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="185" file="0223" n="223" rhead="Conicor. Lib. VI."/>
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            <s xml:id="echoid-s7017" xml:space="preserve">Secentur abſcißæ G B, & </s>
            <s xml:id="echoid-s7018" xml:space="preserve">H E in ijſdem rationibus, ducanturque ordinatim
              <lb/>
            applicatæ vt in precedenti factum eſt. </s>
            <s xml:id="echoid-s7019" xml:space="preserve">Quoniam G B ad B I eſt, vt H E ad E
              <lb/>
            K, & </s>
            <s xml:id="echoid-s7020" xml:space="preserve">inuertendo Z B ad B G eſt, vt a E ad E H, ergo ex æquali ordinata Z
              <lb/>
            B latus tranſuerſum ad B I latus rectum erit, vt a E latus tranſuerſum alte-
              <lb/>
            rius ſectionis ad E K eius latus rectum: </s>
            <s xml:id="echoid-s7021" xml:space="preserve">eſt verò rectangulum Z G B ad qua-
              <lb/>
            dratum ordinatim applicatæ G A, vt latus tranſuerſum Z B ad rectum B I;
              <lb/>
            </s>
            <s xml:id="echoid-s7022" xml:space="preserve">pariterque rectangulum a H E ad quadratum ordinatim applicatæ D H, vt
              <lb/>
            tranſuerſum a E ad latus rectum E K, ſuntque prædicta latera figurarum oſtẽ-
              <lb/>
            ſa proportionalia; </s>
            <s xml:id="echoid-s7023" xml:space="preserve">igitur rectangulum Z G B ad quadratum A G eandem pro-
              <lb/>
            portionem habet, quàm rectangulum a H E ad quadratum D H; </s>
            <s xml:id="echoid-s7024" xml:space="preserve">ſed quadratum
              <lb/>
            B G ad rectangulum Z G B eandem proportionem habet, quàm G B ad G Z
              <lb/>
            (propterea quod G B eſt illorum altitudo communis) pariterque quadratum E
              <lb/>
            H ad rectangulum a H E eſt, vt H E ad H a, ſeu vt G B ad G Z; </s>
            <s xml:id="echoid-s7025" xml:space="preserve">igitur qua-
              <lb/>
            dratum G B ad rectangulum Z G B eandem proportionem habebit, quàm qua-
              <lb/>
            dratum E H ad rectangulum a H E; </s>
            <s xml:id="echoid-s7026" xml:space="preserve">quare ex æquali quadratum G B ad qua-
              <lb/>
            dratum G A eandem proportionem habebit, quàm quadratum E H ad quadratũ
              <lb/>
            H D; </s>
            <s xml:id="echoid-s7027" xml:space="preserve">ideoque inuertendo A G ad G B erit vt D H ad H E. </s>
            <s xml:id="echoid-s7028" xml:space="preserve">Rurſus, quia in-
              <lb/>
            uertendo L B ad B G eſt vt N E ad E H; </s>
            <s xml:id="echoid-s7029" xml:space="preserve">ſed G B, atque H E ad latera trã-
              <lb/>
            ſuerſa proportionalia ſunt; </s>
            <s xml:id="echoid-s7030" xml:space="preserve">igitur L B ad B Z erit vt N E ad E a; </s>
            <s xml:id="echoid-s7031" xml:space="preserve">& </s>
            <s xml:id="echoid-s7032" xml:space="preserve">propte-
              <lb/>
            rea, vt prius quadratum L B ad rectangulum Z L B erit, vt quadratum E N
              <lb/>
            ad rectangulum a N E; </s>
            <s xml:id="echoid-s7033" xml:space="preserve">eſtque rectangulum Z L B ad quadratum ordinatim
              <lb/>
              <figure xlink:label="fig-0223-01" xlink:href="fig-0223-01a" number="250">
                <image file="0223-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0223-01"/>
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            applicatæ P L, vt rectangulum a N E ad quadratum T N, (ſcilicet vt latera
              <lb/>
            tranſuerſa ad recta, quæ proportionalia oſtenſa ſunt); </s>
            <s xml:id="echoid-s7034" xml:space="preserve">igitur ex æquali ordinata
              <lb/>
            quadratũ B L ad quadratum P L eandem proportionẽ habebit, quàm quadratũ
              <lb/>
            E N ad quadratum T N; </s>
            <s xml:id="echoid-s7035" xml:space="preserve">quare vt prius dictum eſt, P L ad L B eandem pro-
              <lb/>
            portionem habebit, quàm T N ad N E; </s>
            <s xml:id="echoid-s7036" xml:space="preserve">& </s>
            <s xml:id="echoid-s7037" xml:space="preserve">hoc ſemper contingit in reliquis om-
              <lb/>
            nibus diuiſionibus abſciſſarum in eiſdem rationibus ſectis; </s>
            <s xml:id="echoid-s7038" xml:space="preserve">ſuntque anguli G, & </s>
            <s xml:id="echoid-s7039" xml:space="preserve">
              <lb/>
            H æquales inter ſe, licet non recti, igitur (ex definitione 7.) </s>
            <s xml:id="echoid-s7040" xml:space="preserve">ſegmenta A B C,
              <lb/>
            & </s>
            <s xml:id="echoid-s7041" xml:space="preserve">D E F ſimilia ſunt inter ſe. </s>
            <s xml:id="echoid-s7042" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s7043" xml:space="preserve"/>
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