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 |< < (100) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div378" type="section" level="1" n="121">
          <p style="it">
            <s xml:id="echoid-s4067" xml:space="preserve">
              <pb o="100" file="0138" n="138" rhead="Apollonij Pergæi"/>
            miaxim minorem B D habet eandem, aut
              <lb/>
              <figure xlink:label="fig-0138-01" xlink:href="fig-0138-01a" number="122">
                <image file="0138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0138-01"/>
              </figure>
            maiorem proportionem, quàm latus tran-
              <lb/>
            ſuerſum A C ad eius latus rectum; </s>
            <s xml:id="echoid-s4068" xml:space="preserve">tunc
              <lb/>
            nullus alius ramus ad ſectionem A B C
              <lb/>
            breuiſecans duci poteſt, & </s>
            <s xml:id="echoid-s4069" xml:space="preserve">quælibet linea,
              <lb/>
            breuiſsima vt F H ducta ex puncto F ad
              <lb/>
            axim A C cadit infra ramum E F adpar-
              <lb/>
            tes centri, & </s>
            <s xml:id="echoid-s4070" xml:space="preserve">propterea ſi per F ducatur
              <lb/>
            F I contingens ellipſin quilibet ramus E
              <lb/>
              <note position="left" xlink:label="note-0138-01" xlink:href="note-0138-01a" xml:space="preserve">ex 29. 30.
                <lb/>
              huius.</note>
            F efficiet cum tangente angulum E F I reſ-
              <lb/>
            picientem verticem A acutum: </s>
            <s xml:id="echoid-s4071" xml:space="preserve">Similiter ſi
              <lb/>
            ducatur A K contingens ſectionem in A co-
              <lb/>
              <note position="left" xlink:label="note-0138-02" xlink:href="note-0138-02a" xml:space="preserve">ex 32.
                <lb/>
              lib. 1.</note>
            niungaturque E A, erit quoque angulus E A K acutus, & </s>
            <s xml:id="echoid-s4072" xml:space="preserve">ducta B L contingente
              <lb/>
            ſectionem in B erit angulus E B L rectus; </s>
            <s xml:id="echoid-s4073" xml:space="preserve">quapropter omnes rami ex concurſu
              <lb/>
            E ad quadrantem A B ducti efficiunt cum ſuis tangentibus angulos reſpicientes
              <lb/>
            verticem A acutos, & </s>
            <s xml:id="echoid-s4074" xml:space="preserve">vnus tantummodo E B L eſt rectus; </s>
            <s xml:id="echoid-s4075" xml:space="preserve">igitur ramorum ca-
              <lb/>
              <note position="left" xlink:label="note-0138-03" xlink:href="note-0138-03a" xml:space="preserve">Coroll.
                <lb/>
              67. huius.</note>
            dentium ex E ad quadrantem B A minimus eſt E A, & </s>
            <s xml:id="echoid-s4076" xml:space="preserve">quilibet ramus E F
              <lb/>
            propinquior vertici A minor eſt quolibet remotiore; </s>
            <s xml:id="echoid-s4077" xml:space="preserve">& </s>
            <s xml:id="echoid-s4078" xml:space="preserve">propterea E B erit ma-
              <lb/>
            ximus: </s>
            <s xml:id="echoid-s4079" xml:space="preserve">ſimili modo E B maior erit quolibet ramo E G in quadrante B C exiſten-
              <lb/>
            te; </s>
            <s xml:id="echoid-s4080" xml:space="preserve">Et hic eſt ſenſus, ni fallor illorum verborum; </s>
            <s xml:id="echoid-s4081" xml:space="preserve">demonſtrabitur in lineis
              <lb/>
            tangentibus, quemadmodum antea oſtenſum eſt, &</s>
            <s xml:id="echoid-s4082" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4083" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div382" type="section" level="1" n="122">
          <head xml:id="echoid-head165" xml:space="preserve">Notæ in Propoſit. LXXVII.</head>
          <p style="it">
            <s xml:id="echoid-s4084" xml:space="preserve">POſtea educatur E F, qui eſt maxi-
              <lb/>
              <figure xlink:label="fig-0138-02" xlink:href="fig-0138-02a" number="123">
                <image file="0138-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0138-02"/>
              </figure>
            musramorum, &</s>
            <s xml:id="echoid-s4085" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4086" xml:space="preserve">Repono hic ſimi-
              <lb/>
            liter verba, quæ in textu deſiderantur; </s>
            <s xml:id="echoid-s4087" xml:space="preserve">Po-
              <lb/>
            ſtea educatur alius breuiſecans E F; </s>
            <s xml:id="echoid-s4088" xml:space="preserve">Dico,
              <lb/>
            quod eſt æqualis vni breuiſecanti E G æquè
              <lb/>
            remoto à recto D B, & </s>
            <s xml:id="echoid-s4089" xml:space="preserve">eſt maximus reli-
              <lb/>
            quorum omnium.</s>
            <s xml:id="echoid-s4090" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4091" xml:space="preserve">Quia B D, F H ſunt duæ breuiſſimæ;
              <lb/>
            </s>
            <s xml:id="echoid-s4092" xml:space="preserve">ergo rami egredientes ad ſectionem B F
              <lb/>
            abſcindunt cum A lineas maiores, quàm
              <lb/>
            ſecent breuiſſimæ egredientes ab eorum extremitatibus, & </s>
            <s xml:id="echoid-s4093" xml:space="preserve">rami egredien-
              <lb/>
            tes ad duas peripherias C B, F A abſcindunt cum A, vel C lineas mino-
              <lb/>
            res (52. </s>
            <s xml:id="echoid-s4094" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4095" xml:space="preserve">&</s>
            <s xml:id="echoid-s4096" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4097" xml:space="preserve">Quia in ellipſi ſemiaxis minor B D, & </s>
            <s xml:id="echoid-s4098" xml:space="preserve">breuiſsima F H
              <lb/>
            concurrunt in E; </s>
            <s xml:id="echoid-s4099" xml:space="preserve">ergo quilibet ramus ex E ad peripheriam F B ductus cadit
              <lb/>
              <note position="left" xlink:label="note-0138-04" xlink:href="note-0138-04a" xml:space="preserve">Lem. 8.
                <lb/>
              huius.</note>
            infra breuiſsimam ab eius termino ad axim A C ductam: </s>
            <s xml:id="echoid-s4100" xml:space="preserve">ſimiliter, quia ramus
              <lb/>
            E G æquè recedit ab axi D B, ac ramus E F; </s>
            <s xml:id="echoid-s4101" xml:space="preserve">propterea, ne dum ramus F E
              <lb/>
            æqualis erit ramo E G, ſed ſimiliter quilibet alius ramus incidens inter E B,
              <lb/>
            & </s>
            <s xml:id="echoid-s4102" xml:space="preserve">E G eadet infra breuiſsimam ab eius termino ad axim A C ductam verſus
              <lb/>
              <note position="left" xlink:label="note-0138-05" xlink:href="note-0138-05a" xml:space="preserve">Ibidem.</note>
            D, & </s>
            <s xml:id="echoid-s4103" xml:space="preserve">rami cadentes ad peripherias A F, & </s>
            <s xml:id="echoid-s4104" xml:space="preserve">C G cadunt ſupra breuiſsimas ab
              <lb/>
              <note position="left" xlink:label="note-0138-06" xlink:href="note-0138-06a" xml:space="preserve">Ibidem.</note>
            eorum terminis ad axim C A ductas ad partes A, & </s>
            <s xml:id="echoid-s4105" xml:space="preserve">C.</s>
            <s xml:id="echoid-s4106" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4107" xml:space="preserve">Conſtat itaque, vt dictum eſt de lineis tangentibus, quod E F ſit ma-
              <lb/>
            ximus ramorum ſecantium egredientium ex E ad A B C, quod erat </s>
          </p>
        </div>
      </text>
    </echo>
Impressum