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="249" file="0287" n="287" rhead="Conicor. Lib. VI."/>
              <figure xlink:label="fig-0287-01" xlink:href="fig-0287-01a" number="335">
                <image file="0287-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0287-01"/>
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            rat circumferentiæ in L, & </s>
            <s xml:id="echoid-s9329" xml:space="preserve">iungamus E L, & </s>
            <s xml:id="echoid-s9330" xml:space="preserve">L H, quæ occurrat in K
              <lb/>
            perpendiculari ex puncto E ſuper lineam E H. </s>
            <s xml:id="echoid-s9331" xml:space="preserve">Et quia E K parallela eſt
              <lb/>
            L O erit angulus K æqualis H L O, qui eſt ſemiſſis anguli H L E, & </s>
            <s xml:id="echoid-s9332" xml:space="preserve">hic
              <lb/>
            eſt æqualis duobus angulis K, K E L; </s>
            <s xml:id="echoid-s9333" xml:space="preserve">igitur ſunt æquales; </s>
            <s xml:id="echoid-s9334" xml:space="preserve">quare K L E
              <lb/>
            eſt æquicrus, & </s>
            <s xml:id="echoid-s9335" xml:space="preserve">angulus K L E æqualis eſt A B C; </s>
            <s xml:id="echoid-s9336" xml:space="preserve">quia angulus H L E
              <lb/>
            æqualis eſt M B C; </s>
            <s xml:id="echoid-s9337" xml:space="preserve">quapropter K L E ſimile eſt A B C, quia æqualia
              <lb/>
              <note position="left" xlink:label="note-0287-01" xlink:href="note-0287-01a" xml:space="preserve">c</note>
            crura etiam habet! Si autem ponamus K L E triangulum coni, cuius
              <lb/>
            vertex L, & </s>
            <s xml:id="echoid-s9338" xml:space="preserve">planum illius trianguli erectum ad planum D E F; </s>
            <s xml:id="echoid-s9339" xml:space="preserve">vtique
              <lb/>
            planum ſectionis producit in cono hyperbolen, cuius axis E G, inclina-
              <lb/>
            tus E H; </s>
            <s xml:id="echoid-s9340" xml:space="preserve">eo quod ſi educamus L P, B Q perpendiculares in duobus
              <lb/>
            triangulis, habebit quadratum B Q ad C Q in Q A (quod eſt vt H E
              <lb/>
            ad E I) eandem proportionem, quàm quadratum L P ad P K in P E:
              <lb/>
            </s>
            <s xml:id="echoid-s9341" xml:space="preserve">quare potentes æductæ in illa ſectione ad axim E G, poterunt compa-
              <lb/>
            rata, applicata ad E I erectum; </s>
            <s xml:id="echoid-s9342" xml:space="preserve">ſed potentes, eductæ in ſectione D E F,
              <lb/>
              <note position="right" xlink:label="note-0287-02" xlink:href="note-0287-02a" xml:space="preserve">12. lib. 1.</note>
            poſſunt quoque illa applicata; </s>
            <s xml:id="echoid-s9343" xml:space="preserve">ergo ſectio D E F æqualis eſt ſectioni,
              <lb/>
            prouenienti in cono, cuius vertex eſt L, & </s>
            <s xml:id="echoid-s9344" xml:space="preserve">exiſtit in eodem plano, ha-
              <lb/>
            betque eundem axim: </s>
            <s xml:id="echoid-s9345" xml:space="preserve">quare conus, cuius vertex L continet ſectionem
              <lb/>
              <note position="right" xlink:label="note-0287-03" xlink:href="note-0287-03a" xml:space="preserve">Defin. 9.</note>
            D E F, & </s>
            <s xml:id="echoid-s9346" xml:space="preserve">eſt ſimilis cono A B C.</s>
            <s xml:id="echoid-s9347" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9348" xml:space="preserve">Dico rurſus, quod nullus alius conus ſimilis cono A B C, cuius ver-
              <lb/>
            tex ſit in ea parte, in qua eſt L, præter iam dictum, continebit hanc
              <lb/>
            eandem ſectionem. </s>
            <s xml:id="echoid-s9349" xml:space="preserve">Si enim hoc verum non eſt, contineat illam alius
              <lb/>
              <note position="right" xlink:label="note-0287-04" xlink:href="note-0287-04a" xml:space="preserve">d</note>
            conus ſimilis cono A B C, cuius vertex R in plano L E G; </s>
            <s xml:id="echoid-s9350" xml:space="preserve">atque latera
              <lb/>
            illius ſint E R, R T. </s>
            <s xml:id="echoid-s9351" xml:space="preserve">Quia angulus E R T æqualis eſt E L K, & </s>
            <s xml:id="echoid-s9352" xml:space="preserve">eorum
              <lb/>
            conſequentes æquales inter ſe in eodem circuli ſegmento E L H exiſtent,
              <lb/>
            eo quod T R produſta occurrit axi tranſuerſo E H in H, & </s>
            <s xml:id="echoid-s9353" xml:space="preserve">iungamus R
              <lb/>
            O, & </s>
            <s xml:id="echoid-s9354" xml:space="preserve">ex E educamus E T, quæ ſit parallela coniunctæ rectæ lineæ O R;
              <lb/>
            </s>
            <s xml:id="echoid-s9355" xml:space="preserve">vnde angulus O R H æqualis eſt O R E) propter æqualitatem arcuum
              <lb/>
            ſuorum, & </s>
            <s xml:id="echoid-s9356" xml:space="preserve">ſunt æquales duobus angulis R T E, R E T, ergo E R T eſt
              <lb/>
            æquicrus, & </s>
            <s xml:id="echoid-s9357" xml:space="preserve">angulus T R E æqualis eſt A B C: </s>
            <s xml:id="echoid-s9358" xml:space="preserve">educatur iam R S pa-
              <lb/>
            rallela H E, tunc quadratum R S ad T S in S E eandem proportionem
              <lb/>
            habebit, quàm E H inclinatus ſectionis D E F ad E I erectum illius; </s>
            <s xml:id="echoid-s9359" xml:space="preserve">eo
              <lb/>
            quod ſectionem D E F continet conus, cuius vertex eſt R; </s>
            <s xml:id="echoid-s9360" xml:space="preserve">ſed H E </s>
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