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
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39 1
40 2
< >
page |< < (89) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div346" type="section" level="1" n="112">
          <pb o="89" file="0127" n="127" rhead="Conicor. Lib. V."/>
          <p>
            <s xml:id="echoid-s3659" xml:space="preserve">Erigamus itaque ſuper D perpendicularem D B occurrentem E G in,
              <lb/>
              <note position="left" xlink:label="note-0127-01" xlink:href="note-0127-01a" xml:space="preserve">b</note>
            L; </s>
            <s xml:id="echoid-s3660" xml:space="preserve">ergo eſt dimidium recti, & </s>
            <s xml:id="echoid-s3661" xml:space="preserve">E non eſt indirectum, quia non egredi-
              <lb/>
            tur ex E, niſi vnicus breuiſecans; </s>
            <s xml:id="echoid-s3662" xml:space="preserve">inſuper lineæ breuiſſimæ egredien-
              <lb/>
              <note position="left" xlink:label="note-0127-02" xlink:href="note-0127-02a" xml:space="preserve">c</note>
            tes ab extremitatibus reliquorum ramorum abſcindunt ab axi A C cum
              <lb/>
            C, lineam maiorem, quàm ſecant rami illi. </s>
            <s xml:id="echoid-s3663" xml:space="preserve">(51. </s>
            <s xml:id="echoid-s3664" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3665" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3666" xml:space="preserve">His po-
              <lb/>
            ſitis manifeſtum eſt, quod E C F eſt acutus; </s>
            <s xml:id="echoid-s3667" xml:space="preserve">atque E C minima eſt linea-
              <lb/>
            rum egredientium ex E ad quadrantem E B, & </s>
            <s xml:id="echoid-s3668" xml:space="preserve">illi propinquior, minor
              <lb/>
            eſt remotiore; </s>
            <s xml:id="echoid-s3669" xml:space="preserve">modo demonſtrandum eſt, quod E K maior quoque eſt,
              <lb/>
              <note position="left" xlink:label="note-0127-03" xlink:href="note-0127-03a" xml:space="preserve">d</note>
            quàm E B, producamus itaque B M, M K tangentes, ergo M B E eſt
              <lb/>
            obtuſus, & </s>
            <s xml:id="echoid-s3670" xml:space="preserve">M K E acutus (29. </s>
            <s xml:id="echoid-s3671" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3672" xml:space="preserve">quia breuiſſima egrediens ex K
              <lb/>
            abſcindit cum A minorem lineam, quàm ſecat K E (57. </s>
            <s xml:id="echoid-s3673" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3674" xml:space="preserve">eo quod
              <lb/>
            K cadit inter duas lineas L B, L G; </s>
            <s xml:id="echoid-s3675" xml:space="preserve">& </s>
            <s xml:id="echoid-s3676" xml:space="preserve">iungamus M E; </s>
            <s xml:id="echoid-s3677" xml:space="preserve">ergo duo qua-
              <lb/>
            drata M B, B E minora ſunt, quàm quadratum M E, quare minora,
              <lb/>
            erunt duobus quadratis M K, K E, & </s>
            <s xml:id="echoid-s3678" xml:space="preserve">M B maior eſt, quàm M K, ergo
              <lb/>
              <note position="right" xlink:label="note-0127-04" xlink:href="note-0127-04a" xml:space="preserve">70. huius.</note>
            B E minor eſt, quàm K E; </s>
            <s xml:id="echoid-s3679" xml:space="preserve">& </s>
            <s xml:id="echoid-s3680" xml:space="preserve">ſic demonſtratur, quod G E maior ſit,
              <lb/>
            quàm K E; </s>
            <s xml:id="echoid-s3681" xml:space="preserve">Nam ſi producamus G N tangentem, tunc N G E eſt re-
              <lb/>
            ctus, quia G I eſt breuiſſima, & </s>
            <s xml:id="echoid-s3682" xml:space="preserve">N K E obtuſus; </s>
            <s xml:id="echoid-s3683" xml:space="preserve">ergo G E maior eſt,
              <lb/>
              <note position="right" xlink:label="note-0127-05" xlink:href="note-0127-05a" xml:space="preserve">30. huius.</note>
            quàm E K; </s>
            <s xml:id="echoid-s3684" xml:space="preserve">itaque G E maximus eſt ramorum egredientium ex E ad ſe-
              <lb/>
            ctionem G C, & </s>
            <s xml:id="echoid-s3685" xml:space="preserve">minimus eorum E C, atque propinquior E C minor
              <lb/>
            eſt remotiore.</s>
            <s xml:id="echoid-s3686" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3687" xml:space="preserve">Educamus ex E ad ſectionem A G, E A, E O, oſtendetur quod
              <lb/>
              <note position="left" xlink:label="note-0127-06" xlink:href="note-0127-06a" xml:space="preserve">e</note>
            E G maior ſit, quàm E O, & </s>
            <s xml:id="echoid-s3688" xml:space="preserve">E O, quàm E A. </s>
            <s xml:id="echoid-s3689" xml:space="preserve">Erigamus
              <lb/>
            itaque ad A C perpendicularem A P; </s>
            <s xml:id="echoid-s3690" xml:space="preserve">ergo E A P eſt
              <lb/>
            obtuſus, & </s>
            <s xml:id="echoid-s3691" xml:space="preserve">producamus P O Q tangentem; </s>
            <s xml:id="echoid-s3692" xml:space="preserve">ergo
              <lb/>
            P O E eſt acutus, quia linea breuiſſima egre-
              <lb/>
              <note position="right" xlink:label="note-0127-07" xlink:href="note-0127-07a" xml:space="preserve">57. huius.</note>
            diens ex O ſecat cum A lineam maiorem;
              <lb/>
            </s>
            <s xml:id="echoid-s3693" xml:space="preserve">ergo E O maior eſt, quàm E A: </s>
            <s xml:id="echoid-s3694" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s3695" xml:space="preserve">
              <lb/>
            ſic patet, quod E G maior ſit,
              <lb/>
            quàm E O (29. </s>
            <s xml:id="echoid-s3696" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3697" xml:space="preserve">quia
              <lb/>
            Q G E eſt rectus, & </s>
            <s xml:id="echoid-s3698" xml:space="preserve">
              <lb/>
            Q O E obtuſus,
              <lb/>
            & </s>
            <s xml:id="echoid-s3699" xml:space="preserve">G Q
              <lb/>
            maior, quàm O Q, ergo E G maximus eſt ramorum
              <lb/>
            egredientium ex E ad ſectionem A B C, & </s>
            <s xml:id="echoid-s3700" xml:space="preserve">
              <lb/>
            minimus eorum E C, & </s>
            <s xml:id="echoid-s3701" xml:space="preserve">propinquiores
              <lb/>
            minimo, remotioribus minores ſunt,
              <lb/>
            & </s>
            <s xml:id="echoid-s3702" xml:space="preserve">propinquiores maximo, ma-
              <lb/>
            iores ſunt remotioribus; </s>
            <s xml:id="echoid-s3703" xml:space="preserve">
              <lb/>
            quod erat oſtenden-
              <lb/>
            dum.</s>
            <s xml:id="echoid-s3704" xml:space="preserve"/>
          </p>
          <figure number="110">
            <image file="0127-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0127-01"/>
          </figure>
        </div>
      </text>
    </echo>
Impressum