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="136" file="0174" n="174" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s5313" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s5314" xml:space="preserve">Et ſi in eodem ſegmento ducantur or-
              <lb/>
              <figure xlink:label="fig-0174-01" xlink:href="fig-0174-01a" number="172">
                <image file="0174-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0174-01"/>
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            dinatæ parallelæ baſi B C, atque recta linea
              <lb/>
            A M ſecet omnes æquidiſtantes ipſi B C bifa-
              <lb/>
            riam in punctis M, N, & </s>
            <s xml:id="echoid-s5315" xml:space="preserve">O vocabitur A M:
              <lb/>
            </s>
            <s xml:id="echoid-s5316" xml:space="preserve">Diameter eiuſdem ſegmenti.</s>
            <s xml:id="echoid-s5317" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5318" xml:space="preserve">V. </s>
            <s xml:id="echoid-s5319" xml:space="preserve">Et terminus eiuſdem diametri A ad
              <lb/>
            ſectionem poſitus, vocatur Vertex ſegmenti.</s>
            <s xml:id="echoid-s5320" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5321" xml:space="preserve">Tres prædictæ definitiones ſuperadditæ ab
              <lb/>
            interprete Arabico fuerunt, vt ego puto, quandoquidem omnino neceſſariæ non
              <lb/>
            ſunt.</s>
            <s xml:id="echoid-s5322" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5323" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s5324" xml:space="preserve">Sicuti in prima definitione ſectiones ſibi mutuò congruentes æquales vo-
              <lb/>
            cabantur, ſic pariter, ſi ſegmentum B A C ſuperpoſitum ſegmento E D F ſibi
              <lb/>
            mutuò congruant, ſunt duæ illæ lineæ curuæ æquales inter ſe.</s>
            <s xml:id="echoid-s5325" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5326" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s5327" xml:space="preserve">Declarat Apollonius in hac definitio-
              <lb/>
              <figure xlink:label="fig-0174-02" xlink:href="fig-0174-02a" number="173">
                <image file="0174-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0174-02"/>
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            ne ſeptima, quænam ſegmenta conica ſimilia
              <lb/>
            inter ſe cenſeri debeant. </s>
            <s xml:id="echoid-s5328" xml:space="preserve">Vt ſi fuerint dua-
              <lb/>
            rum conicarum ſectionum ſegmenta B A C,
              <lb/>
            & </s>
            <s xml:id="echoid-s5329" xml:space="preserve">E D F, quarum diametri A M, & </s>
            <s xml:id="echoid-s5330" xml:space="preserve">D L
              <lb/>
            eſſiciant cum ordinatim applicatis, ſeu cum
              <lb/>
            baſibus B C, & </s>
            <s xml:id="echoid-s5331" xml:space="preserve">E F angulos æquales in M,
              <lb/>
            & </s>
            <s xml:id="echoid-s5332" xml:space="preserve">L, & </s>
            <s xml:id="echoid-s5333" xml:space="preserve">in vnaquaque earum ductæ fuerint
              <lb/>
            pares multitudines applicatarum, quæ ſint ba-
              <lb/>
            ſibus æquidiſtantes, vt G H, & </s>
            <s xml:id="echoid-s5334" xml:space="preserve">I K, & </s>
            <s xml:id="echoid-s5335" xml:space="preserve">in
              <lb/>
            eis veriſicentur hæ conditiones, vt habeat B
              <lb/>
            C ad abſciſſam M A eandem proportionem,
              <lb/>
            quàm E F ad abſcißam L D, & </s>
            <s xml:id="echoid-s5336" xml:space="preserve">G H ad ab-
              <lb/>
            ciſſam N A eandem proportionem habeat,
              <lb/>
            quàm I K ad abciſsam O D, & </s>
            <s xml:id="echoid-s5337" xml:space="preserve">tandem ab-
              <lb/>
            ciſsa M A ad abſciſſam A N eandem propor-
              <lb/>
            tionem habeat, quàm abſcißa L D ad abſciſ-
              <lb/>
            ſam D O; </s>
            <s xml:id="echoid-s5338" xml:space="preserve">tunc quidem vocat Apollonius duo
              <lb/>
            ſegmenta B A C, & </s>
            <s xml:id="echoid-s5339" xml:space="preserve">E D F ſimilia inter ſe. </s>
            <s xml:id="echoid-s5340" xml:space="preserve">Et hic primo animaduertendum
              <lb/>
            eſt, dìfinitionem ſegmentorum ſimilium relatam ab Eutocio Aſcalonita in 3. </s>
            <s xml:id="echoid-s5341" xml:space="preserve">prop.
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            </s>
            <s xml:id="echoid-s5342" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s5343" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5344" xml:space="preserve">æquipond. </s>
            <s xml:id="echoid-s5345" xml:space="preserve">Archimedis, non eße integram: </s>
            <s xml:id="echoid-s5346" xml:space="preserve">in ea enim deſiderantur illa
              <lb/>
            verba, quarum baſes cumdiametris continent angulos æquales, ſine quibus
              <lb/>
            definitio eſſet erro-
              <lb/>
              <figure xlink:label="fig-0174-03" xlink:href="fig-0174-03a" number="174">
                <image file="0174-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0174-03"/>
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            nea, vt optime notat
              <lb/>
            Mydorgius. </s>
            <s xml:id="echoid-s5347" xml:space="preserve">Hoc au-
              <lb/>
            tem ita eße verba
              <lb/>
            textus Arabici aper-
              <lb/>
            te declarant, habent
              <lb/>
            enim. </s>
            <s xml:id="echoid-s5348" xml:space="preserve">Et ſimilia
              <lb/>
            ſunt quorum baſes
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            continent cum dia
              <lb/>
            metris angulos re-
              <lb/>
            ctos legẽdum </s>
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