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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          <p style="it">
            <s xml:id="echoid-s7157" xml:space="preserve">
              <pb o="189" file="0227" n="227" rhead="Conicor. Lib. VI."/>
            γ: </s>
            <s xml:id="echoid-s7158" xml:space="preserve">poſtea, quia B
              <lb/>
              <figure xlink:label="fig-0227-01" xlink:href="fig-0227-01a" number="255">
                <image file="0227-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0227-01"/>
              </figure>
            L, & </s>
            <s xml:id="echoid-s7159" xml:space="preserve">D N con-
              <lb/>
            tingunt ſectiones
              <lb/>
            in verticibus a-
              <lb/>
              <note position="right" xlink:label="note-0227-01" xlink:href="note-0227-01a" xml:space="preserve">Conuerſ.
                <lb/>
              32. lib. 1.</note>
            xium efficient an-
              <lb/>
            gulos V B L, & </s>
            <s xml:id="echoid-s7160" xml:space="preserve">
              <lb/>
            γ D N rectos, cũ-
              <lb/>
            que duo anguli V,
              <lb/>
            & </s>
            <s xml:id="echoid-s7161" xml:space="preserve">γ oſtenſi ſint æ-
              <lb/>
            quales, in trian-
              <lb/>
            gulis V B L, γ
              <lb/>
            D N, anguli V
              <lb/>
            L B, & </s>
            <s xml:id="echoid-s7162" xml:space="preserve">γ N D
              <lb/>
            æquales erunt in-
              <lb/>
            ter ſe, & </s>
            <s xml:id="echoid-s7163" xml:space="preserve">qui de-
              <lb/>
            inceps A L R, & </s>
            <s xml:id="echoid-s7164" xml:space="preserve">C N S ſunt æquales inter ſe; </s>
            <s xml:id="echoid-s7165" xml:space="preserve">& </s>
            <s xml:id="echoid-s7166" xml:space="preserve">ideo triangula A R L, & </s>
            <s xml:id="echoid-s7167" xml:space="preserve">C
              <lb/>
            S N ſimilia ſunt inter ſe.</s>
            <s xml:id="echoid-s7168" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7169" xml:space="preserve">Et propterea figuræ earundem diametrorum ſunt ſimiles, &</s>
            <s xml:id="echoid-s7170" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7171" xml:space="preserve">Quia
              <lb/>
              <note position="left" xlink:label="note-0227-02" xlink:href="note-0227-02a" xml:space="preserve">C</note>
            ex hypotheſi M A ad A E erat, vt O C ad C F; </s>
            <s xml:id="echoid-s7172" xml:space="preserve">atque (propter ſimilitudinem
              <lb/>
            triangulorum A E V, & </s>
            <s xml:id="echoid-s7173" xml:space="preserve">C F γ) vt E A ad duplam ipſius A V, ſeu ad latus
              <lb/>
            tranſuerſum A T, ita eſt F C ad duplam ipſius C γ, ſeu ad latus tranſuerſum
              <lb/>
            C X alterius ſectionis; </s>
            <s xml:id="echoid-s7174" xml:space="preserve">ergo ex æquali ordinata erit M A ad A T, vt O C ad
              <lb/>
            C X; </s>
            <s xml:id="echoid-s7175" xml:space="preserve">oſtenſum autem fuit latus tranſuerſum T A ad A P latus rectum eius ha-
              <lb/>
            bere eandem proportionem, quàm alterius ſectionis latus tranſuerſum X C ad
              <lb/>
            eius latus rectum C Q; </s>
            <s xml:id="echoid-s7176" xml:space="preserve">ergo ex æquali ordinata M A ad A P eandem propor-
              <lb/>
            tionem habet, quàm O C ad C Q; </s>
            <s xml:id="echoid-s7177" xml:space="preserve">quare duæ abſciſſæ A M, & </s>
            <s xml:id="echoid-s7178" xml:space="preserve">O C eandem
              <lb/>
            proportionem habent ad latera recta, atque ad tranſuerſa earundem diametro-
              <lb/>
            rum, atque efficiunt baſes H G, & </s>
            <s xml:id="echoid-s7179" xml:space="preserve">K I cum diametris angulos M, & </s>
            <s xml:id="echoid-s7180" xml:space="preserve">O æqua-
              <lb/>
              <note position="right" xlink:label="note-0227-03" xlink:href="note-0227-03a" xml:space="preserve">Defin. 7.
                <lb/>
              huius.</note>
            les inter ſe: </s>
            <s xml:id="echoid-s7181" xml:space="preserve">propterea quod æquales ſunt angulis E A V, & </s>
            <s xml:id="echoid-s7182" xml:space="preserve">F C γ æqualibus
              <lb/>
            (propter æquidiſtantiam rectarum H G, & </s>
            <s xml:id="echoid-s7183" xml:space="preserve">A E; </s>
            <s xml:id="echoid-s7184" xml:space="preserve">nec non K I, & </s>
            <s xml:id="echoid-s7185" xml:space="preserve">C F) igitur
              <lb/>
            erunt duo ſegmenta H A G, & </s>
            <s xml:id="echoid-s7186" xml:space="preserve">K C I ſimilia inter ſe.</s>
            <s xml:id="echoid-s7187" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7188" xml:space="preserve">Quia propter ſimilitudinem duorum ſegmentorum continebunt poten-
              <lb/>
              <note position="left" xlink:label="note-0227-04" xlink:href="note-0227-04a" xml:space="preserve">d</note>
            tes cum ſuis abſciſſis angulos æquales: </s>
            <s xml:id="echoid-s7189" xml:space="preserve">& </s>
            <s xml:id="echoid-s7190" xml:space="preserve">erit proportio potẽtium ad ab-
              <lb/>
            ſciſſa eadem, & </s>
            <s xml:id="echoid-s7191" xml:space="preserve">proportio abſciſſarum in vna earum ad alia ſimilia eadẽ,
              <lb/>
            quia V a in a E ad quadratum A a, eſt vt Y c in c F ad quadratum C c,
              <lb/>
            & </s>
            <s xml:id="echoid-s7192" xml:space="preserve">duo anguli a, & </s>
            <s xml:id="echoid-s7193" xml:space="preserve">c ſunt æquales; </s>
            <s xml:id="echoid-s7194" xml:space="preserve">ergo angulus Y æqualis eſt angulo
              <lb/>
            V, & </s>
            <s xml:id="echoid-s7195" xml:space="preserve">angulus C, nempe O æqualis A, nempe M propter ſimilitudinem
              <lb/>
            duorum ſegmentorum; </s>
            <s xml:id="echoid-s7196" xml:space="preserve">igitur A E V ſimile eſt Y F C, & </s>
            <s xml:id="echoid-s7197" xml:space="preserve">angulus E; </s>
            <s xml:id="echoid-s7198" xml:space="preserve">&</s>
            <s xml:id="echoid-s7199" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s7200" xml:space="preserve">In hoc textu nonnulla verba deficiunt, aliqua verò tranſpoſita ſunt, vt nullus
              <lb/>
            ſenſus colligi poſſit: </s>
            <s xml:id="echoid-s7201" xml:space="preserve">tamen eum reſtitui poße cenſeo vt ibidem videre eſt. </s>
            <s xml:id="echoid-s7202" xml:space="preserve">Quo-
              <lb/>
            niam duo ſegmenta H A G, & </s>
            <s xml:id="echoid-s7203" xml:space="preserve">K C I ſupponuntur ſimilia efficient diametri A
              <lb/>
            M, & </s>
            <s xml:id="echoid-s7204" xml:space="preserve">C O cum baſibus G H, & </s>
            <s xml:id="echoid-s7205" xml:space="preserve">K I angulos M, & </s>
            <s xml:id="echoid-s7206" xml:space="preserve">O æquales, licet non rectos; </s>
            <s xml:id="echoid-s7207" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0227-05" xlink:href="note-0227-05a" xml:space="preserve">Lem. 8.
                <lb/>
              huius.</note>
            eruntque figuræ earumdem diametrorum ſimiles inter ſe: </s>
            <s xml:id="echoid-s7208" xml:space="preserve">& </s>
            <s xml:id="echoid-s7209" xml:space="preserve">propterea habebit
              <lb/>
            T A ad eius erectum eandem proportionem, quàm X C ad eius latus rectum;
              <lb/>
            </s>
            <s xml:id="echoid-s7210" xml:space="preserve">
              <note position="right" xlink:label="note-0227-06" xlink:href="note-0227-06a" xml:space="preserve">15. huius.</note>
            igitur ſectiones A B, & </s>
            <s xml:id="echoid-s7211" xml:space="preserve">C D ſimiles ſunt, ideſt ductis axibus V B, & </s>
            <s xml:id="echoid-s7212" xml:space="preserve">γ D
              <lb/>
              <note position="right" xlink:label="note-0227-07" xlink:href="note-0227-07a" xml:space="preserve">47. lib. 2.</note>
            erunt figuræ axium ſimiles inter ſe: </s>
            <s xml:id="echoid-s7213" xml:space="preserve">ducuntur verò à punctis A, & </s>
            <s xml:id="echoid-s7214" xml:space="preserve">C ad axes
              <lb/>
              <note position="right" xlink:label="note-0227-08" xlink:href="note-0227-08a" xml:space="preserve">12. huius.</note>
            ordinatim applicati A a, & </s>
            <s xml:id="echoid-s7215" xml:space="preserve">C c, atque contingentes A E, & </s>
            <s xml:id="echoid-s7216" xml:space="preserve">C F; </s>
            <s xml:id="echoid-s7217" xml:space="preserve">igitur re-
              <lb/>
              <note position="right" xlink:label="note-0227-09" xlink:href="note-0227-09a" xml:space="preserve">37. lib. 1.</note>
            </s>
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