Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Page concordance

< >
Scan Original
231 498
232 499
233 500
234 501
235 502
236 503
237 504
238 505
239 506
240
241
242
243 507
244 508
245 509
246 510
247 511
248 512
249 513
250 514
251 515
252 516
253 517
254 518
255 519
256 520
257
258
259
260
< >
page |< < (474) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div231" type="section" level="1" n="115">
          <p>
            <s xml:id="echoid-s4234" xml:space="preserve">
              <pb o="474" file="0194" n="204" rhead="HUGENII EXCEPTIO"/>
            & </s>
            <s xml:id="echoid-s4235" xml:space="preserve">in ſequentibus dicam de Circulo debet intelligi pariter de
              <lb/>
            ſectore Circuli.</s>
            <s xml:id="echoid-s4236" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4237" xml:space="preserve">Præter hanc approximationem D. </s>
            <s xml:id="echoid-s4238" xml:space="preserve">Gregorius aliam pro-
              <lb/>
            ponit in fine ſuæ
              <emph style="sc">XXV</emph>
            Propoſitionis, quam admirandam di-
              <lb/>
            cit, cujus demonſtrationem ſe ignorare fatetur; </s>
            <s xml:id="echoid-s4239" xml:space="preserve">hæc eſt, in-
              <lb/>
            ter duos terminos, ſtatim memoratos {1/3} a + {2/3} d & </s>
            <s xml:id="echoid-s4240" xml:space="preserve">{4/3} c - {1/3} a,
              <lb/>
            inventis quatuor mediis quantitatibus in proportione Arith-
              <lb/>
            metica, aſſerit maximam harum quantitatum adeo Circuli
              <lb/>
            magnitudini vicinam eſſe, ut, ſi in numeris, qui deſignant
              <lb/>
            Polygona ſimilia a & </s>
            <s xml:id="echoid-s4241" xml:space="preserve">d, prima notarum triens ſit eadem,
              <lb/>
            error ad unitatem non pertingat.</s>
            <s xml:id="echoid-s4242" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4243" xml:space="preserve">Sed invenio hanc approximationem in Circulo veram non
              <lb/>
            eſſe licet in Hyperbola locum habeat, &</s>
            <s xml:id="echoid-s4244" xml:space="preserve">, dum in hac utimur
              <lb/>
            maxima quatuor mediarum Arithmeticarum proportiona-
              <lb/>
            lium, minimam pro approximatione Circuli adhibendam
              <lb/>
            eſſe.</s>
            <s xml:id="echoid-s4245" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4246" xml:space="preserve">Ita minima quatuor mediarum proportionalium inter
              <lb/>
            terminos dictos primæ approximationis erit {16 c + 2 d - 3 a/15}, uti
              <lb/>
            facile eſt videre per Calculum; </s>
            <s xml:id="echoid-s4247" xml:space="preserve">& </s>
            <s xml:id="echoid-s4248" xml:space="preserve">probare poſſum non ſo-
              <lb/>
            lum experientiâ, ſed & </s>
            <s xml:id="echoid-s4249" xml:space="preserve">per demonſtrationem quantitatem
              <lb/>
            hanc, poſitis numeris quorum prima notarum triens eadem
              <lb/>
            eſt, ex primentibus polygonis a & </s>
            <s xml:id="echoid-s4250" xml:space="preserve">d, a vera Circuli ma-
              <lb/>
            gnitudine non aberrare niſi in duabus ultimis notis, & </s>
            <s xml:id="echoid-s4251" xml:space="preserve">ple-
              <lb/>
            rumque in omnibus notis & </s>
            <s xml:id="echoid-s4252" xml:space="preserve">ulterius cum vera magnitudi-
              <lb/>
            ne conincidere, quam tamen ſemper ſuperat, cum e contra-
              <lb/>
            rio maxima quatuor Mediarum, qua utitur D
              <emph style="super">us</emph>
            Gregorius in
              <lb/>
            Hyperbola deficiat.</s>
            <s xml:id="echoid-s4253" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4254" xml:space="preserve">Inveni præterea, approximationem hanc pro Circulo non
              <lb/>
            æque accuratam eſſe, ac eſt illa quam dedi in Tractatu deCircu-
              <lb/>
            li magnitudine, juxta quam, quando a, c & </s>
            <s xml:id="echoid-s4255" xml:space="preserve">d deſignant eadem
              <lb/>
            Polygona, ac ſupra, terminus excedens contentum Circuli
              <lb/>
            eſt a + {10cc - 10aa /6c + 9a} Neque demonſtratio difficilis eſt,
              <note symbol="* it" position="left" xlink:label="note-0194-01" xlink:href="note-0194-01a" xml:space="preserve">vide ſupra
                <lb/>
              p. 383. in
                <lb/>
              ſ
                <unsure/>
              ine.</note>
            ſi neges illum terminum eſſe minorem ideoque magis </s>
          </p>
        </div>
      </text>
    </echo>
Impressum