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

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        <div xml:id="echoid-div331" type="section" level="1" n="34">
          <head xml:id="echoid-head37" xml:space="preserve">
            <emph style="sc">Lect</emph>
          . IX.</head>
          <p>
            <s xml:id="echoid-s11496" xml:space="preserve">QUod ingreſſi ſumus iter actutùm rectà proſequemur.</s>
            <s xml:id="echoid-s11497" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11498" xml:space="preserve">1. </s>
            <s xml:id="echoid-s11499" xml:space="preserve">Sint rectæ AB, VD ſibi parallelæ; </s>
            <s xml:id="echoid-s11500" xml:space="preserve">quas ſecat poſitione data
              <lb/>
            DB; </s>
            <s xml:id="echoid-s11501" xml:space="preserve">tranſeant verò per B lineæ EBE, FBF ità ad ſe relatæ, ut
              <lb/>
              <note position="left" xlink:label="note-0248-01" xlink:href="note-0248-01a" xml:space="preserve">Fig. 94.</note>
            ductâ quâvis PG ad DB parallelâ, ſit perpetuò PF inter PG, PE
              <lb/>
            eodem ordine deſignato media _Arithmeticè_; </s>
            <s xml:id="echoid-s11502" xml:space="preserve">tangat autem recta BS
              <lb/>
            curvam EBE; </s>
            <s xml:id="echoid-s11503" xml:space="preserve">oportet lineæ FB F tangentem (ad B) deſignare.</s>
            <s xml:id="echoid-s11504" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11505" xml:space="preserve">Sint Numeri N, M proportionalium PF, PE (quales
              <note position="left" xlink:label="note-0248-02" xlink:href="note-0248-02a" xml:space="preserve">(_a_) 12. Lect.
                <lb/>
              VII.</note>
            imus ſupra) exponentes; </s>
            <s xml:id="echoid-s11506" xml:space="preserve">fiátque N. </s>
            <s xml:id="echoid-s11507" xml:space="preserve">M :</s>
            <s xml:id="echoid-s11508" xml:space="preserve">: DS. </s>
            <s xml:id="echoid-s11509" xml:space="preserve">DT; </s>
            <s xml:id="echoid-s11510" xml:space="preserve">connectatúr-
              <lb/>
            que TB; </s>
            <s xml:id="echoid-s11511" xml:space="preserve">hæc lineam FBF continget.</s>
            <s xml:id="echoid-s11512" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11513" xml:space="preserve">Nam utcúnque ducta ſit recta PG, dictas lineas ſecans, utì cernis:
              <lb/>
            </s>
            <s xml:id="echoid-s11514" xml:space="preserve">Eſtque FG. </s>
            <s xml:id="echoid-s11515" xml:space="preserve">EG :</s>
            <s xml:id="echoid-s11516" xml:space="preserve">: N. </s>
            <s xml:id="echoid-s11517" xml:space="preserve">M :</s>
            <s xml:id="echoid-s11518" xml:space="preserve">: DS. </s>
            <s xml:id="echoid-s11519" xml:space="preserve">DT :</s>
            <s xml:id="echoid-s11520" xml:space="preserve">: LG. </s>
            <s xml:id="echoid-s11521" xml:space="preserve">KG;</s>
            <s xml:id="echoid-s11522" xml:space="preserve">
              <note position="left" xlink:label="note-0248-03" xlink:href="note-0248-03a" xml:space="preserve">(_b_@@ Lect.
                <lb/>
              VII.</note>
            cùm ergò ſit KG &</s>
            <s xml:id="echoid-s11523" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11524" xml:space="preserve">EG; </s>
            <s xml:id="echoid-s11525" xml:space="preserve">erit LG &</s>
            <s xml:id="echoid-s11526" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11527" xml:space="preserve">FG; </s>
            <s xml:id="echoid-s11528" xml:space="preserve">unde liquet
              <note position="left" xlink:label="note-0248-04" xlink:href="note-0248-04a" xml:space="preserve">(_c_) _Conſtr_.</note>
            TB extra curvam FBF totam conſiſtere.</s>
            <s xml:id="echoid-s11529" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">(_d_) 3. Lect. 7.</note>
          <note position="left" xml:space="preserve">(_e_) _Hyp_.</note>
          <p>
            <s xml:id="echoid-s11530" xml:space="preserve">II. </s>
            <s xml:id="echoid-s11531" xml:space="preserve">Reliquis perſtantibus iiſdem, ſit jam PF inter PG, PE media pro-
              <lb/>
            portionalis Geometrìcè (eodem ordine media nempe, quo fuit priùs
              <lb/>
            Arithmeticè) eadem BT curvam FB F continget.</s>
            <s xml:id="echoid-s11532" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11533" xml:space="preserve">Etenim è mediis Arithmeticè Geometricéque proportionalibus hoc-
              <lb/>
              <note position="left" xlink:label="note-0248-07" xlink:href="note-0248-07a" xml:space="preserve">(_a_) 17. Lect.
                <lb/>
              7.</note>
            ce modo conſtructæ lineæ ſeſe mutuo contingunt ad B; </s>
            <s xml:id="echoid-s11534" xml:space="preserve">ergò cùm recta BT tangat unam, hæc alteram quoque continget.</s>
            <s xml:id="echoid-s11535" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11536" xml:space="preserve">_Exemplum_. </s>
            <s xml:id="echoid-s11537" xml:space="preserve">Sit PF inter PG, PE è fex mediis tertia; </s>
            <s xml:id="echoid-s11538" xml:space="preserve">erit er-
              <lb/>
            go M = 7; </s>
            <s xml:id="echoid-s11539" xml:space="preserve">& </s>
            <s xml:id="echoid-s11540" xml:space="preserve">N = 3; </s>
            <s xml:id="echoid-s11541" xml:space="preserve">adeóque DS. </s>
            <s xml:id="echoid-s11542" xml:space="preserve">DT :</s>
            <s xml:id="echoid-s11543" xml:space="preserve">: 3.</s>
            <s xml:id="echoid-s11544" xml:space="preserve">7.</s>
            <s xml:id="echoid-s11545" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11546" xml:space="preserve">III. </s>
            <s xml:id="echoid-s11547" xml:space="preserve">Manente porrò quoad cætera proximè præcedente hypotheſi,
              <lb/>
              <note position="left" xlink:label="note-0248-08" xlink:href="note-0248-08a" xml:space="preserve">Fig. 95.</note>
            ſumptóque quovis in curva FBF puncto F; </s>
            <s xml:id="echoid-s11548" xml:space="preserve">etiam ad hoc punctum
              <lb/>
            tangens recta ſimili pacto deſignatur.</s>
            <s xml:id="echoid-s11549" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11550" xml:space="preserve">Nempe per F ducatur recta PG ad ipſam DB parallela, ſecans
              <lb/>
            curvam EXE in E, tum EX tangat curvam EBE in E; </s>
            <s xml:id="echoid-s11551" xml:space="preserve">fiátque N.</s>
            <s xml:id="echoid-s11552" xml:space="preserve"/>
          </p>
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