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
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
91 53
92 54
93 55
94 56
95 57
96 58
97 59
98 60
99 61
100 62
< >
page |< < (130) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div486" type="section" level="1" n="151">
          <p>
            <s xml:id="echoid-s5096" xml:space="preserve">
              <pb o="130" file="0168" n="168" rhead="Apollonij Pergæi"/>
            oſtendetur ex dictis, quod lineæ maximæ mutuò ſe ſecant inter diame
              <lb/>
            trum, & </s>
            <s xml:id="echoid-s5097" xml:space="preserve">rectum, &</s>
            <s xml:id="echoid-s5098" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5099" xml:space="preserve">Textũ corrigi debere maniſeſtum eſt ex dictis ſuperius</s>
          </p>
          <note position="right" xml:space="preserve">b</note>
          <p style="it">
            <s xml:id="echoid-s5100" xml:space="preserve">Quia D Q ad Q I eſt, vt D O ad O
              <lb/>
              <figure xlink:label="fig-0168-01" xlink:href="fig-0168-01a" number="166">
                <image file="0168-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0168-01"/>
              </figure>
            G, &</s>
            <s xml:id="echoid-s5101" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5102" xml:space="preserve">In eadem figura propoſitionis 32.
              <lb/>
            </s>
            <s xml:id="echoid-s5103" xml:space="preserve">præcedentis perſiciatur conſtructio, vt priùs
              <lb/>
            quia duæ K M, H N ſunt breuiſsimæ li-
              <lb/>
              <note position="left" xlink:label="note-0168-02" xlink:href="note-0168-02a" xml:space="preserve">Pr. 15-
                <lb/>
              huius.</note>
            neæ; </s>
            <s xml:id="echoid-s5104" xml:space="preserve">ergo M R ad R D, nec non N P ad
              <lb/>
            P D eandem proportionem habent, ſcilicet
              <lb/>
            eam quàm habent latus rectum ad tranſuer-
              <lb/>
            ſum, ſeu eandem quàm habet ſemierectus
              <lb/>
              <note position="left" xlink:label="note-0168-03" xlink:href="note-0168-03a" xml:space="preserve">15. lib. I.</note>
            E B ad ſemiaxim B D; </s>
            <s xml:id="echoid-s5105" xml:space="preserve">eſt verò C A ad eius
              <lb/>
            latus rectum, ſeu D A ad A F, vt E B ad
              <lb/>
            B D; </s>
            <s xml:id="echoid-s5106" xml:space="preserve">igitur tam M R ad R D, quàm N P
              <lb/>
            ad P D eandem proporiionem habent, quàm
              <lb/>
            D A ad A F; </s>
            <s xml:id="echoid-s5107" xml:space="preserve">ſed propter parallelas C D, R
              <lb/>
            K, P H, c
              <unsure/>
            ſt M K ad K I, vt M R ad R D;
              <lb/>
            </s>
            <s xml:id="echoid-s5108" xml:space="preserve">pariterque N H ad H G eandem proportionẽ
              <lb/>
            habet, quàm N P ad P D; </s>
            <s xml:id="echoid-s5109" xml:space="preserve">atque propter pa-
              <lb/>
            rallelas D B, Q K, O H eſt D Q, ad Q I
              <lb/>
            vt M K ad K I, & </s>
            <s xml:id="echoid-s5110" xml:space="preserve">D O ad O G eſt vt N H
              <lb/>
            ad H G; </s>
            <s xml:id="echoid-s5111" xml:space="preserve">ergo tam D Q ad Q I, quàm D
              <lb/>
            O ad O G eandem proportionem habent, quàm D A ad A F, ſeu quàm axis mi-
              <lb/>
              <note position="left" xlink:label="note-0168-04" xlink:href="note-0168-04a" xml:space="preserve">20. 21. 22.
                <lb/>
              huius.</note>
            nor A C ad ſuum erectum, & </s>
            <s xml:id="echoid-s5112" xml:space="preserve">propterea tam K I, quàm H G eſt ramus maxi-
              <lb/>
            mus; </s>
            <s xml:id="echoid-s5113" xml:space="preserve">igitur ſi duæ lineæ breuiſſimæ H G, & </s>
            <s xml:id="echoid-s5114" xml:space="preserve">K I producantur quouſque axim
              <lb/>
            minorem ſecent in punctis G, & </s>
            <s xml:id="echoid-s5115" xml:space="preserve">I efficientur rami omnium maximi. </s>
            <s xml:id="echoid-s5116" xml:space="preserve">Poſtea quia
              <lb/>
            D Q ad Q I, eſt vt D O ad O G; </s>
            <s xml:id="echoid-s5117" xml:space="preserve">permutando D Q ad D O eandem propor-
              <lb/>
            tionem habebit, quàm Q I ad O G; </s>
            <s xml:id="echoid-s5118" xml:space="preserve">& </s>
            <s xml:id="echoid-s5119" xml:space="preserve">permutando, & </s>
            <s xml:id="echoid-s5120" xml:space="preserve">comparando antecedentes ad
              <lb/>
            differentias terminorum erit D Q ad D I, vt D O ad D G: </s>
            <s xml:id="echoid-s5121" xml:space="preserve">eſtque D Q minor
              <lb/>
            quàm D O; </s>
            <s xml:id="echoid-s5122" xml:space="preserve">igitur Q I minor eſt, quàm O G; </s>
            <s xml:id="echoid-s5123" xml:space="preserve">pariterque D I minor eſt, quàm
              <lb/>
            D G; </s>
            <s xml:id="echoid-s5124" xml:space="preserve">& </s>
            <s xml:id="echoid-s5125" xml:space="preserve">propterea punctum I cadit inter exim B D, & </s>
            <s xml:id="echoid-s5126" xml:space="preserve">ramum H G; </s>
            <s xml:id="echoid-s5127" xml:space="preserve">eſtque
              <lb/>
            etiam potentialis K Q propinquior & </s>
            <s xml:id="echoid-s5128" xml:space="preserve">parallela axi maiori, & </s>
            <s xml:id="echoid-s5129" xml:space="preserve">ideo maior re-
              <lb/>
            motiore H O; </s>
            <s xml:id="echoid-s5130" xml:space="preserve">igitur punctum K cadit inter axim B D, & </s>
            <s xml:id="echoid-s5131" xml:space="preserve">ramum H G; </s>
            <s xml:id="echoid-s5132" xml:space="preserve">& </s>
            <s xml:id="echoid-s5133" xml:space="preserve">
              <lb/>
            propterea ramus K I ſecat ramum H G in puncto L inter puncta H, & </s>
            <s xml:id="echoid-s5134" xml:space="preserve">G:
              <lb/>
            </s>
            <s xml:id="echoid-s5135" xml:space="preserve">
              <note position="left" xlink:label="note-0168-05" xlink:href="note-0168-05a" xml:space="preserve">36. huius.</note>
            ſed duæ breuiſsimæ K M, H N ſe ſecant vltra axim B D: </s>
            <s xml:id="echoid-s5136" xml:space="preserve">igitur occurſus L
              <lb/>
            cadit intra angulum B D C ab axibus compræhenſum. </s>
            <s xml:id="echoid-s5137" xml:space="preserve">Tandem quia K I ſecat
              <lb/>
            H G inter puncta G, & </s>
            <s xml:id="echoid-s5138" xml:space="preserve">H; </s>
            <s xml:id="echoid-s5139" xml:space="preserve">ergo efficit angulum externum K I A maio-
              <lb/>
            rem interno, & </s>
            <s xml:id="echoid-s5140" xml:space="preserve">oppoſito G: </s>
            <s xml:id="echoid-s5141" xml:space="preserve">& </s>
            <s xml:id="echoid-s5142" xml:space="preserve">propterea ramus K I propinquior vertici B,
              <lb/>
            quàm H G efficiet cum axe minore C A angulum A I K maiorem.</s>
            <s xml:id="echoid-s5143" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div489" type="section" level="1" n="152">
          <head xml:id="echoid-head201" xml:space="preserve">Notæ in Propoſit. XXXV.</head>
          <p style="it">
            <s xml:id="echoid-s5144" xml:space="preserve">SI tranſeat per centrum ellipſis vna duarum breuiſſimarum; </s>
            <s xml:id="echoid-s5145" xml:space="preserve">vtique ra-
              <lb/>
              <note position="right" xlink:label="note-0168-06" xlink:href="note-0168-06a" xml:space="preserve">a</note>
            mi, &</s>
            <s xml:id="echoid-s5146" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5147" xml:space="preserve">Hæc propoſitio parum differt à 54. </s>
            <s xml:id="echoid-s5148" xml:space="preserve">& </s>
            <s xml:id="echoid-s5149" xml:space="preserve">55. </s>
            <s xml:id="echoid-s5150" xml:space="preserve">buius, vbi oſtenſum
              <lb/>
            eſt, quod ſi duo rami E B, E G breuiſecantes ex eodem concurſu E ad ellipſim
              <lb/>
            A B ducuntur, quilibet alius ramus E F, extra breuiſecantes poſitus, cadet ſu-
              <lb/>
            pra breuiſsimam ex puncto F ad axim A C ductam: </s>
            <s xml:id="echoid-s5151" xml:space="preserve">hic vero ſupponuntur </s>
          </p>
        </div>
      </text>
    </echo>
Impressum