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-div804" type="section" level="1" n="247">
          <p style="it">
            <s xml:id="echoid-s9557" xml:space="preserve">
              <pb o="255" file="0293" n="293" rhead="Conicor. Lib. VI."/>
            alius circulus F D a perpendicularis ad planum trianguli per axim L E K; </s>
            <s xml:id="echoid-s9558" xml:space="preserve">erat
              <lb/>
            autem ex conſtructione planum byperboles D E F perpendiculare ad idem planum
              <lb/>
            per axim E L K; </s>
            <s xml:id="echoid-s9559" xml:space="preserve">igitur duorum planorum communis ſectio, quæ ſit F G D per-
              <lb/>
            pendicularis quoque erit ad planum trianguli L E K: </s>
            <s xml:id="echoid-s9560" xml:space="preserve">& </s>
            <s xml:id="echoid-s9561" xml:space="preserve">ideo efficiet angulos F
              <lb/>
            G E, & </s>
            <s xml:id="echoid-s9562" xml:space="preserve">F G a rectos, & </s>
            <s xml:id="echoid-s9563" xml:space="preserve">G E H producta ſubtendit angulum externum trian-
              <lb/>
            guli conici E L K; </s>
            <s xml:id="echoid-s9564" xml:space="preserve">quapropter planum D E F efficiet in cono E L K byperbolen,
              <lb/>
            cuius axis tranſnerſus erit H E.</s>
            <s xml:id="echoid-s9565" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9566" xml:space="preserve">Alias eontineat illam alius conus ſimilis cono A B C, ſitque vertex
              <lb/>
              <note position="left" xlink:label="note-0293-01" xlink:href="note-0293-01a" xml:space="preserve">d</note>
            eius R in plano L E G, & </s>
            <s xml:id="echoid-s9567" xml:space="preserve">duo latera trianguli illius ſint E R, T R; </s>
            <s xml:id="echoid-s9568" xml:space="preserve">ergo
              <lb/>
            angulus E R T æqualis eſt E L K, & </s>
            <s xml:id="echoid-s9569" xml:space="preserve">eſt in cir cumferentia arcus E L H;
              <lb/>
            </s>
            <s xml:id="echoid-s9570" xml:space="preserve">ergo T R ſi producatur, occurret H: </s>
            <s xml:id="echoid-s9571" xml:space="preserve">&</s>
            <s xml:id="echoid-s9572" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9573" xml:space="preserve">Senſus buius textus corrupti ta-
              <lb/>
            lis eſt: </s>
            <s xml:id="echoid-s9574" xml:space="preserve">Si enim fieri poteſt, vt aliquis alius conus, vt E R T, qui ſimilis ſit
              <lb/>
            cono A B C, vel E L K, contineat eandem byperbolam D E F, & </s>
            <s xml:id="echoid-s9575" xml:space="preserve">conorum,
              <lb/>
            vertices R, & </s>
            <s xml:id="echoid-s9576" xml:space="preserve">L ad eaſdem partes tendant, erunt duo plana iriangulorum per
              <lb/>
            axes conorum ducta perpendicularia ad planum ſectionis D E F; </s>
            <s xml:id="echoid-s9577" xml:space="preserve">alias E G non
              <lb/>
            eßet axis hyperbole D E F; </s>
            <s xml:id="echoid-s9578" xml:space="preserve">Et quia coni ſitpponuntur ſimiles erunt quoque
              <lb/>
              <note position="right" xlink:label="note-0293-02" xlink:href="note-0293-02a" xml:space="preserve">E ex Def. 8.</note>
            triangula per axes E L K, & </s>
            <s xml:id="echoid-s9579" xml:space="preserve">E R T ſimilia int er ſe; </s>
            <s xml:id="echoid-s9580" xml:space="preserve">& </s>
            <s xml:id="echoid-s9581" xml:space="preserve">ideo anguli verticales.
              <lb/>
            </s>
            <s xml:id="echoid-s9582" xml:space="preserve">L K, & </s>
            <s xml:id="echoid-s9583" xml:space="preserve">E R T æquales inter ſe erunt, atque ſu bſequentes anguli E L H, & </s>
            <s xml:id="echoid-s9584" xml:space="preserve">E R
              <lb/>
            H æquales quoque inter ſe erunt, & </s>
            <s xml:id="echoid-s9585" xml:space="preserve">ſubtendunt commune latus tranſuerſum H
              <lb/>
            E; </s>
            <s xml:id="echoid-s9586" xml:space="preserve">igitur duo anguli E L H, & </s>
            <s xml:id="echoid-s9587" xml:space="preserve">E R H in eodem circuli ſegmento conſiſtunt. </s>
            <s xml:id="echoid-s9588" xml:space="preserve">
              <lb/>
            Textus igitur corrigi debebat vt dictum eſt.</s>
            <s xml:id="echoid-s9589" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9590" xml:space="preserve">Atque T S æqualis eſt ipſi E, & </s>
            <s xml:id="echoid-s9591" xml:space="preserve">T S ad S E eſt, vt T R ad R H, quæ
              <lb/>
              <note position="left" xlink:label="note-0293-03" xlink:href="note-0293-03a" xml:space="preserve">e</note>
            eſt vt E V ad V N; </s>
            <s xml:id="echoid-s9592" xml:space="preserve">ergo E V æqualis eſt V H, &</s>
            <s xml:id="echoid-s9593" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9594" xml:space="preserve">In duobus triangulis
              <lb/>
            iſoſcelijs inter ſe ſimilibus A B C, & </s>
            <s xml:id="echoid-s9595" xml:space="preserve">E R T ab æqualibus angulis verticalibus
              <lb/>
            A B C, & </s>
            <s xml:id="echoid-s9596" xml:space="preserve">E R T ducuntur rectæ lineæ B Q, R S ſecantes baſes in Q, & </s>
            <s xml:id="echoid-s9597" xml:space="preserve">S:
              <lb/>
            </s>
            <s xml:id="echoid-s9598" xml:space="preserve">eſtque quadratum R S ad rectangulum E S T, vt quadratum B Q ad rectangu-
              <lb/>
            lum A Q C, & </s>
            <s xml:id="echoid-s9599" xml:space="preserve">ſecatur A C bifariam in Q; </s>
            <s xml:id="echoid-s9600" xml:space="preserve">oſtendendum eſt E T in duas par-
              <lb/>
            tes æquales in S quoque ſecari. </s>
            <s xml:id="echoid-s9601" xml:space="preserve">Si enim boc verum non eſt E T in alio puncto
              <lb/>
            bifariam diuidetur vt in b iungaturquè R
              <lb/>
              <figure xlink:label="fig-0293-01" xlink:href="fig-0293-01a" number="341">
                <image file="0293-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0293-01"/>
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            b. </s>
            <s xml:id="echoid-s9602" xml:space="preserve">Quoniam à verticibus triangulorum,
              <lb/>
            A B C, & </s>
            <s xml:id="echoid-s9603" xml:space="preserve">R E T iſoſcelium ducuntur re-
              <lb/>
            ctæ lineæ B Q, R b diuidentes baſes bifa-
              <lb/>
            riam in Q, b, ergo anguli ad Q, & </s>
            <s xml:id="echoid-s9604" xml:space="preserve">b
              <lb/>
            ſunt recti, & </s>
            <s xml:id="echoid-s9605" xml:space="preserve">erant anguli A, & </s>
            <s xml:id="echoid-s9606" xml:space="preserve">E æquales
              <lb/>
            (propter ſimilitudinem eorundem triangu-
              <lb/>
            lorum) igitur triangula A B Q, & </s>
            <s xml:id="echoid-s9607" xml:space="preserve">E R b
              <lb/>
            ſimilia ſunt, ideoq; </s>
            <s xml:id="echoid-s9608" xml:space="preserve">B Q ad Q A erit vt R b
              <lb/>
            ad b E, & </s>
            <s xml:id="echoid-s9609" xml:space="preserve">quadratũ B Q ad quadratum Q A erit vt quadratũ R b ad quadratũ
              <lb/>
            b E; </s>
            <s xml:id="echoid-s9610" xml:space="preserve">erat autem quadratum R S ad rectangulum E S T vt quadratum B Q ad
              <lb/>
            quadratum Q A; </s>
            <s xml:id="echoid-s9611" xml:space="preserve">ergo quadratum R b ad quadratum b E eandem proportionem
              <lb/>
            habet, quàm quadratum R S ad rectangulum E S T; </s>
            <s xml:id="echoid-s9612" xml:space="preserve">eſtque quadratum R b
              <lb/>
            minus quadrato R S (cum perpendicularis R b minor ſit quàm R S) quarè qua-
              <lb/>
            dratum ex b E ſemiſſe totius E T minus erit rectangulo E S T ſub ſegmentis
              <lb/>
            inæqualibus eiusdem E T contento; </s>
            <s xml:id="echoid-s9613" xml:space="preserve">quod eſt abſurdum: </s>
            <s xml:id="echoid-s9614" xml:space="preserve">quarè neceſſario E T
              <lb/>
            bifariam ſecatur in S. </s>
            <s xml:id="echoid-s9615" xml:space="preserve">Poſtea propter parallela R S, & </s>
            <s xml:id="echoid-s9616" xml:space="preserve">H E, vt T S ad S E
              <lb/>
            ita erit T R ad R H; </s>
            <s xml:id="echoid-s9617" xml:space="preserve">& </s>
            <s xml:id="echoid-s9618" xml:space="preserve">propter parallelas R V, & </s>
            <s xml:id="echoid-s9619" xml:space="preserve">E T erit E V ad V H, vt
              <lb/>
            T R ad R H, ſeu T S ad S E: </s>
            <s xml:id="echoid-s9620" xml:space="preserve">oſtenſa autem fuit T S æqualis S E; </s>
            <s xml:id="echoid-s9621" xml:space="preserve">igitur </s>
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