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="409" file="0447" n="448" rhead="Aſſumpt. Liber."/>
            recta linea E G ſecatur in A extrema, ac media ratione, cuius maius ſegmen-
              <lb/>
            tum eſt E A latus decagoni, & </s>
            <s xml:id="echoid-s13598" xml:space="preserve">recta A H ſimiliter diuiditur in G, cuius ma-
              <lb/>
            ius ſegmentum eſt G H decagoni latus, & </s>
            <s xml:id="echoid-s13599" xml:space="preserve">tota E H ſecatur in A, & </s>
            <s xml:id="echoid-s13600" xml:space="preserve">G ex-
              <lb/>
            trema, ac media ratione, pariterque recta E B ſimiliter ſecatur in H, cuius
              <lb/>
              <figure xlink:label="fig-0447-01" xlink:href="fig-0447-01a" number="523">
                <image file="0447-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0447-01"/>
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            minus ſegmentum H B eſt æquale lateri exagoni circulo inſcripti. </s>
            <s xml:id="echoid-s13601" xml:space="preserve">Breuius ta-
              <lb/>
            men propoſitio ſic demonſtrari poſſet.</s>
            <s xml:id="echoid-s13602" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13603" xml:space="preserve">Quia oſtenſa eſt C D æqualis D G, & </s>
            <s xml:id="echoid-s13604" xml:space="preserve">A D æqualis eſt eidem D C; </s>
            <s xml:id="echoid-s13605" xml:space="preserve">cum
              <lb/>
            ambo ſint latera decagoni, ergo D G æqualis eſt D A. </s>
            <s xml:id="echoid-s13606" xml:space="preserve">Poſtea iuncta A C, quid
              <lb/>
            angulus A H D, vel C H D quinta pars eſt duorum rectorum, ergo angulus
              <lb/>
            C D H ad baſim iſoſcelij, duæ quintæ partes erit duorum rectorum, & </s>
            <s xml:id="echoid-s13607" xml:space="preserve">ideo an-
              <lb/>
            gulus C D H duplus erit anguli D H E, eſtque externus angulus C D H æqua-
              <lb/>
            lis duobus internis, & </s>
            <s xml:id="echoid-s13608" xml:space="preserve">oppoſitis D H E, & </s>
            <s xml:id="echoid-s13609" xml:space="preserve">D E H in triangulo D E H, ergo
              <lb/>
            angulus C D H duplus quoque erit reliqui anguli E, & </s>
            <s xml:id="echoid-s13610" xml:space="preserve">propterea angulus D
              <lb/>
            H E æqualis erit angulo E, & </s>
            <s xml:id="echoid-s13611" xml:space="preserve">ſubtenſa latera D E, D H æqualia quoque erunt,
              <lb/>
            ſed prius D A, D G æqualia erant ſubtendentia angulos æquales, & </s>
            <s xml:id="echoid-s13612" xml:space="preserve">reliqui
              <lb/>
            anguli eiuſdem ſpeciei ſunt, igitur E A æqualis eſt H G. </s>
            <s xml:id="echoid-s13613" xml:space="preserve">Reliqua manifeſta
              <lb/>
            ſunt.</s>
            <s xml:id="echoid-s13614" xml:space="preserve"/>
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            <s xml:id="echoid-s13615" xml:space="preserve">In præfatione huius operis memini non eße omnino improbabile hunc libellum
              <lb/>
            Archimedis non alium fuiſſe ab illo antiquo lemmatum libro ab Eutocio reper-
              <lb/>
            to, quod præcipuè ex verbis eiuſdem Eutocij in Comment. </s>
            <s xml:id="echoid-s13616" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s13617" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13618" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13619" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13620" xml:space="preserve">de
              <lb/>
            Sphæra, & </s>
            <s xml:id="echoid-s13621" xml:space="preserve">Cylindro comprobatum fuit: </s>
            <s xml:id="echoid-s13622" xml:space="preserve">illa fideliſſimè translata ex textu Græco ab
              <lb/>
            amicis doctiſſimis cum iam in præfatione excuſa eßent aliam tranſlationem ex
              <lb/>
            Arabico Manuſcripto Sereniſſimi Magni Ducis miſit Excell. </s>
            <s xml:id="echoid-s13623" xml:space="preserve">Abrahamus Ecchel-
              <lb/>
            lenſis deſumptam ex editione Abuſahli Alkuhi qui pariter librum ordinatio-
              <lb/>
            nis lemmatum Archimedis conſcripſit, vt in proemio huius operis teſtatur
              <lb/>
            Almochtaſſo. </s>
            <s xml:id="echoid-s13624" xml:space="preserve">Verba eius ſunt hæc, quæ paulo clarius propoſitum confirmare vi-
              <lb/>
            dentur: </s>
            <s xml:id="echoid-s13625" xml:space="preserve">& </s>
            <s xml:id="echoid-s13626" xml:space="preserve">meminit Eutocius Aſcalonita in Comment. </s>
            <s xml:id="echoid-s13627" xml:space="preserve">huius libri, quod
              <lb/>
            Archimedes promiſerit demonſtrationem huius in hoc ſuo libro, quod
              <lb/>
            in nullo exemplari reperitur, quod promiſit. </s>
            <s xml:id="echoid-s13628" xml:space="preserve">Atque ita vnuſquiſque tam
              <lb/>
            Dyoniſodorus, quàm Diocles poſt illum progreſſus eſt per aliam viam,
              <lb/>
            quàm ille (ſcilicet Archimedes) in hoc libro in diuiſione Sphæræ in
              <lb/>
            duas partes, quæ datam habeant proportionem. </s>
            <s xml:id="echoid-s13629" xml:space="preserve">Dixit, & </s>
            <s xml:id="echoid-s13630" xml:space="preserve">ego reperi </s>
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