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

Page concordance

< >
Scan Original
191
192
193
194
195 2
196 3
197 4
198 5
199 6
200 7
201 8
202 9
203 10
204 11
205 12
206 13
207 14
208 15
209 16
210 17
211 18
212 19
213 20
214 21
215 22
216 23
217 24
218 25
219 26
220 27
< >
page |< < (38) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div222" type="section" level="1" n="31">
          <pb o="38" file="0216" n="231" rhead=""/>
          <p>
            <s xml:id="echoid-s9289" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s9290" xml:space="preserve">Huic ſuppar modus dictas @rectas AP, TP comparandi
              <lb/>
            tali _Theoremate_ continetur: </s>
            <s xml:id="echoid-s9291" xml:space="preserve">Si ad rectam aliquam lineam (hoc eſt
              <lb/>
            ad cjus ſingula quæque puncta) applicentur rectæ lineæ parallelæ, ad
              <lb/>
              <note position="left" xlink:label="note-0216-01" xlink:href="note-0216-01a" xml:space="preserve">Fig. 23, 24.</note>
            rectam AD conſimiliter diviſam applicatarum differentiis proportio-
              <lb/>
            nales, reſultantis hinc plani ad parallelogrammum æque altum, ad
              <lb/>
            eandémque baſin poſitum, rectarum AP, TP proportionem exhi-
              <lb/>
            bebit. </s>
            <s xml:id="echoid-s9292" xml:space="preserve">Ut ſi rectæ AD, α δ ſimiliter (in partes ſcilicet æquales in-
              <lb/>
            definitè multas) dividantur; </s>
            <s xml:id="echoid-s9293" xml:space="preserve">& </s>
            <s xml:id="echoid-s9294" xml:space="preserve">rectæ β μ, γ μ, δ μ rectis BM, NM,
              <lb/>
            OM (quæ differentiæ ſunt rectarum ad AD applicatarum, incipi-
              <lb/>
            endo à puncto A) proportionales ſint, erit ut figura α δ μ ad paral-
              <lb/>
            lelogrammum α
              <unsure/>
            δ μ φ, ita AP ad TP. </s>
            <s xml:id="echoid-s9295" xml:space="preserve">Cum enim recta quæpiam
              <lb/>
            ex applicatis ad AD; </s>
            <s xml:id="echoid-s9296" xml:space="preserve">puta _v.</s>
            <s xml:id="echoid-s9297" xml:space="preserve">g._ </s>
            <s xml:id="echoid-s9298" xml:space="preserve">DM æquetur omnibus ſeipsâ mi-
              <lb/>
            norum differentiis (ipſis nempe BM, NM, OM) & </s>
            <s xml:id="echoid-s9299" xml:space="preserve">trilineum
              <lb/>
            α δ μ conſtituatur è rectis β μ, γ μ δ μ eâdem proportione creſcen-
              <lb/>
            tibus; </s>
            <s xml:id="echoid-s9300" xml:space="preserve">ut & </s>
            <s xml:id="echoid-s9301" xml:space="preserve">recta CM æquatur ipſis BM, NM; </s>
            <s xml:id="echoid-s9302" xml:space="preserve">& </s>
            <s xml:id="echoid-s9303" xml:space="preserve">ei reſpondens
              <lb/>
            trilineum α γ μ quaſi conflatur è parallelis β μ, γ μ pari ratione
              <lb/>
            creſcentibus; </s>
            <s xml:id="echoid-s9304" xml:space="preserve">& </s>
            <s xml:id="echoid-s9305" xml:space="preserve">hoc ſemper eveniat; </s>
            <s xml:id="echoid-s9306" xml:space="preserve">omnino patet trilinea α δ μ,
              <lb/>
            α γ μ, α β μ rectis DM, CM, BM proportionari; </s>
            <s xml:id="echoid-s9307" xml:space="preserve">proindéque
              <lb/>
            modum hunc in priorem recidere; </s>
            <s xml:id="echoid-s9308" xml:space="preserve">nec ab eo reipsâ differre. </s>
            <s xml:id="echoid-s9309" xml:space="preserve">Notetur
              <lb/>
            autem hic rectas β μ, γ μ, δ μ velocitates repræſentare, quas pun-
              <lb/>
            ctum mobile curvam delineans obtinet in reſpectivis ejus punctis M;
              <lb/>
            </s>
            <s xml:id="echoid-s9310" xml:space="preserve">ut & </s>
            <s xml:id="echoid-s9311" xml:space="preserve">trilinea α β μ, α γ μ, α δ μ velocitates aggregatas exhibent ab
              <lb/>
            initio ad definita reſpectiva temporis inſtantia; </s>
            <s xml:id="echoid-s9312" xml:space="preserve">quibus (ut jam olim
              <lb/>
            præmonitum) reſpondentia ſpatia BM, CM, DM proportionantur.</s>
            <s xml:id="echoid-s9313" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9314" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s9315" xml:space="preserve">E ſupradictis porrò conſectatur, quòd ſi _Circulus,_
              <lb/>
            _Ellipſis_, ejuſmodíque curvæ recurrentes hoc progenitæ concipiantur
              <lb/>
            modo, punctum eas deſcribens infinitam in recursûs puncto veloci-
              <lb/>
            tatem habebit. </s>
            <s xml:id="echoid-s9316" xml:space="preserve">Nempe ſi quadrans AFM ità generetur; </s>
            <s xml:id="echoid-s9317" xml:space="preserve">quoniam
              <lb/>
              <note position="left" xlink:label="note-0216-02" xlink:href="note-0216-02a" xml:space="preserve">Fig. 25.</note>
            tangens TM diametro AZ eſt parallela, nec illa proinde cum hac
              <lb/>
            niſi ad infinitam diſtantiam convenit; </s>
            <s xml:id="echoid-s9318" xml:space="preserve">ergô velocitas in M ad veloci-
              <lb/>
            tatem uniformis motûs per AY ſe habebit, ut infinita recta ad ipſam
              <lb/>
            PM; </s>
            <s xml:id="echoid-s9319" xml:space="preserve">unde velocitas iſta ad M prorſus infinita ſit oportet. </s>
            <s xml:id="echoid-s9320" xml:space="preserve">Ità quidem
              <lb/>
              <note position="left" xlink:label="note-0216-03" xlink:href="note-0216-03a" xml:space="preserve">II. _preced_.</note>
            quoad hujuſmodi curvas; </s>
            <s xml:id="echoid-s9321" xml:space="preserve">at quoad alias ad infinitum ſenſim continu-
              <lb/>
            atas (quales _parabolæ & </s>
            <s xml:id="echoid-s9322" xml:space="preserve">byperbolæ_) deſcendentis puncti velocitas in
              <lb/>
            quovis deſignato curvæ puncto finita eſt. </s>
            <s xml:id="echoid-s9323" xml:space="preserve">Verùm his omiſſis ad alias
              <lb/>
            propoſitæ curvæ proprietates exponendas progrediamur.</s>
            <s xml:id="echoid-s9324" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum