec non menda, quæ occurrunt in figuris propter igno-
              <lb/>
            rantiam amanuenſium, erantque in co Doricæ dictiones, quarum vſus
              <lb/>
            Archimedi familiaris erat, & </s>
            <s xml:id="echoid-s13631" xml:space="preserve">vocabula ipſi propria; </s>
            <s xml:id="echoid-s13632" xml:space="preserve">hinc vtebatur loco
              <lb/>
            ſectionum parabolæ, & </s>
            <s xml:id="echoid-s13633" xml:space="preserve">hyperbolæ, rectanguli, & </s>
            <s xml:id="echoid-s13634" xml:space="preserve">obtuſanguli coni ſe-
              <lb/>
            ctionibus quamobrem operam ipſi nauaui, donec aſſecutus ſum iſtam
              <lb/>
            propoſitionem, & </s>
            <s xml:id="echoid-s13635" xml:space="preserve">eſt iſta, &</s>
            <s xml:id="echoid-s13636" xml:space="preserve">c.</s>
            <s xml:id="echoid-s13637" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13638" xml:space="preserve">Modo quia in prædicto libro antiquo ab Eutocio reperto recenſentur duæ pro-
              <lb/>
            poſitiones, quarum vnam promiſerat ſe demonſtraturum Archimedes, & </s>
            <s xml:id="echoid-s13639" xml:space="preserve">vtra-
              <lb/>
            que in noſtro opuſculo iniuria temporum deficit: </s>
            <s xml:id="echoid-s13640" xml:space="preserve">earum altera forſan erit 16.
              <lb/>
            </s>
            <s xml:id="echoid-s13641" xml:space="preserve">illa propoſitio in proemio ab Almochtaßo numerata vbi ait propoſitiones huius
              <lb/>
            opuſculi ſexdecim eſſe, cum tamen poſtrema ſit 15. </s>
            <s xml:id="echoid-s13642" xml:space="preserve">quare inutile forſan non
              <lb/>
            erit eas hic reponere, præcipuè quia Eutocius non rite eas reſtituit, nec omninò
              <lb/>
            repurgauit à mendis, quibus ſcatebat exemplar antiquum ab ipſo inuentum. </s>
            <s xml:id="echoid-s13643" xml:space="preserve">Et
              <lb/>
            primo noto, quod Eutocius eas vocat theoremata, cum potius problemata ſint, & </s>
            <s xml:id="echoid-s13644" xml:space="preserve">
              <lb/>
            ſic etiam ab eodem Eutocio poſtmodum appellantur. </s>
            <s xml:id="echoid-s13645" xml:space="preserve">Forſan hoc accidit, quia
              <lb/>
            in libro illo antiquo in formam theorematum ſcripta erant, ſed Eutocius vt ad
              <lb/>
            propoſitionem Archimedis ea accomodaret, forma problematica ea expoſuit. </s>
            <s xml:id="echoid-s13646" xml:space="preserve">
              <lb/>
            Rurſus Eutocius primum theorema ſe expoſiturum pollicetur, vt deinde analyſi
              <lb/>
            problematis Archimedei accomodetur. </s>
            <s xml:id="echoid-s13647" xml:space="preserve">Vnde conijcere licet alterum theorema
              <lb/>
            additum, vel alteratum ab Eutocio, vel ab aliquo alio fuiſſe, in quo proponit,
              <lb/>
            quod, ſi aliqua recta linea ſecta ſit in duo ſegmenta, quorum vnum duplum
              <lb/>
            ſit alterius, ſolidum parallelepipedum rectangulum contentum ſub quadrato ma-
              <lb/>
            ioris, & </s>
            <s xml:id="echoid-s13648" xml:space="preserve">ſub minore ſegmento maximum erit omnium ſimilium ſolidorum, quæ
              <lb/>
            ex diuiſione eiuſdem rectæ lineæ in quolibet alio eius puncto conſurgunt. </s>
            <s xml:id="echoid-s13649" xml:space="preserve">Et
              <lb/>
            hoc quidem oſtenditur per ſectiones conicas, contra artis præcepta; </s>
            <s xml:id="echoid-s13650" xml:space="preserve">peccatum
              <lb/>
            enim eſt non paruum apud Geometras, problema planum per conicas ſectiones
              <lb/>
            reſoluere cum via plana abſolui poſſit, hoc autem preclari nonnulli viri pariter
              <lb/>
            adnotarunt, & </s>
            <s xml:id="echoid-s13651" xml:space="preserve">præſtiterunt, vt nuper accepi.</s>
            <s xml:id="echoid-s13652" xml:space="preserve"/>
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          <head xml:id="echoid-head474" xml:space="preserve">PROPOSITIO XVI.</head>
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            <s xml:id="echoid-s13653" xml:space="preserve">SI recta linea A B ſit tripla A C, non vero tripla ipſius A
              <lb/>
            D; </s>
            <s xml:id="echoid-s13654" xml:space="preserve">Dico parallelepipedum rectangulũ contentum ſub qua-
              <lb/>
            drato C B in A C maius eſſe parallelepipedo ſub quadrato D
              <lb/>
            B in A D.</s>
            <s xml:id="echoid-s13655" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13656" xml:space="preserve">Producatur A B in E, vt ſit B E æqualis B C. </s>
            <s xml:id="echoid-s13657" xml:space="preserve">Quoniam B C dupla
              <lb/>
            erat ipſius A C, erit E C quadrupla ipſius A C, & </s>
            <s xml:id="echoid-s13658" xml:space="preserve">propterea rectan-
              <lb/>
            gulum A C E æquale erit quadruplo quadrati A C, ſcilicet æquale erit
              <lb/>
            quadrato C B: </s>
            <s xml:id="echoid-s13659" xml:space="preserve">Eſt vero in primo caſu, rectangulum A D E maius re-
              <lb/>
            ctangulo A C E, in ſecundo vero minus, (eo quod punctum D in pri-
              <lb/>
            mo caſu propinquius eſt ſemipartitioni totius A E, quàm C, in ſecuudo
              <lb/>
            verò remotius); </s>
            <s xml:id="echoid-s13660" xml:space="preserve">igitur ſi fiat C D ad D O, vt quadratum C B ad </s>
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