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

Page concordance

< >
Scan Original
91 53
92 54
93 55
94 56
95 57
96 58
97 59
98 60
99 61
100 62
101 63
102 64
103 65
104 66
105 67
106 68
107 69
108 70
109 71
110 72
111 73
112 74
113 75
114 76
115 77
116 78
117 79
118 80
119 81
120 82
< >
page |< < (138) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <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>
          </p>
        </div>
      </text>
    </echo>
Impressum