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-div1022" type="section" level="1" n="325">
          <pb o="341" file="0379" n="380" rhead="Conicor. Lib. VII."/>
          <p style="it">
            <s xml:id="echoid-s11921" xml:space="preserve">In hyperbola reperire diametrum, cuius figuræ duo quadrata laterum
              <lb/>
              <note position="right" xlink:label="note-0379-01" xlink:href="note-0379-01a" xml:space="preserve">PROP.
                <lb/>
              5. Addit.</note>
            æqualia ſint quadratis laterum figuræ axis: </s>
            <s xml:id="echoid-s11922" xml:space="preserve">oportet autem vt quadra-
              <lb/>
            tum axis C A minus ſit ſemiquadrato ex differentia laterum ſiguræ eius
              <lb/>
            C A, & </s>
            <s xml:id="echoid-s11923" xml:space="preserve">A F.</s>
            <s xml:id="echoid-s11924" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11925" xml:space="preserve">Quia ex hypotheſi quadratum axis A C minus eſt ſemiquadrato ex differen-
              <lb/>
            tia laterum figuræ A C, A F, vt in nota propoſit. </s>
            <s xml:id="echoid-s11926" xml:space="preserve">46. </s>
            <s xml:id="echoid-s11927" xml:space="preserve">dictum eſt, quadratum
              <lb/>
            ex A H minus eſt ſemiquadrato ex G H: </s>
            <s xml:id="echoid-s11928" xml:space="preserve">fiat duplum e H ad H G, vt G H
              <lb/>
              <note position="right" xlink:label="note-0379-02" xlink:href="note-0379-02a" xml:space="preserve">Lem. 10.
                <lb/>
              huius.</note>
            ad H A, & </s>
            <s xml:id="echoid-s11929" xml:space="preserve">lateris C e ducatur diameter b a, cuius erectus c a, ergo duplum
              <lb/>
            rectanguli ex ſumma G A, e H in A H æquale eſt ſummæ quadratorum ex G A,
              <lb/>
              <note position="right" xlink:label="note-0379-03" xlink:href="note-0379-03a" xml:space="preserve">I em. 12.
                <lb/>
              huius.</note>
            & </s>
            <s xml:id="echoid-s11930" xml:space="preserve">ex A H, & </s>
            <s xml:id="echoid-s11931" xml:space="preserve">ſumma quadratorum ex a b, & </s>
            <s xml:id="echoid-s11932" xml:space="preserve">ex a c æqualis erit quadrato-
              <lb/>
            rum ſummæ ex A C, & </s>
            <s xml:id="echoid-s11933" xml:space="preserve">ex A F, quod erat oſtendendum.</s>
            <s xml:id="echoid-s11934" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11935" xml:space="preserve">In eadem hyperbola diametrum reperire, cuius figuræ duo quadrata,
              <lb/>
              <note position="right" xlink:label="note-0379-04" xlink:href="note-0379-04a" xml:space="preserve">PROP. 6.
                <lb/>
              Addit</note>
            laterum æqualia ſint quadratis laterum figuræ datæ diametri I L: </s>
            <s xml:id="echoid-s11936" xml:space="preserve">opor-
              <lb/>
            tet autem vt I L cadat inter axim, & </s>
            <s xml:id="echoid-s11937" xml:space="preserve">diametrum P Q, cuius qua-
              <lb/>
            dratum ſubduplum ſit quadrati ex differentia P Q, & </s>
            <s xml:id="echoid-s11938" xml:space="preserve">ex P R.</s>
            <s xml:id="echoid-s11939" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11940" xml:space="preserve">Sit C E latus diametri I L, & </s>
            <s xml:id="echoid-s11941" xml:space="preserve">fiat duplum V H ad H G, vt G H ad H E,
              <lb/>
            & </s>
            <s xml:id="echoid-s11942" xml:space="preserve">ponatur S T diameter lateris C V, cuius erectus ſit S Z: </s>
            <s xml:id="echoid-s11943" xml:space="preserve">erit igitur duplũ
              <lb/>
              <note position="right" xlink:label="note-0379-05" xlink:href="note-0379-05a" xml:space="preserve">Lem. 10.</note>
            rectanguli ex G E, & </s>
            <s xml:id="echoid-s11944" xml:space="preserve">V H in E H æquale quadratis ex G E, & </s>
            <s xml:id="echoid-s11945" xml:space="preserve">ex E H, & </s>
            <s xml:id="echoid-s11946" xml:space="preserve">
              <lb/>
            propterea ſumma quadratorum ex T S, & </s>
            <s xml:id="echoid-s11947" xml:space="preserve">ex S Z æqualis erit quadratorum,
              <lb/>
              <note position="right" xlink:label="note-0379-06" xlink:href="note-0379-06a" xml:space="preserve">Lem. 12.
                <lb/>
              huius.</note>
            ſummæ ex L I, & </s>
            <s xml:id="echoid-s11948" xml:space="preserve">ex I K, quod erat propoſitum.</s>
            <s xml:id="echoid-s11949" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11950" xml:space="preserve">Deducitur pariter ex 5. </s>
            <s xml:id="echoid-s11951" xml:space="preserve">propoſitione additarum in eadem hyperbola tres dia-
              <lb/>
            metros reperiri poſſe, quarum laterum ſummæ quadratorum æquales ſint in-
              <lb/>
            ter ſe.</s>
            <s xml:id="echoid-s11952" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11953" xml:space="preserve">Et ex 6. </s>
            <s xml:id="echoid-s11954" xml:space="preserve">propoſitione additarum deducitur, quod quatuor diametrorum eiuſ-
              <lb/>
            dem hyperbolæ laterum ſummæ quadratorum æquales eße posſunt inter ſe.</s>
            <s xml:id="echoid-s11955" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11956" xml:space="preserve">Et educamus inter A P inclinatam I L: </s>
            <s xml:id="echoid-s11957" xml:space="preserve">quia quadruplum quadrati M
              <lb/>
              <note position="left" xlink:label="note-0379-07" xlink:href="note-0379-07a" xml:space="preserve">a</note>
            H æquale eſt quadrato H G, &</s>
            <s xml:id="echoid-s11958" xml:space="preserve">c. </s>
            <s xml:id="echoid-s11959" xml:space="preserve">Suppleri debent ea, quæ deficiunt, alioqui
              <lb/>
            conſtructio imperfecta eßet: </s>
            <s xml:id="echoid-s11960" xml:space="preserve">duci igitur debet C B parallela diametro I L,
              <lb/>
            quæ occurrat ſectioni ad punctum B, à quo ad axim perpendicularis ducatur
              <lb/>
            B E ſecans axim in E.</s>
            <s xml:id="echoid-s11961" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1032" type="section" level="1" n="326">
          <head xml:id="echoid-head403" xml:space="preserve">SECTIO NONA</head>
          <head xml:id="echoid-head404" xml:space="preserve">Continens Propoſit. XXXXI. XXXXVII.
            <lb/>
          & XXXXVIII.</head>
          <p>
            <s xml:id="echoid-s11962" xml:space="preserve">IN ellipſi duo latera figuræ maioris axis tranſuerſi minora ſunt
              <lb/>
              <note position="left" xlink:label="note-0379-08" xlink:href="note-0379-08a" xml:space="preserve">a</note>
            duobus lateribus figuræ cuiuslibet alterius diametri, & </s>
            <s xml:id="echoid-s11963" xml:space="preserve">duo
              <lb/>
            latera figuræ diametri axi maiori proximioris minora ſunt duo-
              <lb/>
            bus lateribus figuræ diametri remotioris.</s>
            <s xml:id="echoid-s11964" xml:space="preserve"/>
          </p>
        </div>
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