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
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
121 83
122 84
123 85
124 86
125 87
126 88
127 89
128 90
129 91
130 92
< >
page |< < (34) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div143" type="section" level="1" n="63">
          <pb o="34" file="0072" n="72" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div146" type="section" level="1" n="64">
          <head xml:id="echoid-head96" xml:space="preserve">PROPOSITIO LI.</head>
          <p>
            <s xml:id="echoid-s1817" xml:space="preserve">DEindè ſit D A maior quàm A C , ſitque prius ſectio pa-
              <lb/>
            rabole , & </s>
            <s xml:id="echoid-s1818" xml:space="preserve">ſecetur ex D A ipſa D F æqualis A C, & </s>
            <s xml:id="echoid-s1819" xml:space="preserve">A
              <lb/>
            G fiat pars tertia ipſius A F, educaturque B G perpendicularis
              <lb/>
            ad axim, & </s>
            <s xml:id="echoid-s1820" xml:space="preserve">vt D F ad F G, ita fiat B G ad lineam H (& </s>
            <s xml:id="echoid-s1821" xml:space="preserve">hæc
              <lb/>
            eſt Trutina) coniungaturque B E ; </s>
            <s xml:id="echoid-s1822" xml:space="preserve">& </s>
            <s xml:id="echoid-s1823" xml:space="preserve">ſiquidem D E fuerit ma-
              <lb/>
              <note position="right" xlink:label="note-0072-01" xlink:href="note-0072-01a" xml:space="preserve">a</note>
            ior quàm H. </s>
            <s xml:id="echoid-s1824" xml:space="preserve">Dico, quod nullus ramus breuiſecans duci poteſt.</s>
            <s xml:id="echoid-s1825" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1826" xml:space="preserve">Quoniam D E maior eſt, quàm H habebit D E ad B G, nempe D I
              <lb/>
              <note position="right" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve">b</note>
            ad I G maiorem rationem , quàm G F ad F D, & </s>
            <s xml:id="echoid-s1827" xml:space="preserve">componatur propor-
              <lb/>
            tio , vt demonſtretur , quod I G minor ſit , quàm D F, quæ æqualis
              <lb/>
            eſt ipſi A C; </s>
            <s xml:id="echoid-s1828" xml:space="preserve">breuiſſima itaque egrediens ex B abſcindit ex ſagitta A
              <lb/>
            D maiorem lineam , quàm A I (13. </s>
            <s xml:id="echoid-s1829" xml:space="preserve">ex quinto) ; </s>
            <s xml:id="echoid-s1830" xml:space="preserve">poſtea ducamus ex E
              <lb/>
            ad ſectionem ramos E K, E L ad vtramque partem B E, & </s>
            <s xml:id="echoid-s1831" xml:space="preserve">duas per-
              <lb/>
            pendiculares
              <lb/>
              <figure xlink:label="fig-0072-01" xlink:href="fig-0072-01a" number="50">
                <image file="0072-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0072-01"/>
              </figure>
            KM, LN, pro-
              <lb/>
            ducamus vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s1832" xml:space="preserve">ad QO tan-
              <lb/>
            gẽtem ſectio-
              <lb/>
            nem in B; </s>
            <s xml:id="echoid-s1833" xml:space="preserve">& </s>
            <s xml:id="echoid-s1834" xml:space="preserve">
              <lb/>
            quoniã ſectio
              <lb/>
            eſt, parabole,
              <lb/>
            & </s>
            <s xml:id="echoid-s1835" xml:space="preserve">OQ tãgens
              <lb/>
            eſt, igitur OG
              <lb/>
              <note position="left" xlink:label="note-0072-03" xlink:href="note-0072-03a" xml:space="preserve">35. lib. 1.</note>
            eſt dupla ip-
              <lb/>
            ſius A G, quę
              <lb/>
            eſt ſemiſſis ip-
              <lb/>
            ſi us F G; </s>
            <s xml:id="echoid-s1836" xml:space="preserve">ergo
              <lb/>
              <note position="right" xlink:label="note-0072-04" xlink:href="note-0072-04a" xml:space="preserve">c</note>
            G F æqualis
              <lb/>
            eſt G O, erit
              <lb/>
            igitur G O ad
              <lb/>
            O M, nempe
              <lb/>
            B G ad P M
              <lb/>
            in maiori pro-
              <lb/>
            portione, quã
              <lb/>
            M F ad F G;
              <lb/>
            </s>
            <s xml:id="echoid-s1837" xml:space="preserve">
              <note position="right" xlink:label="note-0072-05" xlink:href="note-0072-05a" xml:space="preserve">d</note>
            itaque M K in F M minus eſt , quàm B G in G F, quod eſt minus quàm
              <lb/>
            E D in D F propterea quod E D maior eſt quàm H; </s>
            <s xml:id="echoid-s1838" xml:space="preserve">igitur E D in D F
              <lb/>
            multò maius eſt, quàm K M in MF, quare ED ad M K, nempe D R ad
              <lb/>
            R M maiorem rationem habet, quàm M F ad F D, & </s>
            <s xml:id="echoid-s1839" xml:space="preserve">componendo patet,
              <lb/>
              <note position="right" xlink:label="note-0072-06" xlink:href="note-0072-06a" xml:space="preserve">e</note>
            quod D F maior ſit, quàm R M. </s>
            <s xml:id="echoid-s1840" xml:space="preserve">Igitur breuiſſima egrediens ex K (13.
              <lb/>
            </s>
            <s xml:id="echoid-s1841" xml:space="preserve">
              <note position="right" xlink:label="note-0072-07" xlink:href="note-0072-07a" xml:space="preserve">f</note>
            ex quinto) cadit extra R K; </s>
            <s xml:id="echoid-s1842" xml:space="preserve">Et ſimili modo conſtat, quod </s>
          </p>
        </div>
      </text>
    </echo>
Impressum