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 |< < (69) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div270" type="section" level="1" n="90">
          <pb o="69" file="0107" n="107" rhead="Conicor. Lib. V."/>
          <p style="it">
            <s xml:id="echoid-s2952" xml:space="preserve">Sit A D dimidium axis recti ſectionis ellipticæ A B C, &</s>
            <s xml:id="echoid-s2953" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2954" xml:space="preserve">Sit A D di-
              <lb/>
              <note position="left" xlink:label="note-0107-01" xlink:href="note-0107-01a" xml:space="preserve">b</note>
            midium axis minoris, & </s>
            <s xml:id="echoid-s2955" xml:space="preserve">recti ellipſis A B C, ſitque menſura A E maior, quàm
              <lb/>
            A D, & </s>
            <s xml:id="echoid-s2956" xml:space="preserve">E A ad A D habeat maiorem, aut eandem proportionem, quàm habet
              <lb/>
            latus tranſuerſum B C ad eius rectum latus.</s>
            <s xml:id="echoid-s2957" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2958" xml:space="preserve">Ponatur ramus E F, & </s>
            <s xml:id="echoid-s2959" xml:space="preserve">producamus ex F, &</s>
            <s xml:id="echoid-s2960" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2961" xml:space="preserve">Ducatur quilibet ramus
              <lb/>
              <note position="left" xlink:label="note-0107-02" xlink:href="note-0107-02a" xml:space="preserve">c</note>
            ſecans E F, & </s>
            <s xml:id="echoid-s2962" xml:space="preserve">ex F ad vtrumque axim perpendiculares F H, F I, quæ ſecent
              <lb/>
            eos in H, & </s>
            <s xml:id="echoid-s2963" xml:space="preserve">I. </s>
            <s xml:id="echoid-s2964" xml:space="preserve">Et quia D H minor eſt, quàm D A, habebit eadem E D ad
              <lb/>
            D H maiorem proportionem, quàm ad D A, & </s>
            <s xml:id="echoid-s2965" xml:space="preserve">componendo E H ad H D, ma-
              <lb/>
            iorem proportionem habebit, quàm E A ad A D; </s>
            <s xml:id="echoid-s2966" xml:space="preserve">eſt vero E F ad F G, vt E
              <lb/>
            H ad H D (propter parallelas D G, H F) nec non D I ad I G eſt, vt E F ad
              <lb/>
            F G (propter parallelas E D, I F) ergo D I ad I G maiorem proportionem ha-
              <lb/>
            bet, quàm E A ad A D: </s>
            <s xml:id="echoid-s2967" xml:space="preserve">habebat autem E A ad A D maiorem, aut eandem
              <lb/>
            proportionem, quàm latus tranſuer ſum B C ad eius rectum latus; </s>
            <s xml:id="echoid-s2968" xml:space="preserve">igitur D I ad
              <lb/>
            I G maiorem proportionem habebit, quàm latus tranſuer ſum B C ad eius rectum
              <lb/>
            latus: </s>
            <s xml:id="echoid-s2969" xml:space="preserve">fiat iam D I ad I K, vt latus tranſuer ſum B C ad eius latus rectum,
              <lb/>
            iungaturque F K, erit I K maior, quàm I G, & </s>
            <s xml:id="echoid-s2970" xml:space="preserve">F K linea breuiſsima, quæ ſe-
              <lb/>
              <note position="right" xlink:label="note-0107-03" xlink:href="note-0107-03a" xml:space="preserve">10. huius.</note>
            cat ſegmentum axis K B maius, quàm B G, vnde E F non erit breuiſcans.</s>
            <s xml:id="echoid-s2971" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div275" type="section" level="1" n="91">
          <head xml:id="echoid-head125" xml:space="preserve">Notæ in Propoſ. XLV.</head>
          <p style="it">
            <s xml:id="echoid-s2972" xml:space="preserve">SI autem fuerit ratio E A ad A D minor, quàm proportio figuræ, &</s>
            <s xml:id="echoid-s2973" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s2974" xml:space="preserve">
              <note position="left" xlink:label="note-0107-04" xlink:href="note-0107-04a" xml:space="preserve">a</note>
            Habeat E A ad A D minorẽ proportionem, quàm latus tranſuer ſum B C ad
              <lb/>
            eius rectum latus, & </s>
            <s xml:id="echoid-s2975" xml:space="preserve">fiat E H ad H D, vt latus tranſuer ſum ad rectum; </s>
            <s xml:id="echoid-s2976" xml:space="preserve">ha-
              <lb/>
            bebit E H ad H D maiorem proportionem, quàm E A ad A D, & </s>
            <s xml:id="echoid-s2977" xml:space="preserve">diuidendo
              <lb/>
            eadem E D ad D H habebit maiorem proportionem, quàm ad D A; </s>
            <s xml:id="echoid-s2978" xml:space="preserve">& </s>
            <s xml:id="echoid-s2979" xml:space="preserve">pro-
              <lb/>
            pterea D H minor erit, quàm D A; </s>
            <s xml:id="echoid-s2980" xml:space="preserve">vnde ex puncto H ſi eleuetur H F perpen-
              <lb/>
            dicularis ad D A intra ſectionem cadet, & </s>
            <s xml:id="echoid-s2981" xml:space="preserve">ſecabit eam alicubi, vt in F: </s>
            <s xml:id="echoid-s2982" xml:space="preserve">duca-
              <lb/>
            tur poſtea ex F recta F E, quæ ſecet axim in G, & </s>
            <s xml:id="echoid-s2983" xml:space="preserve">F I perpendicularis ad axim
              <lb/>
            B C eum ſecans in I. </s>
            <s xml:id="echoid-s2984" xml:space="preserve">Et quoniam, propter parallelas G D, F H, eſt E F ad F
              <lb/>
            G, vt E H ad H D, pariterque, propter parallelas E D, I F, eſt D I ad I G, vt
              <lb/>
            E F ad F G, quare D I ad I G eandem proportionem habet, quàm E H ad H
              <lb/>
            D, ſeu quàm latus tranſuer ſum B C ad eius latus rectum; </s>
            <s xml:id="echoid-s2985" xml:space="preserve">& </s>
            <s xml:id="echoid-s2986" xml:space="preserve">propterea F G eſt
              <lb/>
              <note position="right" xlink:label="note-0107-05" xlink:href="note-0107-05a" xml:space="preserve">10. huius.</note>
            breuiſsima.</s>
            <s xml:id="echoid-s2987" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2988" xml:space="preserve">Et quoniam iam eductæ ſunt ex E duæ breuiſecantes, &</s>
            <s xml:id="echoid-s2989" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2990" xml:space="preserve">Textus Ara-
              <lb/>
              <note position="left" xlink:label="note-0107-06" xlink:href="note-0107-06a" xml:space="preserve">b</note>
            bicus vſque ad finem propoſitionis eſt omnino corruptus, cum ſupponat propoſi-
              <lb/>
            tionem non demonſtratam, vt in propoſitione 56. </s>
            <s xml:id="echoid-s2991" xml:space="preserve">notaui; </s>
            <s xml:id="echoid-s2992" xml:space="preserve">Itaque, ſic eum reſti-
              <lb/>
            tui poſſe cenſeo. </s>
            <s xml:id="echoid-s2993" xml:space="preserve">Quoniam ex conſurſu E breuiſsimæ F G, & </s>
            <s xml:id="echoid-s2994" xml:space="preserve">ſemiaxis recti
              <lb/>
            minoris D A rami educti ad ſectionem F A ſecant axis ſegmenta vſque ad
              <lb/>
            verticem B maiora, quàm abſcindant breuiſsimæ ab eorum terminis ad axim
              <lb/>
            ductæ, ſcilicet breuiſsimæ cadunt ſupra ramos (ex Lemmate 8. </s>
            <s xml:id="echoid-s2995" xml:space="preserve">præmiſſo) ſimi-
              <lb/>
            liter rami ex concur ſu E ad ſectionem B F ducti cadunt ſupra breuiſsimas ab
              <lb/>
            eorum terminis ad axim extenſas (ex eodem Lemmate 8.) </s>
            <s xml:id="echoid-s2996" xml:space="preserve">& </s>
            <s xml:id="echoid-s2997" xml:space="preserve">hoc erat oſten-
              <lb/>
            dendum.</s>
            <s xml:id="echoid-s2998" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum