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-div976" type="section" level="1" n="309">
          <pb o="323" file="0361" n="362" rhead="Conicor. Lib. VII."/>
          <p style="it">
            <s xml:id="echoid-s11442" xml:space="preserve">Dato latere recto I K diametri hyperboles I L reperire latus rectum
              <lb/>
              <note position="right" xlink:label="note-0361-01" xlink:href="note-0361-01a" xml:space="preserve">PROP. 2.
                <lb/>
              Addit.</note>
            alterius Diametri, quod æquale ſit lateri recto I K: </s>
            <s xml:id="echoid-s11443" xml:space="preserve">oportet autem,
              <lb/>
            vt Diameter I L cadat inter axim, @ aliam Diametrum, quæ ſub-
              <lb/>
            dupla ſit ſui erecti.</s>
            <s xml:id="echoid-s11444" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11445" xml:space="preserve">Reperiatur Diameter Q P, quæ ſubdupla ſit ſui erecti P R, eiuſque latus
              <lb/>
              <note position="right" xlink:label="note-0361-02" xlink:href="note-0361-02a" xml:space="preserve">ex 35. hu.</note>
            ſit M C; </s>
            <s xml:id="echoid-s11446" xml:space="preserve">ergo ex hypotheſi I L cadet inter axim A C, & </s>
            <s xml:id="echoid-s11447" xml:space="preserve">Diametrum P Q,
              <lb/>
            & </s>
            <s xml:id="echoid-s11448" xml:space="preserve">propterea terminus E lateris C E cadet inter A, & </s>
            <s xml:id="echoid-s11449" xml:space="preserve">M, igitur reperiri po-
              <lb/>
            terit V G, quæ ad G E eandem proportionem habeat, quàm maior M H ad
              <lb/>
            minorem H E, & </s>
            <s xml:id="echoid-s11450" xml:space="preserve">vt prius, lateris C V ducatur diameter S T, cuius latus
              <lb/>
            rectum S Z: </s>
            <s xml:id="echoid-s11451" xml:space="preserve">dico S Z æquale eße I K: </s>
            <s xml:id="echoid-s11452" xml:space="preserve">quia V G ad G E eſt, vt M H, ſeu
              <lb/>
              <note position="right" xlink:label="note-0361-03" xlink:href="note-0361-03a" xml:space="preserve">Lem. 4.
                <lb/>
              huius.
                <lb/>
              Lem. 5.
                <lb/>
              huius.</note>
            G H ad H E, ergo rectangulum ſub V G E in E H æquale eſt quadrato G E,
              <lb/>
            ideoque S Z æquale I K; </s>
            <s xml:id="echoid-s11453" xml:space="preserve">quod erat propoſitum.</s>
            <s xml:id="echoid-s11454" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11455" xml:space="preserve">Deducitur ex prima propoſitione additarum quod in aliqua hyperbola reperi-
              <lb/>
            ri poßunt tria diametrorum latera recta æqualia inter ſe; </s>
            <s xml:id="echoid-s11456" xml:space="preserve">ſi nimirum in hyper-
              <lb/>
            bola, cuius axis C A minor ſit medietate eius lateris recti, reperiantur vtrin-
              <lb/>
            que duæ diametri b a, quarum latera recta a c æqualia ſint ipſi A F; </s>
            <s xml:id="echoid-s11457" xml:space="preserve">tunc
              <lb/>
            quidem tria illa latera recta æqualia erunt inter ſe: </s>
            <s xml:id="echoid-s11458" xml:space="preserve">reliqua verò latera recta
              <lb/>
            diametrorum cadentium inter A, & </s>
            <s xml:id="echoid-s11459" xml:space="preserve">a maiora erunt latere recto A F; </s>
            <s xml:id="echoid-s11460" xml:space="preserve">& </s>
            <s xml:id="echoid-s11461" xml:space="preserve">la-
              <lb/>
            tera recta diametrorum cadentium vltra punctum a ad partes B maiora ſunt
              <lb/>
              <note position="right" xlink:label="note-0361-04" xlink:href="note-0361-04a" xml:space="preserve">ex 35.
                <lb/>
              huius.</note>
            latere recto a c, propterea quod magis recedunt ab omnium minimo latere re-
              <lb/>
            cto P R.</s>
            <s xml:id="echoid-s11462" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11463" xml:space="preserve">Simili modo in eadem hyperbola reperiri poßunt quatuor diametrorum latera
              <lb/>
            recta æqualia inter ſe, ſi nimirum ex ſecunda propoſitione additarum dato la-
              <lb/>
            tere recto I K diametri I L reperiatur æquale latus rectum S Z alterius diame-
              <lb/>
            tri S T, & </s>
            <s xml:id="echoid-s11464" xml:space="preserve">ex altera parte axis ducantur duæ aliæ diametri æquè ab axi re-
              <lb/>
            motæ ac illæ, erunt quatuor recta latera earum æqualia inter ſe, & </s>
            <s xml:id="echoid-s11465" xml:space="preserve">maiora
              <lb/>
            quolibet latere recto diametri cadentis inter I, & </s>
            <s xml:id="echoid-s11466" xml:space="preserve">S ad vtraſque partes axis:
              <lb/>
            </s>
            <s xml:id="echoid-s11467" xml:space="preserve">minora verò erunt quolibet latere recto diametri cadentis vltra punctum I ad
              <lb/>
            partes verticis A, vel infra puncta S ad partes a, vt deducitur ex 35. </s>
            <s xml:id="echoid-s11468" xml:space="preserve">huius.</s>
            <s xml:id="echoid-s11469" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div984" type="section" level="1" n="310">
          <head xml:id="echoid-head383" xml:space="preserve">SECTIO SEPTIMA</head>
          <head xml:id="echoid-head384" xml:space="preserve">Continens Propoſit. XXXVIII. XXXIX.
            <lb/>
          & XXXX.</head>
          <head xml:id="echoid-head385" xml:space="preserve">PROPOSITIO XXXVIII.</head>
          <p>
            <s xml:id="echoid-s11470" xml:space="preserve">IN hyperbole axis inclinatus ſi non fuerit minortriente erecti
              <lb/>
            ipſius, erunt duo latera figuræ axis minora, quàm duo late-
              <lb/>
            ra figuræ cuiuslibet inclinatæ coniugatarum, quæ in eadem ſe-
              <lb/>
            ctione conſiſtunt, & </s>
            <s xml:id="echoid-s11471" xml:space="preserve">duo latera figuræ inclinati proximioris axi
              <lb/>
            minora ſunt, quàm duo latera figuræ remotioris inclinati.</s>
            <s xml:id="echoid-s11472" xml:space="preserve"/>
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