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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            Quoniam O L ad L I oſtenſa fuit, vt Q M ad M K; </s>
            <s xml:id="echoid-s7649" xml:space="preserve">atque prius oſtenſa ſuit
              <lb/>
            B L ad L I, vt E M ad M K; </s>
            <s xml:id="echoid-s7650" xml:space="preserve">ergo inuertendo I L ad L B erit, vt K M ad
              <lb/>
            M E; </s>
            <s xml:id="echoid-s7651" xml:space="preserve">& </s>
            <s xml:id="echoid-s7652" xml:space="preserve">propterea ex æqualitate O L ad L B erit vt Q M ad M E; </s>
            <s xml:id="echoid-s7653" xml:space="preserve">ſed B L
              <lb/>
              <note position="left" xlink:label="note-0242-01" xlink:href="note-0242-01a" xml:space="preserve">ex 12.
                <lb/>
              huius.</note>
            ad L N eſt, vt E M ad M P; </s>
            <s xml:id="echoid-s7654" xml:space="preserve">igitur ex æqualitate O L ad L N erit vt Q M
              <lb/>
            ad M P; </s>
            <s xml:id="echoid-s7655" xml:space="preserve">ſuntque duo anguli L, & </s>
            <s xml:id="echoid-s7656" xml:space="preserve">M recti; </s>
            <s xml:id="echoid-s7657" xml:space="preserve">ergo triangula O L N, & </s>
            <s xml:id="echoid-s7658" xml:space="preserve">Q M P
              <lb/>
            æquiangula erunt; </s>
            <s xml:id="echoid-s7659" xml:space="preserve">& </s>
            <s xml:id="echoid-s7660" xml:space="preserve">propterea anguli O, & </s>
            <s xml:id="echoid-s7661" xml:space="preserve">Qæquales inter ſe erunt; </s>
            <s xml:id="echoid-s7662" xml:space="preserve">ſed quia
              <lb/>
            contingentes verticales V e, & </s>
            <s xml:id="echoid-s7663" xml:space="preserve">γ f parallelæ ſunt or dinatim applicatis N A, P
              <lb/>
            D ad diametros V R, & </s>
            <s xml:id="echoid-s7664" xml:space="preserve">γ S; </s>
            <s xml:id="echoid-s7665" xml:space="preserve">igitur angulus V e B æqualis erit angulo N O L;
              <lb/>
            </s>
            <s xml:id="echoid-s7666" xml:space="preserve">pariterque angulus γ f E æqualis erit angulo P Q M; </s>
            <s xml:id="echoid-s7667" xml:space="preserve">& </s>
            <s xml:id="echoid-s7668" xml:space="preserve">propterea anguli e, & </s>
            <s xml:id="echoid-s7669" xml:space="preserve">
              <lb/>
            f æquales erunt inter ſe.</s>
            <s xml:id="echoid-s7670" xml:space="preserve"/>
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            <s xml:id="echoid-s7671" xml:space="preserve">Ergo propter ſimilitudinem duarum ſectionum T Z in Z e ad quadra-
              <lb/>
              <note position="right" xlink:label="note-0242-02" xlink:href="note-0242-02a" xml:space="preserve">d</note>
            tum Z V eandem proportionem habebit quàm X a in a f ad quadratum
              <lb/>
            a Y, & </s>
            <s xml:id="echoid-s7672" xml:space="preserve">angulus e æqualis eſt angulo f; </s>
            <s xml:id="echoid-s7673" xml:space="preserve">igitur V e T ſimile eſt Y f X,
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            & </s>
            <s xml:id="echoid-s7674" xml:space="preserve">pariter, &</s>
            <s xml:id="echoid-s7675" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7676" xml:space="preserve">Quoniam in ſectionibus ſimilibus V B, & </s>
            <s xml:id="echoid-s7677" xml:space="preserve">γ E axes tranſuerſi
              <lb/>
              <note position="left" xlink:label="note-0242-03" xlink:href="note-0242-03a" xml:space="preserve">12. huius.</note>
            lateribus rectis proportionales ſunt, & </s>
            <s xml:id="echoid-s7678" xml:space="preserve">ductæ ſunt ad axes ordinatim applicatæ
              <lb/>
            V Z, γ a, & </s>
            <s xml:id="echoid-s7679" xml:space="preserve">contingentes V e, γ f, eſtque rectangulum T Z e ad quadratum
              <lb/>
              <note position="left" xlink:label="note-0242-04" xlink:href="note-0242-04a" xml:space="preserve">37. lib. 1.</note>
            Z V, vt latus tranſuerſum ad rectum, pariterque rectangulum X a f ad qua-
              <lb/>
            dratum a γ, vt axis tranſuerſus ad erectum; </s>
            <s xml:id="echoid-s7680" xml:space="preserve">igitur rectangulũ T Z e adqua-
              <lb/>
            dratum Z V eandem proportionem habet, quàm rectangulum X a f ad quadra-
              <lb/>
            tum a γ, & </s>
            <s xml:id="echoid-s7681" xml:space="preserve">à verticibus V, γ duorum triangulorum V e T, & </s>
            <s xml:id="echoid-s7682" xml:space="preserve">γ f X ductæ
              <lb/>
            ſunt ad baſes rectæ linæ V Z, γ a efficientes angulos rectos, cum ordinatim
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              <figure xlink:label="fig-0242-01" xlink:href="fig-0242-01a" number="276">
                <image file="0242-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0242-01"/>
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            applicatæ ſint ad axes; </s>
            <s xml:id="echoid-s7683" xml:space="preserve">atque angulus V e Z oſtenſus eſt æqualis angulo γ f a,
              <lb/>
            igitur tertius angulus Z V e æqualis erit tertio angulo a γ f; </s>
            <s xml:id="echoid-s7684" xml:space="preserve">& </s>
            <s xml:id="echoid-s7685" xml:space="preserve">ideo duo triã-
              <lb/>
              <note position="left" xlink:label="note-0242-05" xlink:href="note-0242-05a" xml:space="preserve">Propof. 6
                <lb/>
              præmiſſ.</note>
            gula V T e, & </s>
            <s xml:id="echoid-s7686" xml:space="preserve">γ X f ſimilia erunt inter ſe: </s>
            <s xml:id="echoid-s7687" xml:space="preserve">& </s>
            <s xml:id="echoid-s7688" xml:space="preserve">propterea circa angulos æquales
              <lb/>
            T, & </s>
            <s xml:id="echoid-s7689" xml:space="preserve">X latus e T ad T V eandem proportionem habebit, quàm f X ad X γ:
              <lb/>
            </s>
            <s xml:id="echoid-s7690" xml:space="preserve">cumque duæ contingentes verticales V e, γ f parallelæ ſint ordinatim applicatis
              <lb/>
            N A, & </s>
            <s xml:id="echoid-s7691" xml:space="preserve">P D ad diametros V R, γ S, erit O e ad R V, vt e T ad T V; </s>
            <s xml:id="echoid-s7692" xml:space="preserve">pa-
              <lb/>
            riterque Q f ad S γ erit, vt f X ad X r: </s>
            <s xml:id="echoid-s7693" xml:space="preserve">erat autem e T ad T V, vt f X ad
              <lb/>
            X γ; </s>
            <s xml:id="echoid-s7694" xml:space="preserve">igitur pariter O e ad R V eandem proportionem habebit, quàm Q f ad
              <lb/>
              <note position="left" xlink:label="note-0242-06" xlink:href="note-0242-06a" xml:space="preserve">12. huius.</note>
            S γ; </s>
            <s xml:id="echoid-s7695" xml:space="preserve">ſed B I ad I A eſt, vt E K ad K D.</s>
            <s xml:id="echoid-s7696" xml:space="preserve"/>
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