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
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
101 63
102 64
103 65
104 66
105 67
106 68
107 69
108 70
109 71
110 72
< >
page |< < (96) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div362" type="section" level="1" n="118">
          <pb o="96" file="0134" n="134" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div371" type="section" level="1" n="119">
          <head xml:id="echoid-head162" xml:space="preserve">Notæ in Propoſ. LXXIV.</head>
          <p>
            <s xml:id="echoid-s3926" xml:space="preserve">ERgo E F per centrum non tranſit, cadat ſuper C D, & </s>
            <s xml:id="echoid-s3927" xml:space="preserve">quia produ-
              <lb/>
              <note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">a</note>
            cti ſunt ex E duo breuiſecantes; </s>
            <s xml:id="echoid-s3928" xml:space="preserve">ergo C F excedit dimidium erecti,
              <lb/>
            & </s>
            <s xml:id="echoid-s3929" xml:space="preserve">E F æqualis eſt Trutinæ (52. </s>
            <s xml:id="echoid-s3930" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3931" xml:space="preserve">patet itaque, vt antea demonſtra-
              <lb/>
            uimus, quod E G ſit maximus ramorum, & </s>
            <s xml:id="echoid-s3932" xml:space="preserve">E C minimus, &</s>
            <s xml:id="echoid-s3933" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s3934" xml:space="preserve">
              <figure xlink:label="fig-0134-01" xlink:href="fig-0134-01a" number="118">
                <image file="0134-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0134-01"/>
              </figure>
            Quoniam in 11. </s>
            <s xml:id="echoid-s3935" xml:space="preserve">huius oſtenſum eſt, quod ſemiaxis minor ellipſis eſt ramus bre-
              <lb/>
            uiſsimus, ergo ſi incidentia perpendicularis E F ſuper axim A C, ideſt punctum
              <lb/>
            F eſt centrum ellipſis educerentur ex concurſu E tres breuiſecantes, nimirum
              <lb/>
            E H, E G, & </s>
            <s xml:id="echoid-s3936" xml:space="preserve">E F producta, quæ eſſet axis minor ellipſis: </s>
            <s xml:id="echoid-s3937" xml:space="preserve">hoc autem eſt con-
              <lb/>
            tra hypotheſim, cum ducti ſint ex E duo breuiſecantes: </s>
            <s xml:id="echoid-s3938" xml:space="preserve">ergo eorum vnus E H
              <lb/>
            menſuram C F ſecat, quæ minor eſſe debet ſemiſſe axis maioris C D; </s>
            <s xml:id="echoid-s3939" xml:space="preserve">igitur
              <lb/>
            ex conuerſa propoſitione 50. </s>
            <s xml:id="echoid-s3940" xml:space="preserve">huius, menſura C F maior erit ſemiſſe lateris re-
              <lb/>
            cti, & </s>
            <s xml:id="echoid-s3941" xml:space="preserve">(ex conuerſa propoſ. </s>
            <s xml:id="echoid-s3942" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3943" xml:space="preserve">huius) erit perpendicularis E F æqualis Tru-
              <lb/>
            tinæ. </s>
            <s xml:id="echoid-s3944" xml:space="preserve">Demonſtratio huius propoſitionis neglecta ab Apollonio, propterea quod
              <lb/>
            eodem ferè modo, ac præcedens oſtendi poteſt, breuiſsimè perficietur in hunc
              <lb/>
            modum.</s>
            <s xml:id="echoid-s3945" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3946" xml:space="preserve">Quoniam à concurſu E vnicus tantum breuiſecans E H ad quadrantem C B
              <lb/>
              <note position="left" xlink:label="note-0134-02" xlink:href="note-0134-02a" xml:space="preserve">Propoſ.
                <lb/>
              67. huius.</note>
            ducitur; </s>
            <s xml:id="echoid-s3947" xml:space="preserve">igitur C E minimus eſt omnium ramorum cadentium ad ſectionis pe-
              <lb/>
            ripheriam C B, & </s>
            <s xml:id="echoid-s3948" xml:space="preserve">E C vertici B propinquior minor eſt remotiore E H, & </s>
            <s xml:id="echoid-s3949" xml:space="preserve">E
              <lb/>
            H minor, quàm E B: </s>
            <s xml:id="echoid-s3950" xml:space="preserve">rurſus, quia ramorum cadentium ex E ad peripheriam
              <lb/>
              <note position="left" xlink:label="note-0134-03" xlink:href="note-0134-03a" xml:space="preserve">Ex 29. 30.
                <lb/>
              huius.</note>
            B G vnus tantummodo breuiſecans E G conſtituit cum tangente N G </s>
          </p>
        </div>
      </text>
    </echo>
Impressum