Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Page concordance

< >
Scan Original
171
172 9
173
174
175 10
176
177
178 11
179
180
181 12
182
183
184 13
185
186
187 14
188
189
190 15
191
192
193
194
195 2
196 3
197 4
198 5
199 6
200 7
< >
page |< < (78) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div350" type="section" level="1" n="35">
          <pb o="78" file="0256" n="271" rhead=""/>
          <p>
            <s xml:id="echoid-s11997" xml:space="preserve">Hujuſmodi plura quædam cogitaram hîc inſerere; </s>
            <s xml:id="echoid-s11998" xml:space="preserve">verùm hæc ex-
              <lb/>
            iſtimo ſufficere ſubindicando modo, juxta quem, citra _Calculi moleſti-_
              <lb/>
            _am, curvarum tangentes_ exquirere licet, unáque conſtructiones de-
              <lb/>
            monſtrare. </s>
            <s xml:id="echoid-s11999" xml:space="preserve">Subjiciam tamen unum aut alterum non aſpernanda, ut vi-
              <lb/>
            detur _Theoremata_ perquam generalia.</s>
            <s xml:id="echoid-s12000" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12001" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s12002" xml:space="preserve">Sit linea quæpiam ZGE, cujus axis VD; </s>
            <s xml:id="echoid-s12003" xml:space="preserve">ad quam impri-
              <lb/>
            mìs applicatæ perpendiculares (VZ, PG, DE) ab initio VZ con-
              <lb/>
              <note position="left" xlink:label="note-0256-01" xlink:href="note-0256-01a" xml:space="preserve">Fig. 109.</note>
            tinuè utcunque creſcant; </s>
            <s xml:id="echoid-s12004" xml:space="preserve">ſit item linea VIF talis, ut ductâ quâcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s12005" xml:space="preserve">rectâ EDF ad VD perpendiculari (quæ _curvas_ ſecet punctis E, F,
              <lb/>
            ipſam VD in D) ſit ſemper _rectangulum_ ex DF, & </s>
            <s xml:id="echoid-s12006" xml:space="preserve">deſignatâ quâ-
              <lb/>
            dam R æquale _ſpatio_ reſpectivè _intercepto_ VDEZ; </s>
            <s xml:id="echoid-s12007" xml:space="preserve">fiat autem DE. </s>
            <s xml:id="echoid-s12008" xml:space="preserve">
              <lb/>
            DF:</s>
            <s xml:id="echoid-s12009" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s12010" xml:space="preserve">DT; </s>
            <s xml:id="echoid-s12011" xml:space="preserve">& </s>
            <s xml:id="echoid-s12012" xml:space="preserve">connectatur recta TF; </s>
            <s xml:id="echoid-s12013" xml:space="preserve">hæc curvam VIF
              <lb/>
            continget.</s>
            <s xml:id="echoid-s12014" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12015" xml:space="preserve">Sumatur enim in linea VIF punctum quodpiam I (illud primò ſu-
              <lb/>
              <note position="left" xlink:label="note-0256-02" xlink:href="note-0256-02a" xml:space="preserve">Fig. 110.</note>
            pra punctum F, verſus initium V) & </s>
            <s xml:id="echoid-s12016" xml:space="preserve">per hoc ducantur rectæ IG ad
              <lb/>
            VZ, ac KL ad VD parallelæ (quæ lineas expoſitas ſecent, ut vides)
              <lb/>
            éſtque tum LF. </s>
            <s xml:id="echoid-s12017" xml:space="preserve">LK:</s>
            <s xml:id="echoid-s12018" xml:space="preserve">: (DF. </s>
            <s xml:id="echoid-s12019" xml:space="preserve">DT:</s>
            <s xml:id="echoid-s12020" xml:space="preserve">:) DE. </s>
            <s xml:id="echoid-s12021" xml:space="preserve">R; </s>
            <s xml:id="echoid-s12022" xml:space="preserve">adeóque LF x
              <lb/>
            R = LK x DE. </s>
            <s xml:id="echoid-s12023" xml:space="preserve">Eſt autem (ex præſtituta linearum iſtarum natura)
              <lb/>
            LF x R æquale ſpatio PDEG; </s>
            <s xml:id="echoid-s12024" xml:space="preserve">ergò LK x DE = PDEG &</s>
            <s xml:id="echoid-s12025" xml:space="preserve">lt;
              <lb/>
            </s>
            <s xml:id="echoid-s12026" xml:space="preserve">DP x DE. </s>
            <s xml:id="echoid-s12027" xml:space="preserve">Unde eſt LK &</s>
            <s xml:id="echoid-s12028" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s12029" xml:space="preserve">DP; </s>
            <s xml:id="echoid-s12030" xml:space="preserve">vel LK &</s>
            <s xml:id="echoid-s12031" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s12032" xml:space="preserve">LI.</s>
            <s xml:id="echoid-s12033" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12034" xml:space="preserve">Rurſus accipiatur quodvis punctum I, infra punctum F, reliquáq;
              <lb/>
            </s>
            <s xml:id="echoid-s12035" xml:space="preserve">fiant, utì priùs; </s>
            <s xml:id="echoid-s12036" xml:space="preserve">ſimilíque jam planè diſcurſu conſtabit fore LK x DE
              <lb/>
            = PDEG &</s>
            <s xml:id="echoid-s12037" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s12038" xml:space="preserve">DP x DE, unde jam erit LK &</s>
            <s xml:id="echoid-s12039" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s12040" xml:space="preserve">DP, vel LI. </s>
            <s xml:id="echoid-s12041" xml:space="preserve">E
              <lb/>
            quibus liquidò patet totam rectam TKFK intra (ſeu extra) curvam
              <lb/>
            VIFI exiſtere.</s>
            <s xml:id="echoid-s12042" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12043" xml:space="preserve">Iiſdem quoad cætera poſitis, ſi _ordinatæ_ VZ, PG, DE, &</s>
            <s xml:id="echoid-s12044" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12045" xml:space="preserve">con-
              <lb/>
            tinuè decreſcant, eadem concluſio ſimili ratiocinio colligetur; </s>
            <s xml:id="echoid-s12046" xml:space="preserve">uni-
              <lb/>
            cum obvenit _Diſcrimen_, quòd in hoc caſu (contra quàm in priore)
              <lb/>
            linea VIF concavas ſu
              <unsure/>
            as axi VD obvertat.</s>
            <s xml:id="echoid-s12047" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12048" xml:space="preserve">_Corol_. </s>
            <s xml:id="echoid-s12049" xml:space="preserve">Notetur DE x DT æquari ſpatio VDEZ.</s>
            <s xml:id="echoid-s12050" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12051" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s12052" xml:space="preserve">Exindè deducitur hoc _Tbeorema_: </s>
            <s xml:id="echoid-s12053" xml:space="preserve">Sint duæ lineæ quævis
              <lb/>
            ZGE, VKF ta relatæ, ut ad communem ipſarum axem VD ap-
              <lb/>
              <note position="left" xlink:label="note-0256-03" xlink:href="note-0256-03a" xml:space="preserve">Fig. 111.</note>
            plicatâ quâvis rectâ; </s>
            <s xml:id="echoid-s12054" xml:space="preserve">EDF, ſit ſemper quadratum ex DE æquale _du-_
              <lb/>
            _plo ſpatio_ VDEZ; </s>
            <s xml:id="echoid-s12055" xml:space="preserve">ſumatur autem DQ = DE, & </s>
            <s xml:id="echoid-s12056" xml:space="preserve">connectatur FQ;
              <lb/>
            </s>
            <s xml:id="echoid-s12057" xml:space="preserve">hæc curvæ VKF perpendicularis erit.</s>
            <s xml:id="echoid-s12058" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12059" xml:space="preserve">Concipiatur enim linea VIF, per F tranſiens, talis qualem mox
              <lb/>
            attigimus (cujus ſcilicet ad VD applicatæ ſe habeant ut ſpatia VDEZ;
              <lb/>
            </s>
            <s xml:id="echoid-s12060" xml:space="preserve">hoc eſt ut quadrata ex applicatis à curva VKF in præſente </s>
          </p>
        </div>
      </text>
    </echo>
Impressum