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

Page concordance

< >
Scan Original
181 451
182 452
183 453
184 454
185 455
186 456
187 457
188 458
189 459
190 460
191 461
192 462
193 463
194 464
195 465
196 466
197 467
198 468
199 469
200 470
201 471
202 472
203 473
204 474
205 475
206 476
207 477
208 478
209 479
210 480
< >
page |< < (468) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div227" type="section" level="1" n="113">
          <p>
            <s xml:id="echoid-s4070" xml:space="preserve">
              <pb o="468" file="0188" n="198" rhead="JAC. GREG. RESPONSUM"/>
            Z
              <emph style="super">2</emph>
            = a b; </s>
            <s xml:id="echoid-s4071" xml:space="preserve">eſt igitur Z. </s>
            <s xml:id="echoid-s4072" xml:space="preserve">ſeu ſeriei terminatio r
              <emph style="super">2</emph>
            a b, quam invenire oportuit: </s>
            <s xml:id="echoid-s4073" xml:space="preserve">& </s>
            <s xml:id="echoid-s4074" xml:space="preserve">proinde ad inveniendam cujuſcunque ſeriei convergentis terminationem opus eſt ſolummodo inve- nire quantitatem eodem modo compoſitam ex terminis con- vergentibus primis, quo componitur eadem quantitas ex ter- minis convergentibus ſecundis.</s>
            <s xml:id="echoid-s4075" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div228" type="section" level="1" n="114">
          <head xml:id="echoid-head156" xml:space="preserve">CONSECTARIUM.</head>
          <p style="it">
            <s xml:id="echoid-s4076" xml:space="preserve">Quoniam non refert in Problemate, ſive termini con-
              <lb/>
            vergentes, a, b, ſint primi, ſecundi vel tertii,
              <lb/>
            &</s>
            <s xml:id="echoid-s4077" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4078" xml:space="preserve">manifeſtum eſt, omnis ſeriei convergentis ter-
              <lb/>
            minationem eodem modo eſſe compoſitam ex termi-
              <lb/>
            nis convergentibus primis, quo ex ſecundis, ter-
              <lb/>
            tiis, &</s>
            <s xml:id="echoid-s4079" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4080" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4081" xml:space="preserve">Si quis aliud Exemplum deſideret, ſint primi termini a, b,
              <lb/>
            ſecundi r
              <emph style="super">7</emph>
            a
              <emph style="super">5</emph>
            b
              <emph style="super">2</emph>
            , r2 a b, quantitas eodem modo compo-
              <lb/>
            ſita &</s>
            <s xml:id="echoid-s4082" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4083" xml:space="preserve">eſt a
              <emph style="super">7</emph>
            b
              <emph style="super">4</emph>
            & </s>
            <s xml:id="echoid-s4084" xml:space="preserve">ſeriei terminatio r
              <emph style="super">11</emph>
            a
              <emph style="super">7</emph>
            b
              <emph style="super">4</emph>
            : </s>
            <s xml:id="echoid-s4085" xml:space="preserve">videat Huge-
              <lb/>
            nius, duo exempla legitima hic adducta inquiſitionem Septi-
              <lb/>
            mæ non admittere; </s>
            <s xml:id="echoid-s4086" xml:space="preserve">ope tamen prop. </s>
            <s xml:id="echoid-s4087" xml:space="preserve">decimæ (ſuppoſita ter-
              <lb/>
            tia illa quantitate) facilè reſolvuntur, neque ullo modo con-
              <lb/>
            ſectarium reſpuunt, quod ſolummodo eſſe momenti ſatis
              <lb/>
            ſit indicaſſe; </s>
            <s xml:id="echoid-s4088" xml:space="preserve">plura autem exempla deſideranti millena affe-
              <lb/>
            ram.</s>
            <s xml:id="echoid-s4089" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4090" xml:space="preserve">Ad primam Hugenii objectionem quod ſpectat, miror
              <lb/>
            eum non conſiderâſſe præcedens conſectarium, ubi illa,
              <lb/>
            quæ deſiderat, evidenter deduco ex prop. </s>
            <s xml:id="echoid-s4091" xml:space="preserve">10. </s>
            <s xml:id="echoid-s4092" xml:space="preserve">At agnoſcit
              <lb/>
            hoc verum eſſe in illis ſeriebus, quæ ope noſtræ methodi
              <lb/>
            terminantur: </s>
            <s xml:id="echoid-s4093" xml:space="preserve">velim certè ut aſſignet mihi Nobiliſſimus Vir
              <lb/>
            ſeriem aliquam convergentem cum ſua terminatione, quæ
              <lb/>
            conſectarium noſtrum reſpuat; </s>
            <s xml:id="echoid-s4094" xml:space="preserve">vel ſi eam aſſignare non poſ-
              <lb/>
            ſit, ſolidam dubitandi rationem tantum deſidero. </s>
            <s xml:id="echoid-s4095" xml:space="preserve">Ut au-
              <lb/>
            tem funditus evertatur hæc objectio, ſequentem exhibeo de-
              <lb/>
            monſtrationem Geometricam.</s>
            <s xml:id="echoid-s4096" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum