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-div486" type="section" level="1" n="151">
          <p>
            <s xml:id="echoid-s5096" xml:space="preserve">
              <pb o="130" file="0168" n="168" rhead="Apollonij Pergæi"/>
            oſtendetur ex dictis, quod lineæ maximæ mutuò ſe ſecant inter diame
              <lb/>
            trum, & </s>
            <s xml:id="echoid-s5097" xml:space="preserve">rectum, &</s>
            <s xml:id="echoid-s5098" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5099" xml:space="preserve">Textũ corrigi debere maniſeſtum eſt ex dictis ſuperius</s>
          </p>
          <note position="right" xml:space="preserve">b</note>
          <p style="it">
            <s xml:id="echoid-s5100" xml:space="preserve">Quia D Q ad Q I eſt, vt D O ad O
              <lb/>
              <figure xlink:label="fig-0168-01" xlink:href="fig-0168-01a" number="166">
                <image file="0168-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0168-01"/>
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            G, &</s>
            <s xml:id="echoid-s5101" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5102" xml:space="preserve">In eadem figura propoſitionis 32.
              <lb/>
            </s>
            <s xml:id="echoid-s5103" xml:space="preserve">præcedentis perſiciatur conſtructio, vt priùs
              <lb/>
            quia duæ K M, H N ſunt breuiſsimæ li-
              <lb/>
              <note position="left" xlink:label="note-0168-02" xlink:href="note-0168-02a" xml:space="preserve">Pr. 15-
                <lb/>
              huius.</note>
            neæ; </s>
            <s xml:id="echoid-s5104" xml:space="preserve">ergo M R ad R D, nec non N P ad
              <lb/>
            P D eandem proportionem habent, ſcilicet
              <lb/>
            eam quàm habent latus rectum ad tranſuer-
              <lb/>
            ſum, ſeu eandem quàm habet ſemierectus
              <lb/>
              <note position="left" xlink:label="note-0168-03" xlink:href="note-0168-03a" xml:space="preserve">15. lib. I.</note>
            E B ad ſemiaxim B D; </s>
            <s xml:id="echoid-s5105" xml:space="preserve">eſt verò C A ad eius
              <lb/>
            latus rectum, ſeu D A ad A F, vt E B ad
              <lb/>
            B D; </s>
            <s xml:id="echoid-s5106" xml:space="preserve">igitur tam M R ad R D, quàm N P
              <lb/>
            ad P D eandem proporiionem habent, quàm
              <lb/>
            D A ad A F; </s>
            <s xml:id="echoid-s5107" xml:space="preserve">ſed propter parallelas C D, R
              <lb/>
            K, P H, c
              <unsure/>
            ſt M K ad K I, vt M R ad R D;
              <lb/>
            </s>
            <s xml:id="echoid-s5108" xml:space="preserve">pariterque N H ad H G eandem proportionẽ
              <lb/>
            habet, quàm N P ad P D; </s>
            <s xml:id="echoid-s5109" xml:space="preserve">atque propter pa-
              <lb/>
            rallelas D B, Q K, O H eſt D Q, ad Q I
              <lb/>
            vt M K ad K I, & </s>
            <s xml:id="echoid-s5110" xml:space="preserve">D O ad O G eſt vt N H
              <lb/>
            ad H G; </s>
            <s xml:id="echoid-s5111" xml:space="preserve">ergo tam D Q ad Q I, quàm D
              <lb/>
            O ad O G eandem proportionem habent, quàm D A ad A F, ſeu quàm axis mi-
              <lb/>
              <note position="left" xlink:label="note-0168-04" xlink:href="note-0168-04a" xml:space="preserve">20. 21. 22.
                <lb/>
              huius.</note>
            nor A C ad ſuum erectum, & </s>
            <s xml:id="echoid-s5112" xml:space="preserve">propterea tam K I, quàm H G eſt ramus maxi-
              <lb/>
            mus; </s>
            <s xml:id="echoid-s5113" xml:space="preserve">igitur ſi duæ lineæ breuiſſimæ H G, & </s>
            <s xml:id="echoid-s5114" xml:space="preserve">K I producantur quouſque axim
              <lb/>
            minorem ſecent in punctis G, & </s>
            <s xml:id="echoid-s5115" xml:space="preserve">I efficientur rami omnium maximi. </s>
            <s xml:id="echoid-s5116" xml:space="preserve">Poſtea quia
              <lb/>
            D Q ad Q I, eſt vt D O ad O G; </s>
            <s xml:id="echoid-s5117" xml:space="preserve">permutando D Q ad D O eandem propor-
              <lb/>
            tionem habebit, quàm Q I ad O G; </s>
            <s xml:id="echoid-s5118" xml:space="preserve">& </s>
            <s xml:id="echoid-s5119" xml:space="preserve">permutando, & </s>
            <s xml:id="echoid-s5120" xml:space="preserve">comparando antecedentes ad
              <lb/>
            differentias terminorum erit D Q ad D I, vt D O ad D G: </s>
            <s xml:id="echoid-s5121" xml:space="preserve">eſtque D Q minor
              <lb/>
            quàm D O; </s>
            <s xml:id="echoid-s5122" xml:space="preserve">igitur Q I minor eſt, quàm O G; </s>
            <s xml:id="echoid-s5123" xml:space="preserve">pariterque D I minor eſt, quàm
              <lb/>
            D G; </s>
            <s xml:id="echoid-s5124" xml:space="preserve">& </s>
            <s xml:id="echoid-s5125" xml:space="preserve">propterea punctum I cadit inter exim B D, & </s>
            <s xml:id="echoid-s5126" xml:space="preserve">ramum H G; </s>
            <s xml:id="echoid-s5127" xml:space="preserve">eſtque
              <lb/>
            etiam potentialis K Q propinquior & </s>
            <s xml:id="echoid-s5128" xml:space="preserve">parallela axi maiori, & </s>
            <s xml:id="echoid-s5129" xml:space="preserve">ideo maior re-
              <lb/>
            motiore H O; </s>
            <s xml:id="echoid-s5130" xml:space="preserve">igitur punctum K cadit inter axim B D, & </s>
            <s xml:id="echoid-s5131" xml:space="preserve">ramum H G; </s>
            <s xml:id="echoid-s5132" xml:space="preserve">& </s>
            <s xml:id="echoid-s5133" xml:space="preserve">
              <lb/>
            propterea ramus K I ſecat ramum H G in puncto L inter puncta H, & </s>
            <s xml:id="echoid-s5134" xml:space="preserve">G:
              <lb/>
            </s>
            <s xml:id="echoid-s5135" xml:space="preserve">
              <note position="left" xlink:label="note-0168-05" xlink:href="note-0168-05a" xml:space="preserve">36. huius.</note>
            ſed duæ breuiſsimæ K M, H N ſe ſecant vltra axim B D: </s>
            <s xml:id="echoid-s5136" xml:space="preserve">igitur occurſus L
              <lb/>
            cadit intra angulum B D C ab axibus compræhenſum. </s>
            <s xml:id="echoid-s5137" xml:space="preserve">Tandem quia K I ſecat
              <lb/>
            H G inter puncta G, & </s>
            <s xml:id="echoid-s5138" xml:space="preserve">H; </s>
            <s xml:id="echoid-s5139" xml:space="preserve">ergo efficit angulum externum K I A maio-
              <lb/>
            rem interno, & </s>
            <s xml:id="echoid-s5140" xml:space="preserve">oppoſito G: </s>
            <s xml:id="echoid-s5141" xml:space="preserve">& </s>
            <s xml:id="echoid-s5142" xml:space="preserve">propterea ramus K I propinquior vertici B,
              <lb/>
            quàm H G efficiet cum axe minore C A angulum A I K maiorem.</s>
            <s xml:id="echoid-s5143" xml:space="preserve"/>
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        <div xml:id="echoid-div489" type="section" level="1" n="152">
          <head xml:id="echoid-head201" xml:space="preserve">Notæ in Propoſit. XXXV.</head>
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            <s xml:id="echoid-s5144" xml:space="preserve">SI tranſeat per centrum ellipſis vna duarum breuiſſimarum; </s>
            <s xml:id="echoid-s5145" xml:space="preserve">vtique ra-
              <lb/>
              <note position="right" xlink:label="note-0168-06" xlink:href="note-0168-06a" xml:space="preserve">a</note>
            mi, &</s>
            <s xml:id="echoid-s5146" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5147" xml:space="preserve">Hæc propoſitio parum differt à 54. </s>
            <s xml:id="echoid-s5148" xml:space="preserve">& </s>
            <s xml:id="echoid-s5149" xml:space="preserve">55. </s>
            <s xml:id="echoid-s5150" xml:space="preserve">buius, vbi oſtenſum
              <lb/>
            eſt, quod ſi duo rami E B, E G breuiſecantes ex eodem concurſu E ad ellipſim
              <lb/>
            A B ducuntur, quilibet alius ramus E F, extra breuiſecantes poſitus, cadet ſu-
              <lb/>
            pra breuiſsimam ex puncto F ad axim A C ductam: </s>
            <s xml:id="echoid-s5151" xml:space="preserve">hic vero ſupponuntur </s>
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