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-div602" type="section" level="1" n="202">
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            <s xml:id="echoid-s6358" xml:space="preserve">
              <pb o="164" file="0202" n="202" rhead="Apollonij Pergæi"/>
            tis potius, quàm demonſtrantis
              <lb/>
              <figure xlink:label="fig-0202-01" xlink:href="fig-0202-01a" number="219">
                <image file="0202-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0202-01"/>
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            eſſet dicere. </s>
            <s xml:id="echoid-s6359" xml:space="preserve">Eo quod H F, ad
              <lb/>
            F b poſita fuit vt C B ad B a;
              <lb/>
            </s>
            <s xml:id="echoid-s6360" xml:space="preserve">vbi nam, aut quando hoc ſuppo-
              <lb/>
            ſitum eſt, ſi in definitione non
              <lb/>
            continetur? </s>
            <s xml:id="echoid-s6361" xml:space="preserve">Nec ſuspicari po-
              <lb/>
            teſt caſu hæc verba in textu ir-
              <lb/>
            repſiß, cum in alijs locis repe-
              <lb/>
            tantur, & </s>
            <s xml:id="echoid-s6362" xml:space="preserve">ab eis pendeat tota
              <lb/>
            demonſtratio; </s>
            <s xml:id="echoid-s6363" xml:space="preserve">igitur in defini-
              <lb/>
            tione vulgata addenda eſt illa
              <lb/>
            particula, abſciſſæ fint in ea-
              <lb/>
            dem ratione ad erecta;</s>
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          <p style="it">
            <s xml:id="echoid-s6365" xml:space="preserve">Rurſus in propoſ. </s>
            <s xml:id="echoid-s6366" xml:space="preserve">II. </s>
            <s xml:id="echoid-s6367" xml:space="preserve">& </s>
            <s xml:id="echoid-s6368" xml:space="preserve">I.
              <lb/>
            </s>
            <s xml:id="echoid-s6369" xml:space="preserve">parte 12. </s>
            <s xml:id="echoid-s6370" xml:space="preserve">quando concluſio demonſtrationis eſt quod ſectiones A B, E F ſimi-
              <lb/>
            les ſint: </s>
            <s xml:id="echoid-s6371" xml:space="preserve">tunc quidem quia tenetur oſtendere Apollonius definitionem traditam,
              <lb/>
            conuenire ſectionibus A B, E F, non aßumit incautè abſciſſas homologas C B,
              <lb/>
            H F, ſed ait in II. </s>
            <s xml:id="echoid-s6372" xml:space="preserve">propoſitionc ponamus C B ad B D vt H F ad F I, & </s>
            <s xml:id="echoid-s6373" xml:space="preserve">
              <lb/>
            in 12. </s>
            <s xml:id="echoid-s6374" xml:space="preserve">inquit, nam pofuimus H F ad F b vt C B ad B a &</s>
            <s xml:id="echoid-s6375" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6376" xml:space="preserve">Poſtea in pro-
              <lb/>
            poſitione 16. </s>
            <s xml:id="echoid-s6377" xml:space="preserve">litera a: </s>
            <s xml:id="echoid-s6378" xml:space="preserve">ergo M A ad A P, ideſt abſciſſa ad erectum eſt vt O
              <lb/>
            C ad C Q, ſeu vt homologa abſcißa ad latus rectum, & </s>
            <s xml:id="echoid-s6379" xml:space="preserve">angulus O æqualis
              <lb/>
            eſt M: </s>
            <s xml:id="echoid-s6380" xml:space="preserve">patet igitur, vt diximus in II. </s>
            <s xml:id="echoid-s6381" xml:space="preserve">ex 6. </s>
            <s xml:id="echoid-s6382" xml:space="preserve">quod ſi, &</s>
            <s xml:id="echoid-s6383" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6384" xml:space="preserve">Ex quibus locis
              <lb/>
            ſatis apertè colligitur ( ni fallor ) id quod ſupra rationibus non leuibus inſi-
              <lb/>
            nuaui, quod abſciſſæ proportionales eſſe debent erectis in ſectionibus ſimilibus.</s>
            <s xml:id="echoid-s6385" xml:space="preserve"/>
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          <figure number="220">
            <image file="0202-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0202-02"/>
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          <p style="it">
            <s xml:id="echoid-s6386" xml:space="preserve">Sed hic animaduertendum eſt, eandem definitionem non poſſe æquè aptari ſe-
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            ctionibus conicis, atque ſegmentis conicis ſimilibus, vt perperam cenſuit Mydor-
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            gius: </s>
            <s xml:id="echoid-s6387" xml:space="preserve">nam in ſegmentis conicis ſimilibus A B C, & </s>
            <s xml:id="echoid-s6388" xml:space="preserve">D E F diametrorum æquè
              <lb/>
            ad baſes inclinatarum abſciſſæ homologæ ex ſui natura determinatæ ſunt, quan-
              <lb/>
            doquidem non poßunt eße maiores, neque minores quàm G B, & </s>
            <s xml:id="echoid-s6389" xml:space="preserve">H E, quæ inter
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            baſes A C, & </s>
            <s xml:id="echoid-s6390" xml:space="preserve">D F ſegmentorum conicorum, & </s>
            <s xml:id="echoid-s6391" xml:space="preserve">vertices B, E intercipiuntur;
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            </s>
            <s xml:id="echoid-s6392" xml:space="preserve">at ſi in conicis ſectionibus A B S, & </s>
            <s xml:id="echoid-s6393" xml:space="preserve">K F G ſint axes tranſuerſis a B, & </s>
            <s xml:id="echoid-s6394" xml:space="preserve">b F
              <lb/>
              <note position="left" xlink:label="note-0202-01" xlink:href="note-0202-01a" xml:space="preserve">Propof.
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              12. huius
                <lb/>
              lib. I.</note>
            ad ſua latera recta B D, & </s>
            <s xml:id="echoid-s6395" xml:space="preserve">F I in eadem proportione, tunc quidem ſimiles e-
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            runt curuæ lineæ A B S, & </s>
            <s xml:id="echoid-s6396" xml:space="preserve">K F G, quæ poßunt habere indeterminatas, & </s>
            <s xml:id="echoid-s6397" xml:space="preserve">mul-
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            tiplices longitudines, immo poßunt in inſinitum prolongari, ſi fuerint </s>
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