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-div514" type="section" level="1" n="168">
          <p style="it">
            <s xml:id="echoid-s5394" xml:space="preserve">
              <pb o="138" file="0176" n="176" rhead="Apollonij Pergæi"/>
            rito reiectas à Mydorgio ſuiſſe, nam licet latera tranſuerſa proportiona-
              <lb/>
            lia ſint lateribus rectis, non tamen duæ eiuſdem nominis ſectiones ſimi-
              <lb/>
            les erunt, niſi diametri æquè inclinatæ ſint ad ordinatim ad eas applica-
              <lb/>
            tas: </s>
            <s xml:id="echoid-s5395" xml:space="preserve">tandem deſinitionem Mydorgij ſimilium ſectionum pariter imperfe-
              <lb/>
            ctam eſſe ſuſpicor; </s>
            <s xml:id="echoid-s5396" xml:space="preserve">nam licet duæ ſectiones, quibus competit tradita de-
              <lb/>
            finitio, ſeu paſsio eiuſdem definitionis, ſint reuera ſimiles, non tamen è
              <lb/>
            conuerſo ſimilibus ſectionibus conuenit ſolummodo definitio, ſeu eius paſ-
              <lb/>
            ſio, curn aliquando appoſita paſsio in eiſdem reperiatur: </s>
            <s xml:id="echoid-s5397" xml:space="preserve">quod perinde eſt,
              <lb/>
            ac ſi quis putaret triangulum æquilaterum aliquando latera inæqualia ha-
              <lb/>
            bere poſſe.</s>
            <s xml:id="echoid-s5398" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5399" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s5400" xml:space="preserve">In hac deſinitione manifeſtè aliquid deſideratur: </s>
            <s xml:id="echoid-s5401" xml:space="preserve">inquit enim (Coni
              <lb/>
            fimiles ſunt quorum axium proportio ad diametros ſuarum baſium eadem
              <lb/>
            eſt.) </s>
            <s xml:id="echoid-s5402" xml:space="preserve">Quod quidem verificatur tantummodo in conis rectis: </s>
            <s xml:id="echoid-s5403" xml:space="preserve">at in ſcalenis de-
              <lb/>
            bent neceſſario axes conorum efficere æquales inclinationes ſuper baſes: </s>
            <s xml:id="echoid-s5404" xml:space="preserve">Quod
              <lb/>
            quidem in ſequentibus propoſitionibus manifeſtè ab Apollonio declaratur. </s>
            <s xml:id="echoid-s5405" xml:space="preserve">Ita-
              <lb/>
            que textum hac ratione reſtitui debere puto. </s>
            <s xml:id="echoid-s5406" xml:space="preserve">Coni ſimiles ſunt, quorum axes æ-
              <lb/>
            que ad baſes inclinati ad diametros baſium proportionales ſunt.</s>
            <s xml:id="echoid-s5407" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s5408" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s5409" xml:space="preserve">Sectio genita in ſuperſicie coni à plano eum ſecante, non per verticem
              <lb/>
            eius ducto dicitur in dicto cono poſita, & </s>
            <s xml:id="echoid-s5410" xml:space="preserve">contenta; </s>
            <s xml:id="echoid-s5411" xml:space="preserve">& </s>
            <s xml:id="echoid-s5412" xml:space="preserve">conus ille continere di-
              <lb/>
            citur eandem ſectionem: </s>
            <s xml:id="echoid-s5413" xml:space="preserve">& </s>
            <s xml:id="echoid-s5414" xml:space="preserve">licet coniſectio exhibeatur extra conum; </s>
            <s xml:id="echoid-s5415" xml:space="preserve">dicetur ni-
              <lb/>
            hilominus contineri ab illo cono, in quo ſectio illa accomodari poteſt, ſeu in quo
              <lb/>
            ab aliquo plano ſecante effici poteſt in coni ſuperficie eadem illa coniſectio.</s>
            <s xml:id="echoid-s5416" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div515" type="section" level="1" n="169">
          <head xml:id="echoid-head221" xml:space="preserve">SECTIO PRIMA</head>
          <head xml:id="echoid-head222" xml:space="preserve">Continens Propoſit. I. II. IV. & X.</head>
          <head xml:id="echoid-head223" xml:space="preserve">PROPOSITIO I.</head>
          <p>
            <s xml:id="echoid-s5417" xml:space="preserve">QVælibet duæ ſectiones parabolicæ A B, C D, ſi habue-
              <lb/>
              <note position="right" xlink:label="note-0176-01" xlink:href="note-0176-01a" xml:space="preserve">a</note>
            rint axium erectos A I, C N æquales: </s>
            <s xml:id="echoid-s5418" xml:space="preserve">erunt inter ſe æ-
              <lb/>
            quales. </s>
            <s xml:id="echoid-s5419" xml:space="preserve">Si verò duæ illæ ſectiones fuerint æquales,
              <lb/>
            erunt axium erecta æqualia inter ſe.</s>
            <s xml:id="echoid-s5420" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5421" xml:space="preserve">Quoniam ſuperpoſita axi C H ſuper axim A G, cadet ſectio C D ſu-
              <lb/>
              <note position="right" xlink:label="note-0176-02" xlink:href="note-0176-02a" xml:space="preserve">b</note>
            per ſectionem A B: </s>
            <s xml:id="echoid-s5422" xml:space="preserve">ſi enim cadere non concedatur ſuper illam, ſigne-
              <lb/>
            tur (ſi fieri poteſt) punctum eius D, extra ſectionem A B cadens: </s>
            <s xml:id="echoid-s5423" xml:space="preserve">& </s>
            <s xml:id="echoid-s5424" xml:space="preserve">
              <lb/>
            educatur D F perpendicularis ad axim; </s>
            <s xml:id="echoid-s5425" xml:space="preserve">& </s>
            <s xml:id="echoid-s5426" xml:space="preserve">perficiatur planum rectangu-
              <lb/>
            lum F N, & </s>
            <s xml:id="echoid-s5427" xml:space="preserve">ab axi A G ſecetur A E æqualis C F; </s>
            <s xml:id="echoid-s5428" xml:space="preserve">& </s>
            <s xml:id="echoid-s5429" xml:space="preserve">educatur ex </s>
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    </echo>
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