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
61 23
62 24
63 25
64 26
65 27
66 28
67 29
68 30
69 31
70 32
71 33
72 34
73 35
74 36
75 37
76 38
77 39
78 40
79 41
80 42
81 43
82 44
83 45
84 46
85 47
86 48
87 49
88 50
89 51
90 52
< >
page |< < (80) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div317" type="section" level="1" n="106">
          <p style="it">
            <s xml:id="echoid-s3335" xml:space="preserve">
              <pb o="80" file="0118" n="118" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0118-01" xlink:href="fig-0118-01a" number="99">
                <image file="0118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0118-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s3336" xml:space="preserve">quia A H cadit infra A G ad partes axis cum D A, ad quam illa perpen-
              <lb/>
            dicularis eſt, extendatur vltra axim A E, nec poſsit inter tangentem A G, & </s>
            <s xml:id="echoid-s3337" xml:space="preserve">
              <lb/>
            ſectionem conicam A B, aliqua recta linea intercipi; </s>
            <s xml:id="echoid-s3338" xml:space="preserve">igitur A H cadit intra
              <lb/>
            coniſectionem, & </s>
            <s xml:id="echoid-s3339" xml:space="preserve">angulus E A H eſt acutus.</s>
            <s xml:id="echoid-s3340" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3341" xml:space="preserve">Quoniam ex D non educitur ad ſectionem A C vllus breuiſecans, & </s>
            <s xml:id="echoid-s3342" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s3343" xml:space="preserve">
              <note position="right" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">b</note>
            Sequitur quidem ex hac hypotheſi, quod menſura E A non ſit maior ſemierecto
              <lb/>
              <note position="left" xlink:label="note-0118-02" xlink:href="note-0118-02a" xml:space="preserve">Ex 49. 50.
                <lb/>
              huius.</note>
            aut ſi maior eſt, ſit quoque perpendicularis D E maior Trutina F, ex conuerſa
              <lb/>
            propoſitione 51. </s>
            <s xml:id="echoid-s3344" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3345" xml:space="preserve">huius per deductionem ad inconueniens.</s>
            <s xml:id="echoid-s3346" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3347" xml:space="preserve">Quare ſi centro D interuallo D B, &</s>
            <s xml:id="echoid-s3348" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3349" xml:space="preserve">Circulus enim B I L H A ra-
              <lb/>
              <note position="right" xlink:label="note-0118-03" xlink:href="note-0118-03a" xml:space="preserve">c</note>
            dio D B deſcriptus tranſibit per verticem A cum radius D B poſitus ſit æqualis
              <lb/>
            D A, cumque angulus D B I ſit acutus, ex Lemmate nono, cadet neceſſario B
              <lb/>
            I intra circulum B I L.</s>
            <s xml:id="echoid-s3350" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3351" xml:space="preserve">Ig tur circulus ſecat coniſectionem, &</s>
            <s xml:id="echoid-s3352" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3353" xml:space="preserve">Quia B I cadit extra coniſe-
              <lb/>
              <note position="right" xlink:label="note-0118-04" xlink:href="note-0118-04a" xml:space="preserve">d</note>
            ctionem, quàm tangit, & </s>
            <s xml:id="echoid-s3354" xml:space="preserve">intra circulum B L A, vt dictum eſt, è contra re-
              <lb/>
            cta A H cadit intra eandem coniſectionem, & </s>
            <s xml:id="echoid-s3355" xml:space="preserve">extra ipſum circulum, quem,
              <lb/>
            tangit, cum H A perpendicularis ſit ad circuli radium D A; </s>
            <s xml:id="echoid-s3356" xml:space="preserve">igitur circulus B
              <lb/>
            I L A fertur extra coniſectionem ad partes B I, & </s>
            <s xml:id="echoid-s3357" xml:space="preserve">intra eandem ad partes A
              <lb/>
            H; </s>
            <s xml:id="echoid-s3358" xml:space="preserve">quare neceſſario coniſectionem ſecat.</s>
            <s xml:id="echoid-s3359" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3360" xml:space="preserve">Patet, vt dictum eſt, quod D L G ſit acutus, &</s>
            <s xml:id="echoid-s3361" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3362" xml:space="preserve">Hoc enim ſequitur ex
              <lb/>
              <note position="right" xlink:label="note-0118-05" xlink:href="note-0118-05a" xml:space="preserve">e</note>
            nono Lemmate præmiſſo, reſpicit enim angulus D L G verticem A; </s>
            <s xml:id="echoid-s3363" xml:space="preserve">& </s>
            <s xml:id="echoid-s3364" xml:space="preserve">ideo eſt
              <lb/>
            acutus, & </s>
            <s xml:id="echoid-s3365" xml:space="preserve">cadit neceſſario recta L G intra circulum B L A radio D L deſcri-
              <lb/>
            ptum ad partes L A; </s>
            <s xml:id="echoid-s3366" xml:space="preserve">& </s>
            <s xml:id="echoid-s3367" xml:space="preserve">portio circuli L H A cadit intra coniſectionem L A;
              <lb/>
            </s>
            <s xml:id="echoid-s3368" xml:space="preserve">igitur recta L G cadit intra coniſectionem L A, ſed cadit extra eandem ſectio-
              <lb/>
              <note position="left" xlink:label="note-0118-06" xlink:href="note-0118-06a" xml:space="preserve">35. 36.
                <lb/>
              lib. 1.</note>
            nem, cum contingat eam in L, quod eſt abſurdum.</s>
            <s xml:id="echoid-s3369" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum