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-div1119" type="section" level="1" n="356">
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              <pb o="390" file="0428" n="429" rhead="Archimedis"/>
            ipſius A B, eſtque nota A D medietas differentiæ inter diametrum A C, & </s>
            <s xml:id="echoid-s13081" xml:space="preserve">chor-
              <lb/>
            dam differentiæ F C; </s>
            <s xml:id="echoid-s13082" xml:space="preserve">at propoſitio Archimedea verificatur in quolibet circuli
              <lb/>
            ſegmento ſiue maiori, ſiue minori; </s>
            <s xml:id="echoid-s13083" xml:space="preserve">ex datis enim circumferentijs A C, A B,
              <lb/>
              <figure xlink:label="fig-0428-01" xlink:href="fig-0428-01a" number="493">
                <image file="0428-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0428-01"/>
              </figure>
            A F, & </s>
            <s xml:id="echoid-s13084" xml:space="preserve">F C vna cum cordis A C, & </s>
            <s xml:id="echoid-s13085" xml:space="preserve">F C, haberi quidem poteſt chorda A B
              <lb/>
            paulo difficilius, ſi nimirum ex chorda A C tollatur chorda F C, & </s>
            <s xml:id="echoid-s13086" xml:space="preserve">differen-
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            tia A E bifariam ſecetur in D, & </s>
            <s xml:id="echoid-s13087" xml:space="preserve">ex arcu cognito B C datur angulus A, atque
              <lb/>
            angulus D rectus eſt, ergo triangulum A B D ſpecie notum erit, & </s>
            <s xml:id="echoid-s13088" xml:space="preserve">propterea
              <lb/>
            proportio D A ad A B cognita erit, eſtque D A longitudine data, igitur A B
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            longitudine innoteſcet.</s>
            <s xml:id="echoid-s13089" xml:space="preserve"/>
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            <s xml:id="echoid-s13090" xml:space="preserve">Notandum eſt quod figura appoſita in hac propoſ. </s>
            <s xml:id="echoid-s13091" xml:space="preserve">non exprimit omnes caſus
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            propoſitionis, quandoquidem ſemicirculus eſt A B C, & </s>
            <s xml:id="echoid-s13092" xml:space="preserve">propterea ex præceden-
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            tibus erroribus Arabici expoſitoris ſuſpicari licet non ritè eum percepiſſe Archi-
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            medis mentem.</s>
            <s xml:id="echoid-s13093" xml:space="preserve"/>
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          <head xml:id="echoid-head449" xml:space="preserve">PROPOSITIO IV.</head>
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            <s xml:id="echoid-s13094" xml:space="preserve">A B C ſemicirculus, & </s>
            <s xml:id="echoid-s13095" xml:space="preserve">fiant ſuper
              <lb/>
              <figure xlink:label="fig-0428-02" xlink:href="fig-0428-02a" number="494">
                <image file="0428-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0428-02"/>
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            A C diametrum duo ſemicirculi, quo-
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            rum vnus A D, alter vero D C, & </s>
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            D B perpendicularis, vtique figura pro-
              <lb/>
            ueniens, quam vocat Archimedes AR-
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            BELON, eſt ſuperficies comprehenſa ab
              <lb/>
            arcu ſemicirculi maioris, & </s>
            <s xml:id="echoid-s13097" xml:space="preserve">duabus cir-
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            cumferentijs ſemicirculorum minorum, eſt æqualis circulo, cuius
              <lb/>
            diameter eſt perpendicularis D B.</s>
            <s xml:id="echoid-s13098" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13099" xml:space="preserve">Demonſtratio. </s>
            <s xml:id="echoid-s13100" xml:space="preserve">Quia linea D B media proportionalis eſt inter duas li-
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            neas D A, D C, erit planum A D in D C æquale quadrato D B, & </s>
            <s xml:id="echoid-s13101" xml:space="preserve">
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            ponamus A D in D C cum duobus quadratis A D, D C communiter,
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            fiet planum A D in D C bis cum duobus quadratis A D, D C, nempe
              <lb/>
            quadratum A C, æquale duplo quadrati D B cum duobus quadratis A
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            D, D C, & </s>
            <s xml:id="echoid-s13102" xml:space="preserve">proportio circulorum eadem eſt, ac proportio </s>
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