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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            <s xml:id="echoid-s12314" xml:space="preserve">
              <pb o="357" file="0395" n="396" rhead="Conicor. Lib. VII."/>
            dratis' ex T S, & </s>
            <s xml:id="echoid-s12315" xml:space="preserve">S Z: </s>
            <s xml:id="echoid-s12316" xml:space="preserve">igitur ſumma duorum quadratorum ex Q P, & </s>
            <s xml:id="echoid-s12317" xml:space="preserve">ex
              <lb/>
            P R minor eſt ſumma quadratorum duorum laterum figuræ cuiuſlibet alterius
              <lb/>
            diametri eiuſdem ellipſis.</s>
            <s xml:id="echoid-s12318" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12319" xml:space="preserve">In ellipſi reperire diametrum, cuius duo quadrata laterum figuræ eius
              <lb/>
              <note position="right" xlink:label="note-0395-01" xlink:href="note-0395-01a" xml:space="preserve">PROP. 7.
                <lb/>
              Addit</note>
            æqualia ſint quadratis laterum figuræ axis maioris: </s>
            <s xml:id="echoid-s12320" xml:space="preserve">oportet autem Vt
              <lb/>
            quadratum axis maioris A C maius ſit ſemiquadrato ex ſumma laterum
              <lb/>
            C A F figuræ eius.</s>
            <s xml:id="echoid-s12321" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12322" xml:space="preserve">Quia ex hypotheſi quadratum axis maioris A C maius eſt ſemiquadrato ex
              <lb/>
            ſumma C A F, ergo, vt in nota prop. </s>
            <s xml:id="echoid-s12323" xml:space="preserve">48. </s>
            <s xml:id="echoid-s12324" xml:space="preserve">dictum eſt, duplum quadrati ex A
              <lb/>
            H maius eſt quadrato ex H G; </s>
            <s xml:id="echoid-s12325" xml:space="preserve">fiat duplum rectanguli e H A æquale quadra-
              <lb/>
            to ex G H, & </s>
            <s xml:id="echoid-s12326" xml:space="preserve">lateris C e fiat diameter a b cuius erectus a c. </s>
            <s xml:id="echoid-s12327" xml:space="preserve">Dico hanc eſſe
              <lb/>
            diametrum quæſitam.</s>
            <s xml:id="echoid-s12328" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12329" xml:space="preserve">Quoniam duplum rectanguli e H A æquale eſt quadrato ex G H, ergo dup-
              <lb/>
            lum e H ad H G eſt vt G H ad H A, eritq; </s>
            <s xml:id="echoid-s12330" xml:space="preserve">duplum rectanguli ex differentia
              <lb/>
              <note position="right" xlink:label="note-0395-02" xlink:href="note-0395-02a" xml:space="preserve">Lem 13.</note>
            ipſarum A H, & </s>
            <s xml:id="echoid-s12331" xml:space="preserve">G e in e H æquale quadratis ex G e, & </s>
            <s xml:id="echoid-s12332" xml:space="preserve">ex e H, & </s>
            <s xml:id="echoid-s12333" xml:space="preserve">ſum-
              <lb/>
              <note position="right" xlink:label="note-0395-03" xlink:href="note-0395-03a" xml:space="preserve">Lem. 15.</note>
            ma quadratorum ex b a, & </s>
            <s xml:id="echoid-s12334" xml:space="preserve">ex a c æqualis erit quadratorum ſummæ ex A C,
              <lb/>
            & </s>
            <s xml:id="echoid-s12335" xml:space="preserve">ex A F, quod erat oſtendendum.</s>
            <s xml:id="echoid-s12336" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12337" xml:space="preserve">In eadem ellypſi diametrum reperire, cuius duo quadrata laterum
              <lb/>
              <note position="right" xlink:label="note-0395-04" xlink:href="note-0395-04a" xml:space="preserve">PROP.
                <lb/>
              8. Addit.</note>
            figuræ eius æqualia ſint quadratis laterum figuræ datæ diametri I L:
              <lb/>
            </s>
            <s xml:id="echoid-s12338" xml:space="preserve">oportet autem vt I L cadat inter axim, & </s>
            <s xml:id="echoid-s12339" xml:space="preserve">diametrum P Q, cuius
              <lb/>
            quadratum ſubduplum ſit quadrati ex ſumma laterum Q P R.</s>
            <s xml:id="echoid-s12340" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12341" xml:space="preserve">Sit C E latus diametri I L, & </s>
            <s xml:id="echoid-s12342" xml:space="preserve">fiat duplum V H ad H G, vt G H ad H
              <lb/>
            E, & </s>
            <s xml:id="echoid-s12343" xml:space="preserve">ponatur S T diameter lateris C V, cuius erectus ſit S Z: </s>
            <s xml:id="echoid-s12344" xml:space="preserve">erit igitur
              <lb/>
              <note position="right" xlink:label="note-0395-05" xlink:href="note-0395-05a" xml:space="preserve">Lem. 13.
                <lb/>
              huius.</note>
            duplum rectanguli ex differentia ipſarum E H, & </s>
            <s xml:id="echoid-s12345" xml:space="preserve">G V in V H æquale qua-
              <lb/>
              <note position="right" xlink:label="note-0395-06" xlink:href="note-0395-06a" xml:space="preserve">Lem. 15.
                <lb/>
              huius.</note>
            dratis ex G V, & </s>
            <s xml:id="echoid-s12346" xml:space="preserve">ex V H, ideoque ſumma quadratorum ex L I, & </s>
            <s xml:id="echoid-s12347" xml:space="preserve">
              <lb/>
            ex I K æqualis erit quadratorum ſummæ ex T S, & </s>
            <s xml:id="echoid-s12348" xml:space="preserve">S Z, quod propoſitum
              <lb/>
            ſuerat.</s>
            <s xml:id="echoid-s12349" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s12350" xml:space="preserve">Colligitur ſimiliter ex 7. </s>
            <s xml:id="echoid-s12351" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s12352" xml:space="preserve">additarum, quod in vna ellypſi tres dia-
              <lb/>
            metri reperiri poßunt, quarum ſummæ quadratorum laterum æquales ſint inter
              <lb/>
            ſe: </s>
            <s xml:id="echoid-s12353" xml:space="preserve">& </s>
            <s xml:id="echoid-s12354" xml:space="preserve">ex 8. </s>
            <s xml:id="echoid-s12355" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s12356" xml:space="preserve">additarum deducitur, quod quatuor diametrorum eiuſ-
              <lb/>
            dem ellypſis laterum ſummæ quadratorum æquales poſſunt eſſe inter ſe, ſed
              <lb/>
            oportet vt quadratum axis maioris datæ ellypſis maius ſit, quàm dimidium qua-
              <lb/>
            drati ex ſumma laterum figuræ axis C A F.</s>
            <s xml:id="echoid-s12357" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12358" xml:space="preserve">Duo latera figuræ axis tranſuerſi minora ſunt duobus lateribus ſiguræ
              <lb/>
              <note position="left" xlink:label="note-0395-07" xlink:href="note-0395-07a" xml:space="preserve">a</note>
            cæterarum diametrorum, & </s>
            <s xml:id="echoid-s12359" xml:space="preserve">duo latera figuræ diametri axi proximioris
              <lb/>
            minora ſunt duobus lateribus figuræ remotioris, &</s>
            <s xml:id="echoid-s12360" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12361" xml:space="preserve">Addidi ea, quæ defi-
              <lb/>
            cere videbantur in hoc textu.</s>
            <s xml:id="echoid-s12362" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12363" xml:space="preserve">Iiſdem figuris manentibus cum ſuis ſignis oſtendatur quod duplum
              <lb/>
              <note position="left" xlink:label="note-0395-08" xlink:href="note-0395-08a" xml:space="preserve">b</note>
            quadrati A C, ſi non exceſſerit F, quod diameter eſt illius figuræ minor,
              <lb/>
            quàm diameter ſiguræ I L, & </s>
            <s xml:id="echoid-s12364" xml:space="preserve">diameter figuræ I L, quàm diameter figuræ
              <lb/>
            P Q, &</s>
            <s xml:id="echoid-s12365" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12366" xml:space="preserve">Legendum puto vt in textu apparet.</s>
            <s xml:id="echoid-s12367" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12368" xml:space="preserve">Et ſic oſtendetur quod ſi punctum V inciderit ſuper D A, & </s>
            <s xml:id="echoid-s12369" xml:space="preserve">oſtende-
              <lb/>
              <note position="left" xlink:label="note-0395-09" xlink:href="note-0395-09a" xml:space="preserve">c</note>
            tur D, & </s>
            <s xml:id="echoid-s12370" xml:space="preserve">M, &</s>
            <s xml:id="echoid-s12371" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12372" xml:space="preserve">Legendum puto, vt in textu videre eſt.</s>
            <s xml:id="echoid-s12373" xml:space="preserve"/>
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