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="163" file="0201" n="201" rhead="Conicor. Lib. VI."/>
            ſint ſimilia, quæ quidem, eſt propoſitio 3. </s>
            <s xml:id="echoid-s6317" xml:space="preserve">libri 4. </s>
            <s xml:id="echoid-s6318" xml:space="preserve">Mydorgij, eiuſque præparatio,
              <lb/>
            ſeu conſtructio talis eſt (, & </s>
            <s xml:id="echoid-s6319" xml:space="preserve">appono eius verba immutatis tantummodo literis fi-
              <lb/>
            gurarũ) ſint à ſectione A B ordinatim ad axim B C applicatæ binæ quæ-
              <lb/>
            quæ A C, Q R, & </s>
            <s xml:id="echoid-s6320" xml:space="preserve">vt C B ad B R ita ſit, H F ad F V, ordinatimque à ſe-
              <lb/>
            ctione E F applicentur E H, T V ( ſubſequitur poſtea demonſtratio ſic.)
              <lb/>
            </s>
            <s xml:id="echoid-s6321" xml:space="preserve">Quoniam igitur ſimiles ponuntur ſectiones A B, E F, & </s>
            <s xml:id="echoid-s6322" xml:space="preserve">ſunt H F, F V
              <lb/>
            portiones portionibus C B, B R fimiles, (ideſt proportionales) vt B C
              <lb/>
            ad C A, ita erit F H ad H E, & </s>
            <s xml:id="echoid-s6323" xml:space="preserve">vt B R ad R Q, ita erit F V ad V T,
              <lb/>
            & </s>
            <s xml:id="echoid-s6324" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6325" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6326" xml:space="preserve">Huiuſmodi verba ſubtiliori trutina expendenda ſunt. </s>
            <s xml:id="echoid-s6327" xml:space="preserve">In præparatione, ſeu
              <lb/>
            conſtructione aſſumit abſcißas B C, & </s>
            <s xml:id="echoid-s6328" xml:space="preserve">F H abſque vlla lege, aut determinatione;
              <lb/>
            </s>
            <s xml:id="echoid-s6329" xml:space="preserve">ergo ſumi poſſunt cuiuſcunq; </s>
            <s xml:id="echoid-s6330" xml:space="preserve">longitudinis: </s>
            <s xml:id="echoid-s6331" xml:space="preserve">quare fieri poteſt vt C B ad latus re-
              <lb/>
            ctum B D non habeat eandem proportionem quàm habet F H ad F I, & </s>
            <s xml:id="echoid-s6332" xml:space="preserve">tunc
              <lb/>
              <note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve">Lem. 2.
                <lb/>
              huius.</note>
            licet C B , H F diuidantur proportionaliter, & </s>
            <s xml:id="echoid-s6333" xml:space="preserve">ducantur potentiales, & </s>
            <s xml:id="echoid-s6334" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6335" xml:space="preserve">A C
              <lb/>
            ad C B habebit maiorem, aut minorem proportionem quàm E H ad H F, & </s>
            <s xml:id="echoid-s6336" xml:space="preserve">pa-
              <lb/>
            riter Q R ad R B non habebit eandem rationem, quàm T V ad V F, & </s>
            <s xml:id="echoid-s6337" xml:space="preserve">ſit vl-
              <lb/>
            terius in tota ſerie; </s>
            <s xml:id="echoid-s6338" xml:space="preserve">ſed ex hoc ſequitur, quod poſſint eſſe figuræ axium inter ſe
              <lb/>
              <note position="right" xlink:label="note-0201-02" xlink:href="note-0201-02a" xml:space="preserve">Coroll. 2.
                <lb/>
              Lem. 5.
                <lb/>
              huius.</note>
            non ſimiles; </s>
            <s xml:id="echoid-s6339" xml:space="preserve">Mydorgius autem ſimiles eſſe concludit; </s>
            <s xml:id="echoid-s6340" xml:space="preserve">igitur ex eadem hypotheſi,
              <lb/>
            & </s>
            <s xml:id="echoid-s6341" xml:space="preserve">ex eadem definitione deducitur, quod ſectiones ſimiles habent figuras axium,
              <lb/>
            ſimiles inter ſe, & </s>
            <s xml:id="echoid-s6342" xml:space="preserve">non ſimiles, quod eſt impoſſibile; </s>
            <s xml:id="echoid-s6343" xml:space="preserve">non igitur definitio à My-
              <lb/>
            dorgio tradita legitima, & </s>
            <s xml:id="echoid-s6344" xml:space="preserve">perfecta eſt: </s>
            <s xml:id="echoid-s6345" xml:space="preserve">quod fuerat oſtendendum.</s>
            <s xml:id="echoid-s6346" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6347" xml:space="preserve">Quod vero deſinitio à me reformata tribui poſſit Apollonio conijcitur præcipuè
              <lb/>
            ex demonſtratione ſecundæ partis propor. </s>
            <s xml:id="echoid-s6348" xml:space="preserve">12. </s>
            <s xml:id="echoid-s6349" xml:space="preserve">ibi enim ex hac ſuppoſitione, quod
              <lb/>
              <figure xlink:label="fig-0201-01" xlink:href="fig-0201-01a" number="218">
                <image file="0201-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0201-01"/>
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            ſcilicet duæ ſectiones A B, & </s>
            <s xml:id="echoid-s6350" xml:space="preserve">E F ſint ſimiles deducit earum figuras ſimiles eſſe.
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            </s>
            <s xml:id="echoid-s6351" xml:space="preserve">Ait enim: </s>
            <s xml:id="echoid-s6352" xml:space="preserve">quia eſt A C ad C B vt E H ad H F, & </s>
            <s xml:id="echoid-s6353" xml:space="preserve">eandem proportioné
              <lb/>
            habent earum quadrata, atque quadratum H F ad rectangulum: </s>
            <s xml:id="echoid-s6354" xml:space="preserve">F H b
              <lb/>
            eandem proportionem habet quàm quadratum C B ad rectangulũ B C a
              <lb/>
            ( c
              <unsure/>
            o quod H F ad F b poſita fuit vt C B ad B a) ergo, &</s>
            <s xml:id="echoid-s6355" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6356" xml:space="preserve">Modo ſi ac-
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            curatè hæc verba perpendantur non poterit hic vſurpari vulgata definitio Euto-
              <lb/>
            cij, vel Mydorgij nam cum ſectiones A B, E F ſupponantur ſimiles, ea tan-
              <lb/>
            tummodo quæ in definitione ſimilium ſectionum perhibentur concedi poßunt, & </s>
            <s xml:id="echoid-s6357" xml:space="preserve">
              <lb/>
            nihil amplius; </s>
            <s xml:id="echoid-s6358" xml:space="preserve">igitur ſi in definitione non includitur particula illa [ abſciſſæ H
              <lb/>
            F, C B’ ad erecta, vel tranſuerſa latera F b, B a ſint proportionalia ] deliran-</s>
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