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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            <s xml:id="echoid-s4135" xml:space="preserve">
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            periaturque Trutina K minoris, vel maioris menſuræ F B: </s>
            <s xml:id="echoid-s4136" xml:space="preserve">dico perpen-
              <lb/>
            dicularem C F minorem eſſe Trutina K.</s>
            <s xml:id="echoid-s4137" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4138" xml:space="preserve">Secentur primo in parabola abciſsæ B H, & </s>
            <s xml:id="echoid-s4139" xml:space="preserve">B N æquales trienti exceſſus inæ-
              <lb/>
            qualium menſurarum ſupra ſemierectum (vt præcipitur in propoſitione 51. </s>
            <s xml:id="echoid-s4140" xml:space="preserve">hu-
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            ius) manifeſtum eſt, abſciſſam B N minorem eſſe ipſa B H, quando B F minor
              <lb/>
            eſt, quàm B E, & </s>
            <s xml:id="echoid-s4141" xml:space="preserve">maior, quando B F ſuperat ipſam B E; </s>
            <s xml:id="echoid-s4142" xml:space="preserve">eo quod eorum tri-
              <lb/>
            plæ, vna cum ſemierecto, ideſt menſura B F minor fuerat in primo caſu, & </s>
            <s xml:id="echoid-s4143" xml:space="preserve">
              <lb/>
            maior in ſecundo, quàm menſura B E.</s>
            <s xml:id="echoid-s4144" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4145" xml:space="preserve">In hyperbola vero, & </s>
            <s xml:id="echoid-s4146" xml:space="preserve">ellipſi fiat proportio rectæ H L ad ſemiaxim tranſuer-
              <lb/>
              <note position="left" xlink:label="note-0140-01" xlink:href="note-0140-01a" xml:space="preserve">Lem. 7.
                <lb/>
              huius.</note>
            ſum L B ſubtriplicata eius, quàm inuerſæ L E ſegmentum L G homologum la-
              <lb/>
            teri tranſuerſo habet ad ſemiaxim tranſuerſum (ex præſcripto propoſit. </s>
            <s xml:id="echoid-s4147" xml:space="preserve">52. </s>
            <s xml:id="echoid-s4148" xml:space="preserve">& </s>
            <s xml:id="echoid-s4149" xml:space="preserve">
              <lb/>
            53. </s>
            <s xml:id="echoid-s4150" xml:space="preserve">huius) pariterque fiat proportio N L ad L B ſubtriplicata eius quàm inuer-
              <lb/>
            ſæ minoris L F in primo caſu, & </s>
            <s xml:id="echoid-s4151" xml:space="preserve">maioris in ſecundo, ſegmentum homologum
              <lb/>
            lateri tranſuerſo habet ad L B.</s>
            <s xml:id="echoid-s4152" xml:space="preserve"/>
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          <figure number="125">
            <image file="0140-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0140-01"/>
          </figure>
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            <s xml:id="echoid-s4153" xml:space="preserve">Quoniam in primo caſu maius ſegmentum G L ad eandem L B habet maio-
              <lb/>
            rem proportionem, quàm minus ſegmentum ex L F diſſectum; </s>
            <s xml:id="echoid-s4154" xml:space="preserve">igitur earum;
              <lb/>
            </s>
            <s xml:id="echoid-s4155" xml:space="preserve">ſubtriplicatæ proportiones inæquales erunt, videlicet H L ad L B maiorem pro-
              <lb/>
            portionem habebit, quàm N L ad ipſam L B, & </s>
            <s xml:id="echoid-s4156" xml:space="preserve">propterea H L maior erit,
              <lb/>
            quàm N L, & </s>
            <s xml:id="echoid-s4157" xml:space="preserve">ablata communi L B, erit H B abſciſſa maioris menſuræ ma-
              <lb/>
            ior, quàm N B abſcißa menſuræ minoris. </s>
            <s xml:id="echoid-s4158" xml:space="preserve">Similiter oſtendetur in ſecundo ca-
              <lb/>
            ſu, quod abſciſſa N B maioris menſuræ maior eſt, quàm B H. </s>
            <s xml:id="echoid-s4159" xml:space="preserve">Oſtendedum
              <lb/>
            modo eſt, perpendicularem C F in vtroque caſu minorem eſſe trutina K; </s>
            <s xml:id="echoid-s4160" xml:space="preserve">Si
              <lb/>
              <note position="left" xlink:label="note-0140-02" xlink:href="note-0140-02a" xml:space="preserve">51. 52.
                <lb/>
              huius.</note>
            enim hoc verum non eſt, ſi fieri poteſt, ſit C F maior trutina K; </s>
            <s xml:id="echoid-s4161" xml:space="preserve">igitur ex con-
              <lb/>
            curſu C ad ſectionem B A nullus ramus breuiſecans duci poteſt, quod eſt contra
              <lb/>
            hypotheſim; </s>
            <s xml:id="echoid-s4162" xml:space="preserve">erat enim A I breuiſsima; </s>
            <s xml:id="echoid-s4163" xml:space="preserve">quare C F non erit maior trutina K.
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            </s>
            <s xml:id="echoid-s4164" xml:space="preserve">Sit ſecundo C F æqualis K, ſi fieri poteſt, ergo ramus principalis C O ductus
              <lb/>
            legibus propoſit. </s>
            <s xml:id="echoid-s4165" xml:space="preserve">51. </s>
            <s xml:id="echoid-s4166" xml:space="preserve">52. </s>
            <s xml:id="echoid-s4167" xml:space="preserve">huius cui competit trutina K erit breuiſecans ſin-
              <lb/>
            gularis eorum, qui ad ſectionem duci poſſunt, nec vllus alius, præter C O, bre-
              <lb/>
            uiſecans erit: </s>
            <s xml:id="echoid-s4168" xml:space="preserve">cadit vero ramus C A infra, vel ſupra ramum C O, propterea
              <lb/>
            quod abſciſſæ B H, & </s>
            <s xml:id="echoid-s4169" xml:space="preserve">B N inæquales oſtenſæ ſunt; </s>
            <s xml:id="echoid-s4170" xml:space="preserve">igitur ramus C A diuerſus
              <lb/>
            à breuiſecante ſingulari C O non erit breuiſecans, quod eſt contra hypotheſin;</s>
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