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
51 13
52 14
53 15
54 16
55 17
56 18
57 19
58 20
59 21
60 22
61 23
62 24
63 25
64 26
65 27
66 28
67 29
68 30
69 31
70 32
71 33
72 34
73 35
74 36
75 37
76 38
77 39
78 40
79 41
80 42
< >
page |< < (101) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div382" type="section" level="1" n="122">
          <p style="it">
            <s xml:id="echoid-s4107" xml:space="preserve">
              <pb o="101" file="0139" n="139" rhead="Conicor. Lib. V."/>
            dendum, &</s>
            <s xml:id="echoid-s4108" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4109" xml:space="preserve">Quæ poſtrema verba ſic intelligi, ac corrigi debent. </s>
            <s xml:id="echoid-s4110" xml:space="preserve">Quia qui-
              <lb/>
              <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">Lem. 8.
                <lb/>
              huius.</note>
            libet ramus ex E ad A F ductus cadit ſupra breuiſsimam ad partes A ab eius
              <lb/>
            termino ad axim C A ductam; </s>
            <s xml:id="echoid-s4111" xml:space="preserve">igitur, vt multoties dictum eſt, conſtituit cum
              <lb/>
            ſua tangente angulum reſpicientem verticem A acutum, ſicuti angulus E A K
              <lb/>
            acutus quoque eſt, & </s>
            <s xml:id="echoid-s4112" xml:space="preserve">omnium ramorum ad peripheriam A F cadentiũ tantum-
              <lb/>
            modo angulus E F 1 eſt rectus; </s>
            <s xml:id="echoid-s4113" xml:space="preserve">igitur omnium ramorum ex E ad peripheriam
              <lb/>
              <note position="right" xlink:label="note-0139-02" xlink:href="note-0139-02a" xml:space="preserve">Coroll.
                <lb/>
              Prop. 67.
                <lb/>
              huius.</note>
            A F cadentium maximus eſt F E remotiſsimus à vertice A, eſtque ramus E G
              <lb/>
            æqualis E F, & </s>
            <s xml:id="echoid-s4114" xml:space="preserve">E G maximus eſt ramorum cadentium ex E ad peripheriam
              <lb/>
            G C; </s>
            <s xml:id="echoid-s4115" xml:space="preserve">igitur ramus E F maximus etiam eſt ramorum cadentium ad peripheriam
              <lb/>
            G C: </s>
            <s xml:id="echoid-s4116" xml:space="preserve">poſtea ducto quolibet ramo E M inter F, B, & </s>
            <s xml:id="echoid-s4117" xml:space="preserve">M N tangente ſectionem
              <lb/>
            in M, quæ conueniat cum tangente I F in N, quia E M, vt dictum eſt, cadit
              <lb/>
            infra breuiſsimam ex M ad axim B A ductam, cum qua contingens N M an-
              <lb/>
            gulum rectũ conſtituit, (ex 30. </s>
            <s xml:id="echoid-s4118" xml:space="preserve">huius) ergo angulus E M N reſpiciens verticem
              <lb/>
            A eſt obtuſus, & </s>
            <s xml:id="echoid-s4119" xml:space="preserve">angulus E F N eſt rectus, cum F O ſit breuiſsima, igitur duo
              <lb/>
            quadrata E F, F N maiora ſunt duobus quadratis E M, M N ſimul ſumptis,
              <lb/>
            & </s>
            <s xml:id="echoid-s4120" xml:space="preserve">ablatum quadratum M N ex minori ſumma maius eſt ablato quadrato N F,
              <lb/>
            cum contingens N F vertici A maioris axis propinquior ſit; </s>
            <s xml:id="echoid-s4121" xml:space="preserve">ergo quadratum
              <lb/>
              <note position="right" xlink:label="note-0139-03" xlink:href="note-0139-03a" xml:space="preserve">70. huius.</note>
            E F maius ex quadrato E M, ideoque ramus E F maior erit quolibet ramo E
              <lb/>
            M inter F, & </s>
            <s xml:id="echoid-s4122" xml:space="preserve">B poſito. </s>
            <s xml:id="echoid-s4123" xml:space="preserve">Non ſecus oſtendetur E M maior quàm E B; </s>
            <s xml:id="echoid-s4124" xml:space="preserve">quare
              <lb/>
            ramus E F maximus erit omnium cadentium ad peripheriam F B. </s>
            <s xml:id="echoid-s4125" xml:space="preserve">Eodem mo-
              <lb/>
            do ramus breuiſecans E G maximus erit omnium cadentium ad peripheriam G
              <lb/>
            B; </s>
            <s xml:id="echoid-s4126" xml:space="preserve">& </s>
            <s xml:id="echoid-s4127" xml:space="preserve">propterea ramus E F maximus erit omnium ad peripheriam F B G ca-
              <lb/>
            dentium; </s>
            <s xml:id="echoid-s4128" xml:space="preserve">Quapropter ramus breuiſecans E F æqualis erit vni tantummodo E
              <lb/>
            G æquè ab axi remoto, & </s>
            <s xml:id="echoid-s4129" xml:space="preserve">maximus omnium ramorum ex concurſu E ad ſemi-
              <lb/>
            ellipſim A B C cadentium, quod erat oſtendendum.</s>
            <s xml:id="echoid-s4130" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4131" xml:space="preserve">Sicuti in prioribus propoſitionibus factum eſt, reperientur, quotnam rami in-
              <lb/>
            ter ſe æquales à puncto concurſus ad coniſectionem duci poſſunt, qua occaſione
              <lb/>
            afferam propoſitiones aliquas non iniucundas, quarum prima erit.</s>
            <s xml:id="echoid-s4132" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4133" xml:space="preserve">Si ad coniſectionem B A à concurſu D vnicus tantum breuiſecans D
              <lb/>
              <note position="right" xlink:label="note-0139-04" xlink:href="note-0139-04a" xml:space="preserve">PROP.7.
                <lb/>
              Addit.</note>
            A duci poſsit, & </s>
            <s xml:id="echoid-s4134" xml:space="preserve">ducatur quælibet F C parallela perpendiculari D E
              <lb/>
              <figure xlink:label="fig-0139-01" xlink:href="fig-0139-01a" number="124">
                <image file="0139-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0139-01"/>
              </figure>
            inter productionem breuiſsimæ, & </s>
            <s xml:id="echoid-s4135" xml:space="preserve">axim intercepta quem ſecet in F, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum