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 |< < (71) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div278" type="section" level="1" n="92">
          <pb o="71" file="0109" n="109" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div281" type="section" level="1" n="93">
          <head xml:id="echoid-head129" xml:space="preserve">PROPOSITIO LXX.</head>
          <p>
            <s xml:id="echoid-s3017" xml:space="preserve">P Oſtea in ellipſi iungamus E H, A H, & </s>
            <s xml:id="echoid-s3018" xml:space="preserve">C
              <lb/>
              <figure xlink:label="fig-0109-01" xlink:href="fig-0109-01a" number="90">
                <image file="0109-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0109-01"/>
              </figure>
            ſit extremitas axis recti; </s>
            <s xml:id="echoid-s3019" xml:space="preserve">erit A H minor
              <lb/>
            quàm E H (11. </s>
            <s xml:id="echoid-s3020" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3021" xml:space="preserve">& </s>
            <s xml:id="echoid-s3022" xml:space="preserve">angulus EGH, nempe
              <lb/>
              <note position="left" xlink:label="note-0109-01" xlink:href="note-0109-01a" xml:space="preserve">c</note>
            A G F maior erit, quàm A G H, ſeu E G F,
              <lb/>
            ergo E F minor eſt, quàm F A, & </s>
            <s xml:id="echoid-s3023" xml:space="preserve">hoc erat
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s3024" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div283" type="section" level="1" n="94">
          <head xml:id="echoid-head130" xml:space="preserve">PROPOSITIO LXXI.</head>
          <p>
            <s xml:id="echoid-s3025" xml:space="preserve">P Atet ex hoc, quod ſi producantur ex duo-
              <lb/>
              <note position="left" xlink:label="note-0109-02" xlink:href="note-0109-02a" xml:space="preserve">d</note>
            bus punctis contactus in ellipſi perpendi-
              <lb/>
            culares E M, A L, & </s>
            <s xml:id="echoid-s3026" xml:space="preserve">fuerit E M minor,
              <lb/>
            exempli gratia, tunc tangens educta ab eius
              <lb/>
            extremitate minor quoque eſt, quemadmodum demonſtrauimus, & </s>
            <s xml:id="echoid-s3027" xml:space="preserve">hoc
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s3028" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div285" type="section" level="1" n="95">
          <head xml:id="echoid-head131" xml:space="preserve">Notæ in Propoſit. LXVIII. LXIX. LXX.
            <lb/>
          & LXXI.</head>
          <p style="it">
            <s xml:id="echoid-s3029" xml:space="preserve">S I occurrant duæ tangentes alicui fectioni A B C, aut circulo, vt ſunt,
              <lb/>
              <note position="left" xlink:label="note-0109-03" xlink:href="note-0109-03a" xml:space="preserve">a</note>
            &</s>
            <s xml:id="echoid-s3030" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3031" xml:space="preserve">Ideſt ſi coniſectionem A B C contingant duæ rectæ A F, E F in pun-
              <lb/>
            ctis A, & </s>
            <s xml:id="echoid-s3032" xml:space="preserve">E concurrentes in F, erit portio tangentis inter occurſum, & </s>
            <s xml:id="echoid-s3033" xml:space="preserve">conta-
              <lb/>
            ctum vertici B proximiorem intercepta, minor ea, quæ inter occur ſum, & </s>
            <s xml:id="echoid-s3034" xml:space="preserve">re-
              <lb/>
            motiorem à vertice contactum continetur: </s>
            <s xml:id="echoid-s3035" xml:space="preserve">oportet autem in ellipſi B verticem,
              <lb/>
            eſſe axis maioris. </s>
            <s xml:id="echoid-s3036" xml:space="preserve">Expungo verba, aut circulo, tanquam erronea, & </s>
            <s xml:id="echoid-s3037" xml:space="preserve">incaute
              <lb/>
            ab aliquo textui ſuperaddita. </s>
            <s xml:id="echoid-s3038" xml:space="preserve">Circulum enim tangentes ab eodem puncto ductæ
              <lb/>
            inæquales eſſe nequeunt.</s>
            <s xml:id="echoid-s3039" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3040" xml:space="preserve">Et ducamus A D in parabola, & </s>
            <s xml:id="echoid-s3041" xml:space="preserve">hyperbola, &</s>
            <s xml:id="echoid-s3042" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3043" xml:space="preserve">Et ducamus A D in
              <lb/>
              <note position="left" xlink:label="note-0109-04" xlink:href="note-0109-04a" xml:space="preserve">b</note>
            parabola, & </s>
            <s xml:id="echoid-s3044" xml:space="preserve">hyperbola perpendicularem ſuper axim B D, ſecantem eum in D,
              <lb/>
            atque G F H in I; </s>
            <s xml:id="echoid-s3045" xml:space="preserve">cumque in parabola diameter F G I ſit parallela axi B D,
              <lb/>
            erit angulus A I G rectus æqualis interno, & </s>
            <s xml:id="echoid-s3046" xml:space="preserve">oppoſito ad eaſdem partes, angu-
              <lb/>
            lo D; </s>
            <s xml:id="echoid-s3047" xml:space="preserve">in hyperbola vero cum triangulum H D I ſit rectangulum in D, erit ex-
              <lb/>
            ternus A I G obtuſus, eſtque in triangulo G I A angulus externus A G F maior
              <lb/>
            interno, & </s>
            <s xml:id="echoid-s3048" xml:space="preserve">oppoſito A I G, recto in parabola, & </s>
            <s xml:id="echoid-s3049" xml:space="preserve">obtuſo in hyperbola; </s>
            <s xml:id="echoid-s3050" xml:space="preserve">erit quo-
              <lb/>
            que angulus F G A obtuſus in parabola, & </s>
            <s xml:id="echoid-s3051" xml:space="preserve">hyperbola.</s>
            <s xml:id="echoid-s3052" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3053" xml:space="preserve">Et angulus E G H, &</s>
            <s xml:id="echoid-s3054" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3055" xml:space="preserve">Zuia F H eſt diameter ſecans bifariam E A in
              <lb/>
              <note position="left" xlink:label="note-0109-05" xlink:href="note-0109-05a" xml:space="preserve">c</note>
              <note position="right" xlink:label="note-0109-06" xlink:href="note-0109-06a" xml:space="preserve">30. ex 2.
                <lb/>
              Com.</note>
            G; </s>
            <s xml:id="echoid-s3056" xml:space="preserve">ergo triangula E G H, & </s>
            <s xml:id="echoid-s3057" xml:space="preserve">A G H habent àuo latera ægualia E G, A G, & </s>
            <s xml:id="echoid-s3058" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0109-07" xlink:href="note-0109-07a" xml:space="preserve">11. huius.</note>
            G H, commune; </s>
            <s xml:id="echoid-s3059" xml:space="preserve">eſtque H E, vertici B axis maioris ellipſis propinquior, maior
              <lb/>
            remotiore H A; </s>
            <s xml:id="echoid-s3060" xml:space="preserve">ergo angulus E G H maior erit angulo A G H; </s>
            <s xml:id="echoid-s3061" xml:space="preserve">eſtque angulus
              <lb/>
            A G F æqualis E G H maiori, & </s>
            <s xml:id="echoid-s3062" xml:space="preserve">E G F æqualis minori A G H; </s>
            <s xml:id="echoid-s3063" xml:space="preserve">igitur angulus
              <lb/>
            A G F maior eſt angulo E G F, & </s>
            <s xml:id="echoid-s3064" xml:space="preserve">latera circa inæquales angulos ſunt æqualia
              <lb/>
            ſingula ſingulis, ergo tangens A F maior eſt, quàm E F.</s>
            <s xml:id="echoid-s3065" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum