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-div659" type="section" level="1" n="220">
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            <s xml:id="echoid-s7217" xml:space="preserve">
              <pb o="190" file="0228" n="228" rhead="Apollonij Pergæi"/>
            ctangulum V a E ad quadratum a A eandem proportionem habebit, quàm axis
              <lb/>
            tranſuerſus ad eius erectum, ſeu quàm axis tranſuerſus alterius ſectionis C D
              <lb/>
            ad eius erectum: </s>
            <s xml:id="echoid-s7218" xml:space="preserve">ſed in eadem proportione eſt rectangulum γ c F ad quadratũ
              <lb/>
              <note position="left" xlink:label="note-0228-01" xlink:href="note-0228-01a" xml:space="preserve">37. lib. 1.</note>
            c C; </s>
            <s xml:id="echoid-s7219" xml:space="preserve">igitur in duobus triangulis A V E, & </s>
            <s xml:id="echoid-s7220" xml:space="preserve">C γ F rectæ A a, & </s>
            <s xml:id="echoid-s7221" xml:space="preserve">C c cũ baſibus
              <lb/>
            angulos æquales a, & </s>
            <s xml:id="echoid-s7222" xml:space="preserve">c, nempe rectos efficiunt, cum ordinatim applicatæ ſint ad
              <lb/>
            axes; </s>
            <s xml:id="echoid-s7223" xml:space="preserve">atque duo anguli verticales V A E, & </s>
            <s xml:id="echoid-s7224" xml:space="preserve">γ C F æquales ſint inter ſe, cum
              <lb/>
            propter parallelas æquales ſint angulis O, & </s>
            <s xml:id="echoid-s7225" xml:space="preserve">M æqualibus in ſegmentis ſimilibus;
              <lb/>
            </s>
            <s xml:id="echoid-s7226" xml:space="preserve">
              <note position="left" xlink:label="note-0228-02" xlink:href="note-0228-02a" xml:space="preserve">Propoſ. 7.
                <lb/>
              præmiſſ.</note>
            igitur duo triangula A E V, & </s>
            <s xml:id="echoid-s7227" xml:space="preserve">C F γ æquiangula, & </s>
            <s xml:id="echoid-s7228" xml:space="preserve">ſimilia ſunt inter ſe: </s>
            <s xml:id="echoid-s7229" xml:space="preserve">& </s>
            <s xml:id="echoid-s7230" xml:space="preserve">
              <lb/>
            proptered V A ad A E erit, vt γ C ad C F, &</s>
            <s xml:id="echoid-s7231" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7232" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7233" xml:space="preserve">Ponamus iam P A ad duplam A E, vt Q C ad duplam C F: </s>
            <s xml:id="echoid-s7234" xml:space="preserve">ergo ex
              <lb/>
              <note position="right" xlink:label="note-0228-03" xlink:href="note-0228-03a" xml:space="preserve">e</note>
            æqualitate A T diameter ad A P erectum eius, &</s>
            <s xml:id="echoid-s7235" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7236" xml:space="preserve">In hoc textu nonnulla
              <lb/>
            videntur deficere, eiuſq; </s>
            <s xml:id="echoid-s7237" xml:space="preserve">ſenſus talis erit. </s>
            <s xml:id="echoid-s7238" xml:space="preserve">Quia veluti ſupra dictum eſt, triã-
              <lb/>
            gula R A L, & </s>
            <s xml:id="echoid-s7239" xml:space="preserve">S C N ſimilia ſunt inter ſe, habebit R A ad A L eandem pro-
              <lb/>
            portionem, quàm S C ad C N: </s>
            <s xml:id="echoid-s7240" xml:space="preserve">Ponamus iam P A ad duplam A E, vt R A ad
              <lb/>
            A L, & </s>
            <s xml:id="echoid-s7241" xml:space="preserve">Q C ad duplam C F, vt S C ad C N, erunt A P, & </s>
            <s xml:id="echoid-s7242" xml:space="preserve">C Q latera re-
              <lb/>
            cta diametrorum A M, & </s>
            <s xml:id="echoid-s7243" xml:space="preserve">O C; </s>
            <s xml:id="echoid-s7244" xml:space="preserve">ſed earundem diametrorum figuræ oſtenſæ ſunt
              <lb/>
              <note position="left" xlink:label="note-0228-04" xlink:href="note-0228-04a" xml:space="preserve">50 lib. 1.
                <lb/>
              Lem. 8.</note>
            ſimiles; </s>
            <s xml:id="echoid-s7245" xml:space="preserve">igitur latus tranſuerſum A T ad A P erectum eius eſt, vt latus tran-
              <lb/>
            uerſum X C ad C Q erectum eius. </s>
            <s xml:id="echoid-s7246" xml:space="preserve">Et quia vt latus tranſuerſum ad rectum
              <lb/>
              <figure xlink:label="fig-0228-01" xlink:href="fig-0228-01a" number="256">
                <image file="0228-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0228-01"/>
              </figure>
            ita eſt rectangulum T M A ad quadratum M G, & </s>
            <s xml:id="echoid-s7247" xml:space="preserve">ſimiliter rectangulum X O
              <lb/>
              <note position="left" xlink:label="note-0228-05" xlink:href="note-0228-05a" xml:space="preserve">21. lib. 1.</note>
            C ad quadratum O I eandem proportionem habebit, quàm latus tranſuerſum ad
              <lb/>
            rectum, ſcilicet eandem, quàm habent latera figurarũ earundẽ diametrorũ; </s>
            <s xml:id="echoid-s7248" xml:space="preserve">igi-
              <lb/>
            tur rectangulum T M A ad quadratum M G eandem proportionẽ habebit, quàm
              <lb/>
            rectangulum X O C ad quadratum O I; </s>
            <s xml:id="echoid-s7249" xml:space="preserve">habet verò M G ad M A eandem pro-
              <lb/>
            portionem, quàm I O ad O C propter ſimilitudinem ſegmentorum; </s>
            <s xml:id="echoid-s7250" xml:space="preserve">ergo quadra-
              <lb/>
            tum G M ad quadratum M A erit vt quadratum I O ad quadratum O C: </s>
            <s xml:id="echoid-s7251" xml:space="preserve">& </s>
            <s xml:id="echoid-s7252" xml:space="preserve">
              <lb/>
            propterea ex æquali ordinata rectangulum T M A ad quadratum M A, ſeu T </s>
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