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

Page concordance

< >
Scan Original
61
62
63 39
64 40
65 41
66 42
67 43
68 44
69 45
70 46
71 47
72 48
73 49
74 50
75 51
76 52
77 53
78 54
79 55
80 56
81 57
82 58
83 59
84 60
85 61
86 62
87 63
88 64
89 65
90 66
< >
page |< < (40) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div112" type="section" level="1" n="68">
          <p>
            <s xml:id="echoid-s1412" xml:space="preserve">
              <pb o="40" file="0064" n="64" rhead=""/>
            bus ſe contingunt; </s>
            <s xml:id="echoid-s1413" xml:space="preserve">& </s>
            <s xml:id="echoid-s1414" xml:space="preserve">in duobus tantùm punctis ſe mutuò ſecant. </s>
            <s xml:id="echoid-s1415" xml:space="preserve">Quod tan-
              <lb/>
            dem erat demonſtrandum.</s>
            <s xml:id="echoid-s1416" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div118" type="section" level="1" n="69">
          <head xml:id="echoid-head74" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s1417" xml:space="preserve">PAtet hinc, quod ſi regulæ coni-ſectionum per vertices ſimul adſcripta-
              <lb/>
            rum ſibi ipſis congruant ſectiones quoque erunt inter ſe congruentes,
              <lb/>
            vt in primis quatuor figuris præcedentis ſchematis oſtenſum eſt; </s>
            <s xml:id="echoid-s1418" xml:space="preserve">& </s>
            <s xml:id="echoid-s1419" xml:space="preserve">ſi fuerint
              <lb/>
            inter ſe congruentes, etiam ipſarum regulæ ſimul congruent: </s>
            <s xml:id="echoid-s1420" xml:space="preserve">ſed cum regu-
              <lb/>
            læ ſimul congruunt, congruunt quoque, & </s>
            <s xml:id="echoid-s1421" xml:space="preserve">latera, & </s>
            <s xml:id="echoid-s1422" xml:space="preserve">è conuerſo, cum ad æ-
              <lb/>
            quales angulos inter ſe diſpoſita intelligantur, quare cum latera fuerint inter
              <lb/>
            ſe congruentia ſiue æqualia, ſectiones quoque inter ſe congruentes erunt; </s>
            <s xml:id="echoid-s1423" xml:space="preserve">& </s>
            <s xml:id="echoid-s1424" xml:space="preserve">
              <lb/>
            ſi ſectiones fuerint congruentes etiam ipſarum latera æqualia erunt.</s>
            <s xml:id="echoid-s1425" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1426" xml:space="preserve">Si verò regulę infra recta ſectionum latera ex vertice contingenter appli-
              <lb/>
            cata diſiunctim procedentes nunquam ſimul conueniant, nec ipſæ ſectiones
              <lb/>
            vnquam conuenient, ſed in vertice ſe mutuò contingent, & </s>
            <s xml:id="echoid-s1427" xml:space="preserve">ea inſcripta erit,
              <lb/>
            ſiue minor, cuius regula infra prædictam contingentem diametro ſectionum
              <lb/>
            ſit propior, ſeu cadat tota inter diametrum, & </s>
            <s xml:id="echoid-s1428" xml:space="preserve">regulam alterius ſectionis;
              <lb/>
            </s>
            <s xml:id="echoid-s1429" xml:space="preserve">quæ è contra circumſcripta erit, ſiue maior, vt apparet in 26. </s>
            <s xml:id="echoid-s1430" xml:space="preserve">figuris ſubſe-
              <lb/>
            quentibus.</s>
            <s xml:id="echoid-s1431" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1432" xml:space="preserve">Si tandem ipſarum regulæ infra contingentes ex vertice ſe mutuò ſecent,
              <lb/>
            ſectiones quoque, ſed in duobus tantùm punctis hinc inde à vertice (in quo
              <lb/>
            ſe tangunt) ſe mutuò ſecabunt, in illis nempe, quæ ſunt extrema eiuſdem
              <lb/>
            ordinatim applicatæ, ex regularum interſectione eductæ, ſuper qua duæ co-
              <lb/>
            ni-ſectionum portiones inerunt, quarum ea erit inſcripta, cuius regulæ ſe-
              <lb/>
            gmentum inter prædictam applicatam, & </s>
            <s xml:id="echoid-s1433" xml:space="preserve">contingentem interceptum, pro-
              <lb/>
            pinquius ſit diametro ſectionum, altera verò circumſcripta, ſiue maior cuius
              <lb/>
            regulæ ſegmentum à prædicta diametro magis diſtet, quod omne ſatis patet
              <lb/>
            ex reliquis eiuſdem ſchcmatis figuris.</s>
            <s xml:id="echoid-s1434" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div119" type="section" level="1" n="70">
          <head xml:id="echoid-head75" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s1435" xml:space="preserve">PAtet quoque in Parabolis, & </s>
            <s xml:id="echoid-s1436" xml:space="preserve">in alijs coni-ſectionibus eiuſdem nominis
              <lb/>
            per vertices ſimul adſcriptis, cum eodem tranſuerſo latere, illam, quę
              <lb/>
            minus habet rectum latus inſcriptam, ſiue minorem eſſe ea cuius rectum la-
              <lb/>
            tus maius eſt, & </s>
            <s xml:id="echoid-s1437" xml:space="preserve">è contra. </s>
            <s xml:id="echoid-s1438" xml:space="preserve">Nam in 5. </s>
            <s xml:id="echoid-s1439" xml:space="preserve">13. </s>
            <s xml:id="echoid-s1440" xml:space="preserve">ac 14. </s>
            <s xml:id="echoid-s1441" xml:space="preserve">figura, in quibus ſectiones
              <lb/>
            ſunt eiuſdem nominis, vti etiam in 15. </s>
            <s xml:id="echoid-s1442" xml:space="preserve">& </s>
            <s xml:id="echoid-s1443" xml:space="preserve">16. </s>
            <s xml:id="echoid-s1444" xml:space="preserve">(diximus enim circulum non
              <lb/>
            incongruè haberi poſſe pro Ellipſi) demonſtratum eſt ſectionem DBE, cuius
              <lb/>
            rectum BG minus eſt recto BH ſectionis ABC, totam cadere intra ABC, vn-
              <lb/>
            de erit inſcripta, ſiue minor, & </s>
            <s xml:id="echoid-s1445" xml:space="preserve">è contra, ſectionem ABC cuius rectum maius
              <lb/>
            eſt totam cadere extra DBE, cuius rectum eſt minus: </s>
            <s xml:id="echoid-s1446" xml:space="preserve">quapropter erit ei cir-
              <lb/>
            cumſcripta, ſiue maior.</s>
            <s xml:id="echoid-s1447" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div120" type="section" level="1" n="71">
          <head xml:id="echoid-head76" xml:space="preserve">COROLL. III.</head>
          <p>
            <s xml:id="echoid-s1448" xml:space="preserve">HInc quoque eruitur Hyperbolarum per vertices ſimul adſcriptarum
              <lb/>
            cum æqualibus rectis lateribus, illam, cuius tranſuerſum latus </s>
          </p>
        </div>
      </text>
    </echo>
Impressum