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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          <pb o="151" file="0189" n="189" rhead="Conicor. Lib. VI."/>
          <p style="it">
            <s xml:id="echoid-s5926" xml:space="preserve">In ſestione A B C ducatur ramus breuiſe-
              <lb/>
              <figure xlink:label="fig-0189-01" xlink:href="fig-0189-01a" number="202">
                <image file="0189-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0189-01"/>
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            cans ſingularis I L ſecans axem in G, ſitque
              <lb/>
              <note position="right" xlink:label="note-0189-01" xlink:href="note-0189-01a" xml:space="preserve">51. 52. 53.
                <lb/>
              lib. 5,</note>
            I punctum concur ſus perpendicularis I K, & </s>
            <s xml:id="echoid-s5927" xml:space="preserve">
              <lb/>
            breuiſecantis; </s>
            <s xml:id="echoid-s5928" xml:space="preserve">& </s>
            <s xml:id="echoid-s5929" xml:space="preserve">à quolibet puncto B inter
              <lb/>
            L, & </s>
            <s xml:id="echoid-s5930" xml:space="preserve">verticem A ducatur alius ramus bre-
              <lb/>
            uiſecans B M, qui occurret L I vltra axim
              <lb/>
            in M, & </s>
            <s xml:id="echoid-s5931" xml:space="preserve">inter puncta G, & </s>
            <s xml:id="echoid-s5932" xml:space="preserve">I; </s>
            <s xml:id="echoid-s5933" xml:space="preserve">coniungatur-
              <lb/>
              <note position="right" xlink:label="note-0189-02" xlink:href="note-0189-02a" xml:space="preserve">28. lib. 5.
                <lb/>
              8. Addir.
                <lb/>
              lib. 5.</note>
            que recta linea B 1. </s>
            <s xml:id="echoid-s5934" xml:space="preserve">Quoniam angulus L G A acutus eſt, erit angnlus G M N
              <lb/>
            internus, & </s>
            <s xml:id="echoid-s5935" xml:space="preserve">oppoſitus in triangulo G M N minor illò, & </s>
            <s xml:id="echoid-s5936" xml:space="preserve">ideo acutus, & </s>
            <s xml:id="echoid-s5937" xml:space="preserve">pro-
              <lb/>
              <note position="right" xlink:label="note-0189-03" xlink:href="note-0189-03a" xml:space="preserve">13. 14. 15.
                <lb/>
              lib. 5.</note>
            pterea qui deinceps eſt angulus B M I erit obtuſus, & </s>
            <s xml:id="echoid-s5938" xml:space="preserve">ideo in triangulo I B M
              <lb/>
            latus I B ſubtendens maximum angulum obtuſum maius erit latera B M; </s>
            <s xml:id="echoid-s5939" xml:space="preserve">ſedra-
              <lb/>
            mus I L maior eſt, quàm I B, propterea quod remotior eſt à vertice A, igitur
              <lb/>
              <note position="right" xlink:label="note-0189-04" xlink:href="note-0189-04a" xml:space="preserve">67. lib. 5.</note>
            ramus I L maior erit, quàm B M: </s>
            <s xml:id="echoid-s5940" xml:space="preserve">Secari ergo poterunt æquales rectæ lineæ L R,
              <lb/>
            B S, quæ ſint minores quidẽ, quàm I L, ſed maiores, quàm M B; </s>
            <s xml:id="echoid-s5941" xml:space="preserve">& </s>
            <s xml:id="echoid-s5942" xml:space="preserve">deſcribantur
              <lb/>
            duo circuli, quorum radij ſint S B, & </s>
            <s xml:id="echoid-s5943" xml:space="preserve">R L æquales, atque centra ſint S, & </s>
            <s xml:id="echoid-s5944" xml:space="preserve">R;
              <lb/>
            </s>
            <s xml:id="echoid-s5945" xml:space="preserve">
              <note position="right" xlink:label="note-0189-05" xlink:href="note-0189-05a" xml:space="preserve">Ex 12.
                <lb/>
              Addit.
                <lb/>
              lib. 5.</note>
            Manifeſtum eſt circulum, cuius radius B S contingere coniſectionem A C in
              <lb/>
            puncto B, & </s>
            <s xml:id="echoid-s5946" xml:space="preserve">extrinſecùs incedere, propterea quod radius B S maior eſt maximo
              <lb/>
            breuiſecantium M B à concurſu M educto; </s>
            <s xml:id="echoid-s5947" xml:space="preserve">è contra circulus radio R L deſcri-
              <lb/>
              <note position="right" xlink:label="note-0189-06" xlink:href="note-0189-06a" xml:space="preserve">8. Addit.
                <lb/>
              lib. 5.
                <lb/>
              Ibidem.</note>
            ptus intrinſecùs continget eandem coniſectionem in L cum ramus M L minor ſit
              <lb/>
            ſingulari breuiſecante L I. </s>
            <s xml:id="echoid-s5948" xml:space="preserve">Tandẽ in ſectione D E F ſecetur axis abſcißa D H
              <lb/>
            æqualis A N, & </s>
            <s xml:id="echoid-s5949" xml:space="preserve">in angulo D H P æquali angulo A N B ducatur radius γ H P,
              <lb/>
            qui fiat æqualis S B, & </s>
            <s xml:id="echoid-s5950" xml:space="preserve">cẽtro γ radio verò γ P circulus deſcribatur. </s>
            <s xml:id="echoid-s5951" xml:space="preserve">Et quia in
              <lb/>
            ſectionibus æqualibus abſciſſæ, breuiſecantes, anguli ab eis contenti, & </s>
            <s xml:id="echoid-s5952" xml:space="preserve">circu-
              <lb/>
            li deſcripti ſunt æquales, & </s>
            <s xml:id="echoid-s5953" xml:space="preserve">congruentes; </s>
            <s xml:id="echoid-s5954" xml:space="preserve">igitur circulus radio γ P deſcriptus,
              <lb/>
            contingit coniſectionem D E F extrinſecùs; </s>
            <s xml:id="echoid-s5955" xml:space="preserve">ſicuti circulus radij S B tangebat
              <lb/>
            ſectionem A B C in B extrinſecùs. </s>
            <s xml:id="echoid-s5956" xml:space="preserve">Vterat propoſitum.</s>
            <s xml:id="echoid-s5957" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5958" xml:space="preserve">Hoc demonſtrat o oſtendetur, quod in duabus coniſectionibus A B C,
              <lb/>
              <note position="right" xlink:label="note-0189-07" xlink:href="note-0189-07a" xml:space="preserve">PROP. 1.
                <lb/>
              Addit.</note>
            D E F æqualibus, quarum axes A G, D H duæ portiones B C, & </s>
            <s xml:id="echoid-s5959" xml:space="preserve">
              <lb/>
            E F non æquè ab axium verticibus remotæ non erunt ſibi congruentes.</s>
            <s xml:id="echoid-s5960" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5961" xml:space="preserve">Si enim poſſibile eſt B C, & </s>
            <s xml:id="echoid-s5962" xml:space="preserve">E F ſibi mutuò congruant, & </s>
            <s xml:id="echoid-s5963" xml:space="preserve">ſumatur interme-
              <lb/>
            dium punctum commune, vel duo puncta coincidentia L, & </s>
            <s xml:id="echoid-s5964" xml:space="preserve">P, & </s>
            <s xml:id="echoid-s5965" xml:space="preserve">quia portio-
              <lb/>
            nes B C, E F inæqualiter diſtant à verticibus, ergo puncta coincidentia L, P
              <lb/>
            non erunt æquè à verticibus remota; </s>
            <s xml:id="echoid-s5966" xml:space="preserve">ſit ergo P propinquius vertici D, quàm eſt
              <lb/>
            L vertici A, & </s>
            <s xml:id="echoid-s5967" xml:space="preserve">per L, & </s>
            <s xml:id="echoid-s5968" xml:space="preserve">P ducantur rectæ
              <lb/>
              <figure xlink:label="fig-0189-02" xlink:href="fig-0189-02a" number="203">
                <image file="0189-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0189-02"/>
              </figure>
            lineæ L O, P Q tangentes ſectiones, & </s>
            <s xml:id="echoid-s5969" xml:space="preserve">ex lẽ-
              <lb/>
              <note position="right" xlink:label="note-0189-08" xlink:href="note-0189-08a" xml:space="preserve">33. 34.
                <lb/>
              lib. 1.</note>
            matæ præcedenti deſcribantur duo circuli æ-
              <lb/>
            quales Z P T, & </s>
            <s xml:id="echoid-s5970" xml:space="preserve">V L X radijs I L & </s>
            <s xml:id="echoid-s5971" xml:space="preserve">S
              <lb/>
            P, quorum Z T extrinſecus tangat ſectionẽ
              <lb/>
            in P, & </s>
            <s xml:id="echoid-s5972" xml:space="preserve">V X intrinſecus in L, cumque eo-
              <lb/>
            rum radij I L, S P ſint breuiſecantes, erunt
              <lb/>
            perpendiculares ad L O, P Q contingentes
              <lb/>
              <note position="right" xlink:label="note-0189-09" xlink:href="note-0189-09a" xml:space="preserve">29. 30.
                <lb/>
              lib. 5.</note>
            ſectionem in L, & </s>
            <s xml:id="echoid-s5973" xml:space="preserve">P; </s>
            <s xml:id="echoid-s5974" xml:space="preserve">atque portiones B C, E F ſibi mutuò congruunt, ideſt
              <lb/>
              <note position="right" xlink:label="note-0189-10" xlink:href="note-0189-10a" xml:space="preserve">35. 36.
                <lb/>
              lib. 1.</note>
            conſtituunt vnicam communem peripheriam, ergo rectæ lineæ L O, P Q
              <lb/>
            contingentes eandem ſectionem ſibi mutuò congruent, pariterque breuiſe-
              <lb/>
            cantes æquales L I, P M ad illas perpendiculariter inſiſtentes crunt congruentes
              <lb/>
            quoque; </s>
            <s xml:id="echoid-s5975" xml:space="preserve">& </s>
            <s xml:id="echoid-s5976" xml:space="preserve">propterea circuli V X, Z T ab ijs radijs geniti erunt quoque </s>
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