Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

Page concordance

< >
Scan Original
41 21
42 22
43 23
44 24
45 25
46 26
47 27
48 28
49 29
50 30
51 31
52 32
53 33
54 34
55 35
56 36
57 37
58 38
59
60
61
62
63 39
64 40
65 41
66 42
67 43
68 44
69 45
70 46
< >
page |< < (23) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div62" type="section" level="1" n="37">
          <p>
            <s xml:id="echoid-s866" xml:space="preserve">
              <pb o="23" file="0043" n="43" rhead=""/>
            & </s>
            <s xml:id="echoid-s867" xml:space="preserve">fiat vt AV ad VS, ita AS ad SO, & </s>
            <s xml:id="echoid-s868" xml:space="preserve">per O ordinatim applicetur ONR ſe-
              <lb/>
            ctionem ſecans in N, rectam verò ST in X. </s>
            <s xml:id="echoid-s869" xml:space="preserve">Et cum ſit vt AS ad SO, ita AV ad
              <lb/>
            VS, erit componendo AO ad OS, vt AS ad SV, vel vt AS ad SB, & </s>
            <s xml:id="echoid-s870" xml:space="preserve">permu-
              <lb/>
            tando, & </s>
            <s xml:id="echoid-s871" xml:space="preserve">per conuerſionem rationis, vt AO ad OS, ita SO ad OB, ergo re-
              <lb/>
            ctangulum AOB æquatur quadrato OS: </s>
            <s xml:id="echoid-s872" xml:space="preserve">ſed rectangulum AOB ad quadra-
              <lb/>
            tum ſuæ ordinatim ductæ ON in Hyperbola ſemper eſt vt quadratum CB ad
              <lb/>
            BD (vt iam ſuperius oſtendimus) vel vt quadratum SO ad OX: </s>
            <s xml:id="echoid-s873" xml:space="preserve">quare permu-
              <lb/>
            tando rectangulum AOB ad quadratum SO, erit vt quadratum ON ad qua-
              <lb/>
            dratum OX, ſed eſt rectangulum AOB æquale quadrato SO, ergo & </s>
            <s xml:id="echoid-s874" xml:space="preserve">qua-
              <lb/>
            dratum ON quadrato OX æquale erit, quare puncta N, & </s>
            <s xml:id="echoid-s875" xml:space="preserve">X idem funt, ſed
              <lb/>
            eſt N in ſectione, quare recta TX conuenit cum ſectione in X, vel N, hoc eſt
              <lb/>
            RN & </s>
            <s xml:id="echoid-s876" xml:space="preserve">RX æquales erunt, ſed eſt RX æqualis ipſi DT, & </s>
            <s xml:id="echoid-s877" xml:space="preserve">DT minor M, vnde
              <lb/>
            RN, vel RX erit quoque minor M. </s>
            <s xml:id="echoid-s878" xml:space="preserve">Peruenit ergo aſymptoton
              <unsure/>
            CD cum ſe-
              <lb/>
            ctione ad interuallum RN minus dato interuallo M. </s>
            <s xml:id="echoid-s879" xml:space="preserve">Quod tandem erat de-
              <lb/>
            monſtrandum.</s>
            <s xml:id="echoid-s880" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div64" type="section" level="1" n="38">
          <head xml:id="echoid-head43" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s881" xml:space="preserve">HInc eſt, quodlibet diametri ſegmentum inter quamcunque applicatam,
              <lb/>
            & </s>
            <s xml:id="echoid-s882" xml:space="preserve">rectam ex ipſius occurſu cum ſectione alteri aſymptoton
              <unsure/>
            æquidi-
              <lb/>
            ſtanter ductam, medium eſſe proportionale inter aggregatum ex tranſuer-
              <lb/>
            ſo latere cum prædicto diametri ſegmento, idemque ſegmentum. </s>
            <s xml:id="echoid-s883" xml:space="preserve">Demon-
              <lb/>
            ſtratum eſt enim HP eſſe mediam proportionalem inter AH, & </s>
            <s xml:id="echoid-s884" xml:space="preserve">HB; </s>
            <s xml:id="echoid-s885" xml:space="preserve">& </s>
            <s xml:id="echoid-s886" xml:space="preserve">OS
              <lb/>
            mediam inter AO, & </s>
            <s xml:id="echoid-s887" xml:space="preserve">OB.</s>
            <s xml:id="echoid-s888" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div65" type="section" level="1" n="39">
          <head xml:id="echoid-head44" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s889" xml:space="preserve">PAtet etiam quamcunque rectam, ex puncto tranſuerſi lateris inter cen-
              <lb/>
            trum, & </s>
            <s xml:id="echoid-s890" xml:space="preserve">verticem ſumpto alteri aſymptoton ęquidiſtanter ductam ne-
              <lb/>
            ceſſariò ſectioni occurrere. </s>
            <s xml:id="echoid-s891" xml:space="preserve">Iam enim ſupra oſtendimus rectam STX, quæ
              <lb/>
            ex puncto S in tranſuerſo CB ducta eſt aſymptoton
              <unsure/>
            CD parallela, cum ſe-
              <lb/>
            ctione conuenire in N.</s>
            <s xml:id="echoid-s892" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div66" type="section" level="1" n="40">
          <head xml:id="echoid-head45" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s893" xml:space="preserve">HInc facilè erit oſtendere 13. </s>
            <s xml:id="echoid-s894" xml:space="preserve">ſecundi conicorum aliter, & </s>
            <s xml:id="echoid-s895" xml:space="preserve">affir-
              <lb/>
            matiuè, vt videre licet in ſequenti.</s>
            <s xml:id="echoid-s896" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div67" type="section" level="1" n="41">
          <head xml:id="echoid-head46" xml:space="preserve">THEOR. IV. PROP. XI.</head>
          <p>
            <s xml:id="echoid-s897" xml:space="preserve">Si in loco aſymptotis, & </s>
            <s xml:id="echoid-s898" xml:space="preserve">ſectione terminato quædam recta linea
              <lb/>
              <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">Prop. 13.
                <lb/>
              ſec. conic.</note>
            ducatur alteri aſymptoton æquidiſtans, in vno tantùm puncto cum
              <lb/>
            ſectione conueniet, eamque neceſſariò ſecabit.</s>
            <s xml:id="echoid-s899" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s900" xml:space="preserve">SIt in præcedenti ſchemate in loco ab aſymptotis, & </s>
            <s xml:id="echoid-s901" xml:space="preserve">ſectione terminato
              <lb/>
            quodcunque punctum S, à quo ducta ſit STX aſymptoton
              <unsure/>
            CD </s>
          </p>
        </div>
      </text>
    </echo>
Impressum