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
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
131 93
132 94
133 95
134 96
135 97
136 98
137 99
138 100
139 101
140 102
< >
page |< < (43) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div172" type="section" level="1" n="70">
          <pb o="43" file="0081" n="81" rhead="Conicor. Lib. V."/>
          <figure number="58">
            <image file="0081-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0081-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s2104" xml:space="preserve">Et ſimili modo conſtat, quod breuiſſima egrediens ex puncto L cadit
              <lb/>
              <note position="left" xlink:label="note-0081-01" xlink:href="note-0081-01a" xml:space="preserve">f</note>
            extra S L, &</s>
            <s xml:id="echoid-s2105" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2106" xml:space="preserve">Ad vitandam confuſionem figuræ, & </s>
            <s xml:id="echoid-s2107" xml:space="preserve">prolixitatem demonſtrationis
              <lb/>
            appoſui duas figuras, in quibus duo caſus ijſdem caracteribus notantur, itaque abſq;
              <lb/>
            </s>
            <s xml:id="echoid-s2108" xml:space="preserve">nouo labore, ſi inſpiciatur ſecunda figura, ijſdem verbis prioris caſus, oſtendetur ca-
              <lb/>
            ſus ſecundus.</s>
            <s xml:id="echoid-s2109" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2110" xml:space="preserve">Pariter demonſtrabitur, quemadmodum iam oſtenſumeſt, &</s>
            <s xml:id="echoid-s2111" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2112" xml:space="preserve">Pars ſecun-
              <lb/>
              <note position="left" xlink:label="note-0081-02" xlink:href="note-0081-02a" xml:space="preserve">g</note>
            da huius propoſitionis innuitur tantummodo pauciſsimis verbis; </s>
            <s xml:id="echoid-s2113" xml:space="preserve">quare maioris cla-
              <lb/>
            ritatis gratia integram demonſtrationem hìc afferre libuit.</s>
            <s xml:id="echoid-s2114" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div179" type="section" level="1" n="71">
          <head xml:id="echoid-head103" xml:space="preserve">Demonſtratio ſecundæ partis.</head>
          <head xml:id="echoid-head104" xml:space="preserve">PROPOSITIONIS LI.</head>
          <p style="it">
            <s xml:id="echoid-s2115" xml:space="preserve">Eſto E D æqualis trutinæ H: </s>
            <s xml:id="echoid-s2116" xml:space="preserve">Dico ex concurſu E vnicum tantùm breui-
              <lb/>
            ſecantem ramum duci poſſe.</s>
            <s xml:id="echoid-s2117" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2118" xml:space="preserve">In eadem ſigura, quia ex conſtructione H ad B G eſt, vt G F ad F D, ponitur verò
              <lb/>
            E D æqualis H; </s>
            <s xml:id="echoid-s2119" xml:space="preserve">ergo E D ad B G, ſeu D I ad I G (propter ſimilitudinem triangulo-
              <lb/>
            rum E D I, B G I) eſt, vt G F ad F D, & </s>
            <s xml:id="echoid-s2120" xml:space="preserve">componendo D G ad G I eſt, vt eadem G D
              <lb/>
            ad D F; </s>
            <s xml:id="echoid-s2121" xml:space="preserve">ideoque I G æqualis eſt D F, ſeu A C ſemierecto; </s>
            <s xml:id="echoid-s2122" xml:space="preserve">igitur B I eſt breuiſsima.</s>
            <s xml:id="echoid-s2123" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">8. huius.</note>
          <p style="it">
            <s xml:id="echoid-s2124" xml:space="preserve">Poſte a ducto quolibet ramo E K ſupra breuiſecantem E B (in prima figura, & </s>
            <s xml:id="echoid-s2125" xml:space="preserve">in-
              <lb/>
            fra in ſecunda) occurrente axi in R, & </s>
            <s xml:id="echoid-s2126" xml:space="preserve">ducta K M perpendiculari ad axim, quæ eum
              <lb/>
            ſecet in M, & </s>
            <s xml:id="echoid-s2127" xml:space="preserve">tangentem O B in P. </s>
            <s xml:id="echoid-s2128" xml:space="preserve">Quoniam (vt dictum eſt) O F ſecatur </s>
          </p>
        </div>
      </text>
    </echo>
Impressum