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

Table of contents

< >
[271.] THEOR. XXIII. PROP. XXXX.
Page: 235 (51)
[272.] COROLL. I.
Page: 237 (53)
[273.] COROLL. II.
Page: 237 (53)
[274.] COROLL. III.
Page: 237 (53)
[275.] PROBL. VI. PROP. XXXXI.
Page: 238 (54)
[276.] PROBL. VII. PROP. XXXXII.
Page: 238 (54)
[277.] COROLL.
Page: 239 (55)
[278.] THEOR. XXIV. PROP. XXXXIII.
Page: 240 (56)
[279.] THEOR. XXV. PROP. XXXXIV.
Page: 240 (56)
[280.] SCHOLIVM.
Page: 242 (58)
[281.] THEOR. XXVI. PROP. XLV.
Page: 242 (58)
[282.] COROLL.
Page: 243 (59)
[283.] THEOR. XXVII. PROP. XLVI.
Page: 243 (59)
[284.] COROLL. I.
Page: 245 (61)
[285.] COROLL. II.
Page: 245 (61)
[286.] THEOR. XXVIII. PROP. XLVII.
Page: 245 (61)
[287.] THEOR. XXIX. PROP. XLVIII.
Page: 247 (63)
[288.] THEOR. XXX. PROP. XLIX.
Page: 248 (64)
[289.] THEOR. XXXI. PROP. L.
Page: 249 (65)
[290.] COROLL.
Page: 250 (66)
[291.] THEOR. XXXII. PROP. LI.
Page: 251 (67)
[292.] SCHOLIVM.
Page: 252 (68)
[293.] THEOR. XXXIII. PROP. LII.
Page: 253 (69)
[294.] THEOR. XXXIV. PROP. LIII.
Page: 253 (69)
[295.] ALITER.
Page: 254 (70)
[296.] THEOR. XXXV. PROP. LIV.
Page: 255 (71)
[297.] THEOR. XXXIV. PROP. LV.
Page: 256 (72)
[298.] THEOR. XXXVII. PROP. LVI.
Page: 257 (73)
[299.] PROBL. VIII. PROP. LVII.
Page: 259 (75)
[300.] PROBL. IX. PROP. LVIII.
Page: 260 (76)
< >
page |< < (90) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div790" type="section" level="1" n="311">
          <pb o="90" file="0276" n="276" rhead=""/>
        </div>
        <div xml:id="echoid-div797" type="section" level="1" n="312">
          <head xml:id="echoid-head321" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s7710" xml:space="preserve">HInc elicitur, quod baſis angularis portionis, vel baſis cuiuslibet coni-
              <lb/>
            ſectionis, vel circuli ad punctum medium contingit eiuſdem nominis
              <lb/>
            ſectionem ſimilem, & </s>
            <s xml:id="echoid-s7711" xml:space="preserve">concentricam peripſum punctum dato angulo, vel
              <lb/>
            ſectioni, aut circulo inſcriptam.</s>
            <s xml:id="echoid-s7712" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7713" xml:space="preserve">Nam primò loco ſuperiùs demonſtratum fuit, in vtraque figura, baſim
              <lb/>
            A C ad eius punctum medium G omnino contingere ſectionem I G H per
              <lb/>
            punctum G concentricè inſcriptam, &</s>
            <s xml:id="echoid-s7714" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7715" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div798" type="section" level="1" n="313">
          <head xml:id="echoid-head322" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s7716" xml:space="preserve">SEquitur etiam, quod ſegmenta diametrorum, omnium æqualium por-
              <lb/>
            tionum ex eodem angulo, aut ex eadem coni- ſectione, vel circulo ab-
              <lb/>
            ſciſſarum, cum earum extremis terminis ad baſim, perueniunt ad eandem
              <lb/>
            eiuſdem nominis, ſimilem, & </s>
            <s xml:id="echoid-s7717" xml:space="preserve">inſcriptam concentricam ſectionem.</s>
            <s xml:id="echoid-s7718" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7719" xml:space="preserve">Etenim puncta media baſium ipſarum portionum, quæ iam eandem ſimi-
              <lb/>
            lem inſcriptam concentricam ſectionem contingunt, eadem ſunt, ac prædi-
              <lb/>
            cta diametrorum extrema puncta, &</s>
            <s xml:id="echoid-s7720" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7721" xml:space="preserve">vt ſatis conſtat.</s>
            <s xml:id="echoid-s7722" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div799" type="section" level="1" n="314">
          <head xml:id="echoid-head323" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s7723" xml:space="preserve">OPportunè monendus hic Lector eſt, nos ſuperiùs, & </s>
            <s xml:id="echoid-s7724" xml:space="preserve">in ſe-
              <lb/>
            quentibus, Hyperbolen intra angulum aſymptotalem deſcri-
              <lb/>
            ptam, & </s>
            <s xml:id="echoid-s7725" xml:space="preserve">Parabolen Parabolæ æquidiſtantem, interdum
              <lb/>
            nuncupaſſe ſimiles, & </s>
            <s xml:id="echoid-s7726" xml:space="preserve">concentricas ſectiones, perindè ac ſi
              <lb/>
            angulus rectilineus aſymptotalis, ſectio eſſet ſimilis, & </s>
            <s xml:id="echoid-s7727" xml:space="preserve">concentrica Hy-
              <lb/>
            perbolæ, & </s>
            <s xml:id="echoid-s7728" xml:space="preserve">quaſi Parabole æquidiſtanti Parabolæ concentrica eſſet. </s>
            <s xml:id="echoid-s7729" xml:space="preserve">Ve-
              <lb/>
            rum ſi id accuratius perpendamus, quo ad angulum rectilineum, ani-
              <lb/>
            maduertere licebit ipſum non abs re haberi poſſe tanquam vnam Hyper-
              <lb/>
            bolarum, quarum centrum ſit vertex eiuſdem anguli, & </s>
            <s xml:id="echoid-s7730" xml:space="preserve">aſymptoti ſint
              <lb/>
            eadem anguli latera: </s>
            <s xml:id="echoid-s7731" xml:space="preserve">Omnes enim Hyperbolæ cum ijſdem aſymptotis,
              <lb/>
            ſiue cum eodem centro deſcriptæ, ſed cum diuerſis ſemi-axibus, inter ſe
              <lb/>
            ſimiles ſunt, vti ex doctrina primi huius iam ſatis patuit; </s>
            <s xml:id="echoid-s7732" xml:space="preserve">& </s>
            <s xml:id="echoid-s7733" xml:space="preserve">quò ſe-
              <lb/>
            mi- axes ſunt minores, eò tales Hyperbolæ fiunt anguſtiores (nempe in-
              <lb/>
            ſcriptibiles per vertices ijs, quarum ſemi-axes ſint maiores) ſed tantò
              <lb/>
            magis accedunt ad latera eiuſdem anguli, nunquam tamen eis occur-
              <lb/>
            runt, & </s>
            <s xml:id="echoid-s7734" xml:space="preserve">in hoc ſemi-axium decremento, peruenitur tandem ad MI-
              <lb/>
            NIMV M, nempe ad punctum, ſeu verticem anguli, qui eſt centrum
              <lb/>
            omnium ſimilium Hyperbolarum, & </s>
            <s xml:id="echoid-s7735" xml:space="preserve">ad MINIMAM </s>
          </p>
        </div>
      </text>
    </echo>
Impressum