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
131 93
132 94
133 95
134 96
135 97
136 98
137 99
138 100
139 101
140 102
141 103
142 104
143 105
144 106
145 107
146 108
147 109
148 110
149 111
150 112
151 113
152 114
153 115
154 116
155 117
156 118
157 119
158 120
159 121
160 122
< >
page |< < (105) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div382" type="section" level="1" n="122">
          <pb o="105" file="0143" n="143" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div395" type="section" level="1" n="123">
          <head xml:id="echoid-head166" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4248" xml:space="preserve">HInc conſtat, ſupremam circuli peripheriam A Z cadere in locum à tan-
              <lb/>
            gente X A, & </s>
            <s xml:id="echoid-s4249" xml:space="preserve">coniſectionem B A contentum, infimam vero circuferen-
              <lb/>
            tiam A γ cadere ne dum infra tangentem, ſed etiam infra coniſectionem A G;
              <lb/>
            </s>
            <s xml:id="echoid-s4250" xml:space="preserve">eoquod recta A X cadit extra circuli peripheriam A Z, quàm contingit in A,
              <lb/>
            & </s>
            <s xml:id="echoid-s4251" xml:space="preserve">eadem circumferentia A Z cadit extra ſectionem A B, quàm ſecat in A, vt
              <lb/>
            dictum eſt.</s>
            <s xml:id="echoid-s4252" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4253" xml:space="preserve">Mirabile quidem hoc videri poterit aliquibus, qui contingentiæ angulos, quos
              <lb/>
            vocant, verè angulos eſſe cenſent; </s>
            <s xml:id="echoid-s4254" xml:space="preserve">nam hic duæ circumſerentiæ curuæ, conica
              <lb/>
            nimirum B A G, & </s>
            <s xml:id="echoid-s4255" xml:space="preserve">circularis Z A γ ſe mutuo ſecant in A, & </s>
            <s xml:id="echoid-s4256" xml:space="preserve">tamen ambo
              <lb/>
            tanguntur ab eadẽ recta linea A X in eodem puncto A, in quo illæ ſe mutuò ſecant.
              <lb/>
            </s>
            <s xml:id="echoid-s4257" xml:space="preserve">Vnde colligent etiam, quod anguli contingentiæ facti à coniſectione B A G, & </s>
            <s xml:id="echoid-s4258" xml:space="preserve">
              <lb/>
            recta linea X A non ſunt æquales inter ſe, quando punctum A in vertice axis
              <lb/>
            non exiſtit; </s>
            <s xml:id="echoid-s4259" xml:space="preserve">nam duo anguli contingentiæ circumſerentiæ circularis, & </s>
            <s xml:id="echoid-s4260" xml:space="preserve">rectæ
              <lb/>
            tangentis X A æquales ſunt inter ſe: </s>
            <s xml:id="echoid-s4261" xml:space="preserve">at angulus contingentiæ ſectionis conicæ ſu-
              <lb/>
            premus reſpiciens verticem B maior eſt angulo contingentiæ circularis, vt dictũ
              <lb/>
            eſt: </s>
            <s xml:id="echoid-s4262" xml:space="preserve">infimus vero angulus contingentiæ à ſectione conica, & </s>
            <s xml:id="echoid-s4263" xml:space="preserve">eadem tangente
              <lb/>
            contentus minor eſt eodem angulo contingentiæ circularis, & </s>
            <s xml:id="echoid-s4264" xml:space="preserve">propterea ſupremus
              <lb/>
            angnlus contingentiæ ſectionis conicæ maior erit inferiori.</s>
            <s xml:id="echoid-s4265" xml:space="preserve"/>
          </p>
          <figure number="129">
            <image file="0143-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0143-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s4266" xml:space="preserve">Sit perpendicularis D E
              <lb/>
              <note position="right" xlink:label="note-0143-01" xlink:href="note-0143-01a" xml:space="preserve">PROP.
                <lb/>
              II.
                <lb/>
              Addit.
                <lb/>
              Ex 51. 52.
                <lb/>
              53. huius.</note>
            minor trutina L, ſintque D
              <lb/>
            A, & </s>
            <s xml:id="echoid-s4267" xml:space="preserve">D C duo illi rami,
              <lb/>
            qui tantummodo breuiſecantes
              <lb/>
            eſſe poſſunt omnium ramorum
              <lb/>
            ex concurſu D ad ſectionem
              <lb/>
            B C cadentium; </s>
            <s xml:id="echoid-s4268" xml:space="preserve">atque cen-
              <lb/>
            tro D, interuallo D A deſcri-
              <lb/>
            batur circulus Z A γ; </s>
            <s xml:id="echoid-s4269" xml:space="preserve">pari-
              <lb/>
            terque centro D, interuallo D
              <lb/>
            C deſcribatur circulus O C Q;
              <lb/>
            </s>
            <s xml:id="echoid-s4270" xml:space="preserve">ducanturque rectæ X P, M
              <lb/>
            P contingentes coniſectionem
              <lb/>
            in A, & </s>
            <s xml:id="echoid-s4271" xml:space="preserve">C. </s>
            <s xml:id="echoid-s4272" xml:space="preserve">Dico, circulũ
              <lb/>
            Z A γ contingere coniſectio-
              <lb/>
            nem in A, & </s>
            <s xml:id="echoid-s4273" xml:space="preserve">extra ipſam
              <lb/>
            cadere, at circulum O C Q contingere eandem coniſectionem in C, & </s>
            <s xml:id="echoid-s4274" xml:space="preserve">
              <lb/>
            intra ipſam cadere.</s>
            <s xml:id="echoid-s4275" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4276" xml:space="preserve">Ducantur quilibet rami D F, D G ſupra, & </s>
            <s xml:id="echoid-s4277" xml:space="preserve">infra breuiſecantem D A, ſe-
              <lb/>
            cantes circulum Z A γ in Z, & </s>
            <s xml:id="echoid-s4278" xml:space="preserve">γ; </s>
            <s xml:id="echoid-s4279" xml:space="preserve">pariterque ducantur quilibet rami D </s>
          </p>
        </div>
      </text>
    </echo>
Impressum